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1stQuarter Module (Lesson: Measurements) Measurements In any experiment, two kinds of data may be collected, namely quantitative data, which is in numerical form (e.g., height) and the qualitative data (e.g., color of the eye). Gathering quantitative data requires measurement. The most common quantities that you are likely to measure in physics class are mass, time, and distance. A. Basic Quantities Quantity Length Mass Time Electric Current Temperature (absolute) Amount of substance Luminous intensity
Symbol l m t I T I
Unit m (meter) kg (mass) s (second) A (ampere) K (Kelvin) Mol (mole) Cd (candela)
Scalars and Vector Quantities Scalars and Vectors Scalar quantities are those quantities represented by a magnitude only. A magnitude is a number and the unit of measure. Some examples of scalar quantities are the following: a. The distance between two corners is 5 m. 5 m describe length b. A car moves with an average speed of 40 km/h. 40 km/h describe speed c. The weighing scale reads 20 kg when apples are placed on its pan. 20 kg describe mass d. The sprinter reached the finish line in 11.2 sec. 11.2 s describes length of time e. The capacity of this container is 1.5 liters. 1.5 L describes volume f. The thermometer reads36°C. 36°C describe temperature Scalar quantities may be added or subtracted like ordinary numbers. For example, a square has four equal sides. If each side measures 2 meters, we can determine the perimeter of the figure by simple using addition. 2m P = 4L P = L1 + L2 + L3 + L4 P = 2m + 2m + 2m + 2m P=8m 2m Young Ji International School / College
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Vector quantities are quantities expresses by a magnitude and direction. Examples of vector quantities are the following. a. A boat sails 10 km, east (E) before it stops to fish. 10 km, E describes displacement b. A car is heading 80 km/h, northwest (NW) 80 km/h, NW describes velocity c. A man exerts 490 N in lifting a sack of rice. 490 N, describes force (lifting an object indicates that the direction is upward) d. A bus moves at the rate of 4m/s as it heads South. 4 m/s2, South describes acceleration Drawing Vectors to Scale The arrow is always drawn in representing vectors. The length of the arrow is drawn proportional to the magnitude of the vector. If the given vector is not enough to fit on a sheet of paper, or if the unit is too small for you to work on it, we resolve it by using a convenient scale. Example: The ship sails 20 km, east then turns 40 km, south before it stops to fish. Given: D1 = 20km, E D2 = 40 km, S Scale: 1 cm = 10 km Solution: (length of the arrow that will represent the given vectors) D1 = 20 km, E x 1cm = 2cm, E 10cm D2 = 40 km, S. x 1cm = 4cm, S 10 km Challenge Yourself 1. Identify the following as scalar or vector. a. 5 steps to the right b. 37 joules c. The boiling point of water d. 150 m, SE e. Falling from a cliff 2. Draw the vectors of the following displacement a. The horizontal displacement of car is -20 km. b. A jet fighter‘s displacement is 150 km, 60 ° West of North. c. An ant crawls 20 cm, Sw and 50 cm, 10° South of east. Young Ji International School / College
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Adding Vector Quantities Resultant vector The same of two or more vectors is represented by a single vector called resultant. This vector may be found by using graphical method, the Pythagorean Theorem method, and the Analytical method.
Graphical Method One way of determining the resultant vector is through graphical method. Here, you will be using a single-edge and a protractor. The accuracy of your answer depends on the instruments used and the care by which the drawing is made. The following steps will guide you in finding the resultant vector using graphical method: 1. Choose an appropriate reference frame and scale for the given vectors. 2. Draw vectors one after the other using the head-to-tail fashion. Meaning, you have to draw the first vector starting from the origin of the reference frame, then the succeeding vectors are drawn starting from the head of the most recent vector drawn. 3. For the resultant vector, draw an arrow connecting the tail of the first vector and the head of the last vector drawn. Measure the length of the arrow and determine the angle using a protractor. Determine the direction of the resultant vector based on a chosen axis. Problem 1 An ant crawls 2 cm, East, stops for a while to pick up a bread crumb, then continues 3cm, East. What is the resultant of ant‘s displacement? Given : D1 = 2cm, E D2 = 3cm, E You have seen from the vector diagram that the directions of d1 and d2 are the same, so we simply add their magnitudes. Answer: = (2cm, E) + (3cm, E) = 5cm, E
Problem 2: A boat is rowed up the river with a speed of 5 km/h. if the river is flowing at the rate of 2km/h, can the boat move up the river successfully? If so, what is the magnitude of the resultant velocity of the boat?
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Problem 3: A dog runs 10 m, North; 20 m, 30° North of east; and 15 m, 60° South of east. How far is the dog with respect to the starting point? Distance and Displacement In the study of motion, we define distance as the total length along a path between two points. Distance is a scalar quantity because it describes the length of an object‘s path but not its direction. You would know how long to draw the arrow but not the direction to point it. Displacement gives both the length and the direction of an object‘s path from its starting point straight to its ending point. It is, therefore, a vector quantity. Displacement measures the distance along a straight line between the start and end of an object‘s motion. Displacement also states the overall direction of motion. Displacement can be represented by arrows that are drawn to scale and point in a given direction. The longest possible path in this case is path A. it covers the longest distance. A different distance can be covered using path C. However, if we only consider the change in position or how far one is from the starting point, then we can drawn a straight line from the starting point. We end up with a line similar to path B. The change in position of an object is defined as displacement. The displacement from house to school is equivalent to the distance covered by path B. No matter what path a person takes, the displacement remains the same,. They is, the straight-line distance from the starting point to the final point is the same for any path. A person may cover a longer distance by choosing path. A cover path C but the displacement from the house is the same for both paths. A displacement is a vector quantity that requires both magnitude and direction. On the other hand, distance is a scalar quantity which has no direction. A displacement to the right is assigned a positive value, while a negative value is assigned to a displacement that is directed to the left.
Speed and Velocity Speed is one of the descriptors of motion. It describes how fast an object moves. Speed is defined as the distance covered in a given time interval.
If an athlete records 100 seconds for a 100m dash, we say that his average speed is one meter per second. We use the idea of average speed because we do not know if the Young Ji International School / College
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whole time that he was running, he had maintained his speed at 1m/s, what we do know is that it took him 100 seconds to cover a total distance of 100m.
Average speed = total distance covered Total time interval
or vs = d t
Let us assume path A as 90 m long, path B as 30 m long and path C as 60 m long. If a person who chose path A covered that path in 10 minutes, his average speed is.
Average speed = 90 m 10 m Average speed = 9 m/min. How about his average velocity? Is it the same as his average speed? Velocity Normally, students get confused between speed and velocity. These terms are interchangeably used in a day-to-day conversions. However in physics, these two terms do not mean the same thing. How are they different from each other? Velocity is defined as the total displacement covered in a given time interval. Note that, for velocity, displacement is considered instead of distance. Since displacement is a vector quantity, velocity is also a vector. Average velocity = total displacement Total time interval Let us use the above equation to show the difference between velocity and speed. Path A Average speed = total distance Total time
Average speed = 90 m 10 min Average speed = 9.0 m / min
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Acceleration Acceleration, in physics, is the rate at which the velocity of an object changes over time. An object's acceleration is the net result of any and all forces acting on the object, as described by Newton's Second Law. The SI unit for acceleration is the metre per second squared (m/s2). Accelerations are vector quantities (they have magnitude and direction) and add according to the parallelogram law. As a vector, the calculated net force is equal to the product of the object's mass (a scalar quantity) and the acceleration. For example, when a car starts from a standstill (zero relative velocity) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car changes direction there is acceleration toward the new direction. When accelerating forward, passengers in the car experience a force pushing them back into their seats. They experience sideways forces when changing direction. If the speed of the car decreases, this is acceleration in the opposite direction, sometimes called deceleration. Mathematically, there is no separate formula for deceleration, as both are changes in velocity. Mathematically, instantaneous acceleration—acceleration over an infinitesimal interval of time—is the rate of change of velocity over time: i.e., the derivative of the velocity vector as a function of time. (Here and elsewhere, if motion is in a straight line, vector quantities can be substituted by scalars in the equations.) Average acceleration over a period of time is the change in velocity
divided by the
duration of the period
Acceleration has the dimensions of velocity (L/T) divided by time, i.e., L/T2. The SI unit of acceleration is the metre per second squared (m/s2); this can be called more meaningfully "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second. An object moving in a circular motion—such as a satellite orbiting the earth—is accelerating due to the change of direction of motion, although the magnitude (speed) may be constant. When an object is executing such a motion where it changes direction, but not speed, it is said to be undergoing centripetal (directed towards the center) acceleration. Oppositely, a change in the speed of an object, but not its direction of motion, is a tangential acceleration. Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer.
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In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e., sum of all forces) acting on it (Newton's second law):
where F is the net force acting on the body, m is the mass of the body, and a is the center-ofmass acceleration. As speeds approach the speed of light, relativistic effects become increasingly large and acceleration becomes less. Tangential and centripetal acceleration
An oscillating pendulum, with velocity and acceleration marked. It experiences both tangential and centripetal acceleration.
Components of acceleration for a curved motion. The tangential component at is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector (or in the opposite direction). The normal component (also called centripetal component for circular motion) ac is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path. See also: Local coordinates The velocity of a particle moving on a curved path as a function of time can be written as:
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with v(t) equal to the speed of travel along the path, and
a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of ut, the acceleration of a particle moving on a curved path can be written using the chain rule of differentiation. For the product of two functions of time as:
where un is the unit (inward) normal vector to the particle's trajectory (also called the principal normal), and r is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration and the normal or radial acceleration (or centripetal acceleration in circular motion, see also circular motion and centripetal force). Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by the Frenet–Serret formulas Uniform acceleration Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g(also called acceleration due to gravity). By Newton's Second Law the force, F, acting on a body is given by:
Due to the simple algebraic properties of constant acceleration in the onedimensional case (that is, the case of acceleration aligned with the initial velocity), there are simple formulas relating the quantities displacement s, initial velocity v0, final velocity v, acceleration a, and time t:
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where = displacement = initial velocity = final velocity = uniform acceleration = time. In the case of uniform acceleration of an object that is initially moving in a direction not aligned with the acceleration, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As Galileo showed, the net result is parabolic motion, as in the trajectory of a cannonball, neglecting air resistance. Circular motion Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a constant magnitude but change of direction. In this case, because the direction of the object's motion is constantly changing, being tangential to the circle, the object's linear velocity vector also changes, but its speed does not. This acceleration is a radial acceleration since it is always directed toward the centre of the circle and takes the magnitude:
where is the object's linear speed along the circular path. Equivalently, the radial acceleration vector ( ) may be calculated from the object's angular velocity :
where is a vector directed from the centre of the circle and equal in magnitude to the radius. The negative shows that the acceleration vector is directed towards the centre of the circle (opposite to the radius). The acceleration and the net force acting on a body in uniform circular motion are directed toward the centre of the circle; that is, it is centripetal. Whereas the so-called 'centrifugal force' appearing to act outward on the body is really a pseudo force experienced in the frame of reference of the body in circular motion, due to the body's linear momentum at a tangent to the circle. With nonuniform circular motion, i.e., the speed along the curved path changes, a transverse acceleration is produced equal to the rate of change of the angular speed around the circle times the radius of the circle. That is,
The transverse (or tangential) acceleration is directed at right angles to the radius vector and takes the sign of the angular acceleration ( ).
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Relation to relativity Special relativity Main article: Special relativity The special theory of relativity describes the behavior of objects traveling relative to other objects at speeds approaching that of light in a vacuum. Newtonian mechanics is exactly revealed to be an approximation to reality, valid to great accuracy at lower speeds. As the relevant speeds increase toward the speed of light, acceleration no longer follows classical equations. As speeds approach that of light, the acceleration produced by a given force decreases, becoming infinitesimally small as light speed is approached; an object with mass can approach this speed asymptotically, but never reach it. General relativity Main article: General relativity Unless the state of motion of an object is known, it is totally impossible to distinguish whether an observed force is due to gravity or to acceleration—gravity and inertial acceleration have identical effects. Albert Einstein called this the principle of equivalence, and said that only observers who feel no force at all—including the force of gravity—are justified in concluding that they are not accelerating. Conversions Conversions between common units of acceleration m/s2 1 1 m/s2
ft/s2
3.28084 0.101972 100
1 0.3048 1 ft/s2 00 g0
standard Gal (cm/ gravity ( 2 s) g0)
0.031081 30.4800 0
9.8066 32.1740 1 5
1 cm/ 0.01 s2
980.665
0.03280 0.001019 1 84 72
Newton's laws of motion are three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to said forces. They have been expressed in several different ways over nearly three centuries, and can be summarized as follows:
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1. First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3] 2. Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object. 3. Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[4] Newton used them to explain and investigate the motion of many physical objects and systems.[5] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
Newton's laws are applied to objects which are idealized as single point masses, in the sense that the size and shape of the object's body are neglected in order to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealized as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterize the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalization of Newton's laws of motion for rigid bodies called the Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton‘s laws of motion, then Euler‘s laws can be derived from Newton‘s laws. Euler‘s laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law only holds when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. Young Ji International School / College
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Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light.
Let us begin our explanation of how Newton changed our understanding of the Universe by enumerating his Three Laws of Motion. Newton's First Law of Motion:
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
This we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia". Newton's Second Law of Motion:
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
This is the most powerful of Newton's three Laws, because it allows quantitative calculations of dynamics: how do velocities change when forces are applied. Notice the fundamental difference between Newton's 2nd Law and the dynamics of Aristotle: according to Newton, a force causes only a change in velocity (an acceleration); it does not maintain the velocity as Aristotle held. This is sometimes summarized by saying that under Newton, F = ma, but under Aristotle F = mv, where v is the velocity. Thus, according to Aristotle there is only a velocity if there is a force, but according to Newton an object with a certain velocity maintains that velocity unless a force acts on it to cause an acceleration (that is, a change in the velocity). As we have noted earlier in conjunction with the discussion of Galileo, Aristotle's view seems to be more in accord with common sense, but that is because of a failure to appreciate the role played by frictional forces. Once account is taken of all forces acting in a given situation it is the dynamics of Galileo and Newton, not of Aristotle, that are found to be in accord with the observations.
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Newton's Third Law of Motion:
III. For every action there is an equal and opposite reaction.
Matter is defined as anything that has mass and volume. Mass is a measure of an object's inertia. It is proportional to weight: the more mass an object has, the more weight it has. However, mass is not the same as weight. Weight is a force created by the action of gravity on a substance while mass is a measure of an object's resistance to change in motion. Mass is measured by comparing the substance of interest to a standard kilogram called the International Prototype Kilogram (IPK). The IPK is a metal cylinder where the height and diameter both equal 39.17 millimeters and is made of an alloy of 90% platinum and 10% iridium. Thus, the standard kilogram is defined and all other masses are a comparison to this kilogram. When atom masses are measured in a mass spectrometer, a different internal standard is used. Your take home lesson with regard to mass is that mass is a relative term judged by a comparison. Volume is a measure of the amount of space occupied by an object. Volume can be measured directly with equipment designed using graduations marks or indirectly using length measurements depending on the state (gas, liquid, or solid) of the material. A graduated cylinder, for example, is a tube that can hold a liquid which is marked and labeled at regular intervals, usually every 1 or 10 mL. Once a liquid is placed in the cylinder, one can read the graduation marks and record the volume measurement. Since volume changes with temperature, graduated equipment has limits to the precision with which one can read the measurement. Solid objects that have regular shape can have their volume calculated by measuring their dimensions. In the case of a box, its volume equals length times width times height. It is particularly interesting to note that measuring is different from calculating a specific value. While mass and volume can both be determined directly relative to either a defined standard or line marks on glass, calculating other values from measurements is not considered measuring. For example, once you have measured the mass and volume of a liquid directly, one can then calculate the density of a substance by dividing the mass by the volume. This is considered indirectly determining density. Interestingly enough, one can also measure density directly if an experiment which allows the comparison of density to a standard is set up.
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Another quantity of matter directly or indirectly determined is the amount of substance. This can either represent a counted quantity of objects (e.g. three mice or a dozen bagels) or the indirectly determined number of particles of a substance being dealt with such as how many atoms are contained in a sample of a pure substance. The latter quantity is described in terms of moles. One mole is a specifically defined as the number of particles in 12 grams of the isotope Carbon-12. This number is 6.02214078(18)x 1023 particles. Units of Measure
Mass: the kilogram (kg). Also, the gram (g) and milligram (mg).
1 kg = 1000 g
1000 mg = 1 g.
Volume: the liter (L), milliliter (mL). Also, cubic centimeters (cc) and cubic meters (m3).
1 cc = 1 mL
1000 mL = 1 L
1000 L = 1 m3
Amount: the mole (mol).
1 mol = 6.02214078(18)x 1023 particles
Atoms, Elements, and Compounds The fundamental building block of matter is the atom.
The red dots are protons, the black dots are neutrons, and the blue dots are electrons. Young Ji International School / College
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Any atom is composed of a little nucleus surrounded by a "cloud" of electrons. In the nucleus there are protons and neutrons. However, the term "atom" just refers to a building block of matter; it doesn't specify the identity of the atom. It could be an atom of carbon, or an atom of hydrogen, or any other kind of atom. This is where the term "element" comes into play. When an atom is defined by the number of protons contained in its nucleus, chemists refer to it as an element. All elements have a very specific identity that makes them unique from other elements. For example, an atom with 6 protons in its nucleus is known as the element carbon. When speaking of the element fluorine, chemists mean an atom that contains 9 protons in its nucleus. 
Atom: A fundamental building block of matter composed of protons, neutrons, and electrons.

Element: A uniquely identifiable atom recognized by the number of protons in the nucleus.
Despite the fact that we define an element as a unique identifiable atom, when we speak, for example, 5 elements, we don't usually mean those 5 atoms are of the same type (having the same number of protons in their nucleus). We mean 5 'types' of atoms. It is not necessary there are only 5 atoms. There may be 10, or 100, etc. atoms, but those atoms belong to one of 5 types of atoms. I'd rather define 'element' as 'type of atom'. I think it is more precise. If we'd like to refer to 5 atoms having the same 6 protons in their nucleus, I'd say '5 carbon atoms' or '5 atoms of carbon'. It is important to note that if the number of protons in the nucleus of an atom changes, so does the identity of that element. If we could remove a proton from nitrogen (7 protons), it is no longer nitrogen. We would, in fact, have to identify the atom as carbon (6 protons). Remember, elements are unique and are always defined by the number of protons in the nucleus. The Periodic Table of the Elements shows all known elements organized by the number of protons they have. An element is composed of the same type of atom; elemental carbon contains any number of atoms, all having 6 protons in their nuclei. In contrast, compounds are composed of different type of atoms. More precisely, a compound is a chemical substance that consists of two or more elements. A carbon compound contains some carbon atoms (with 6 protons each) and some other atoms with different numbers of protons. Compounds have properties different from the elements that created them. Water, for example, is composed of hydrogen and oxygen. Hydrogen is an explosive gas and oxygen is a gas that fuels fire. Water has completely different properties, being a liquid that is used to extinguish fires. Young Ji International School / College
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The smallest representative for a compound (which means it retains characteristics of the compound) is called a molecule. Molecules are composed of atoms that have "bonded" together. As an example, the formula of a water molecule is "H2O": two hydrogen atoms and one oxygen atom. Properties of Matter Properties of matter can be divided in two ways: extensive/intensive, or physical/chemical.
Extensive properties depend on the
Physical properties can be measured without changing the chemical's identity. The freezing point of a substance is
amount of matter that is being measured. These include mass and volume.
physical. When water freezes, it's still H2O.
Intensive properties do not depend on the amount of matter. These include density and color.
Chemical properties deal with how one chemical reacts with another. We know that wood is flammable because it becomes heat, ash, and carbon dioxide when heated in the presence of oxygen.
States of Matter One important physical property is the state of matter. Three are common in everyday life: solid, liquid, and gas. The fourth, plasma, is observed in special conditions such as the ones found in the sun and fluorescent lamps. Substances can exist in any of the states. Water is a compound that can be liquid, solid (ice), or gas (steam).
The ice in this picture is a solid. The water in the picture is a liquid. In the air there is water vapor, which is a gas.
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The states of matter depend on the bonding between molecules. Solids Solids have a definite shape and a definite volume. Most everyday objects are solids: rocks, chairs, ice, and anything with a specific shape and size. The molecules in a solid are close together and connected by intermolecular bonds. Solids can be amorphous, meaning that they have no particular structure, or they can be arranged into crystalline structures or networks. For instance, soot, graphite, and diamond are all made of elemental carbon, and they are all solids. What makes them so different? Soot is amorphous, so the atoms are randomly stuck together. Graphite forms parallel layers that can slip past each other. Diamond, however, forms a crystal structure that makes it very strong. Liquids Liquids have a definite volume, but they do not have a definite shape. Instead, they take the shape of their container to the extent they are indeed "contained" by something such as beaker or a cupped hand or even a puddle. If not "contained" by a formal or informal vessel, the shape is determined by other internal (e.g. intermolecular) and external (e.g. gravity, wind, inertial) forces. The molecules are close, but not as close as a solid. The intermolecular bonds are weak, so the molecules are free to slip past each other, flowing smoothly. A property of liquids is viscosity, the measure of "thickness" when flowing. Water is not nearly as viscous as molasses, for example. Gases Gases have no definite volume and no definite shape. They expand to fill the size and shape of their container. The oxygen that we breathe and steam from a pot are both examples of gases. The molecules are very far apart in a gas, and there are minimal intermolecular forces. Each atom is free to move in any direction. Gases undergo effusion and diffusion. Young Ji International School / College
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Effusion occurs when a gas seeps through a small hole, and diffusion occurs when a gas spreads out across a room. If someone leaves a bottle of ammonia on a desk, and there is a hole in it, eventually the entire room will reek of ammonia gas. That is due to the diffusion and effusion. These properties of gas occur because the molecules are not bonded to each other. Technically, a gas is called a vapor if it does not occur at standard temperature and pressure (STP). STP is 0° C and 1.00 atm of pressure. This is why we refer to water vapor rather than water gas.
In gases, intermolecular forces are very weak, hence molecules move randomly colliding with themselves, and with the wall of their container, thus exerting pressure on their container. When heat is given out by gases, the internal molecular energy decreases; eventually, the point is reached when the gas liquifies.
Newton's First Law
Newton's First Law Inertia and Mass State of Motion Balanced and Unbalanced Forces of ways by which motion can be described (words, graphs, diagrams, numbers, etc.) was discussed. In this unit (Newton's Laws of Motion), the ways in which motion can be explained will be discussed. Isaac Newton (a 17th century scientist) put forth a variety of laws that explain why objects move (or don't move) as they do. These three laws have become known as Newton's three laws of motion. The focus of Lesson 1 is Newton's first law of motion - sometimes referred to as the law of inertia. Newton's first law of motion is often stated as An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Two Clauses and a Condition There are two clauses or parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram.
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The behavior of all objects can be described by saying that objects tend to "keep on doing what they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is not acted upon by an unbalanced force. All objects resist changes in their state of motion - they tend to "keep on doing what they're doing." There is an important condition that must be met in order for the first law to be applicable to any given motion. The condition is described by the phrase "... unless acted upon by an unbalanced force." As the long as the forces are not unbalanced - that is, as long as the forces are balanced - the first law of motion applies. This concept of a balanced versus and unbalanced force will be discussed in more detail later in Lesson 1. Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when:   
the container was at rest and you attempted to move it the container was in motion and you attempted to stop it the container was moving in one direction and you attempted to change its direction. The water spills whenever the state of motion of the container is changed. The water resisted this change in its own state of motion. The water tended to "keep on doing what it was doing." The container was moved from rest to a high speed at the starting line; the water remained at rest and spilled onto the table. The container was stopped near the finish line; Young Ji International School / College
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the water kept moving and spilled over container's leading edge. The container was forced to move in a different direction to make it around a curve; the water kept moving in the same direction and spilled over its edge. The behavior of the water during the lap around the track can be explained by Newton's first law of motion.
Everyday Applications of Newton's First Law There are many applications of Newton's first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it is doing." When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when braking from a state of motion the coffee continues forward with the same speed and in the same direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion. Have you ever experienced inertia (resisting changes in your state of motion) in an automobile while it is braking to a stop? The force of the road on the locked wheels provides the unbalanced force to change the car's state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. A person in motion stays in motion with the same speed and in the same direction ... unless acted upon by the unbalanced force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is governed by Newton's laws. The seat belt provides the unbalanced force that brings you from a state of motion to a state of rest. Perhaps you could speculate what would occur when no seat belt is used. Newton's Second Law
Newton's Second Law The Big Misconception Finding Acceleration Finding Individual Forces Free Fall and Air Resistance Double Trouble Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. Objects at equilibrium (the condition in which all forces balance) will not accelerate. Young Ji International School / College
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According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object changing its speed, its direction, or both its speed and direction.
Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.
The BIG Equation Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. This verbal statement can be expressed in equation form as follows:
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a = Fnet / m The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration. Fnet = m • a In this entire discussion, the emphasis has been on the net force. The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is important to remember this distinction. Do not use the value of merely "any 'ole force" in the above equation. It is the net force that is related to acceleration. As discussed in an earlier lesson, the net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. If necessary, review this principle by returning to the practice questions in Lesson 2.
Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written. 1 Newton = 1 kg • m/s2 The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. Your Turn to Practice The Fnet = m • a equation is often used in algebraic problem solving. The table below can be filled by substituting into the equation and solving for the unknown quantity. Try it yourself and then use the click on the buttons to view the answers. Net Force
Mass
Acceleration
(N)
(kg)
(m/s/s)
1.
10
2
See Answer
2.
20
2
See Answer
3.
20
4
See Answer
4.
See Answer
2
5
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5.
10
See Answer
10
Newton's Second Law as a Guide to Thinking The numerical information in the table above demonstrates some important qualitative relationships between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant). Similarly, comparing the values in rows 2 and 4 demonstrates that a halving of the net force results in a halving of the acceleration (if mass is held constant). Acceleration is directly proportional to net force. Furthermore, the qualitative relationship between mass and acceleration can be seen by a comparison of the numerical values in the above table. Observe from rows 2 and 3 that a doubling of the mass results in a halving of the acceleration (if force is held constant). And similarly, rows 4 and 5 show that a halving of the mass results in a doubling of the acceleration (if force is held constant). Acceleration is inversely proportional to mass. The analysis of the table data illustrates that an equation such as Fnet= m*a can be a guide to thinking about how a variation in one quantity might affect another quantity. Whatever alteration is made of the net force, the same change will occur with the acceleration. Double, triple or quadruple the net force, and the acceleration will do the same. On the other hand, whatever alteration is made of the mass, the opposite or inverse change will occur with the acceleration. Double, triple or quadruple the mass, and the acceleration will be onehalf, one-third or one-fourth its original value.
The Direction of the Net Force and Acceleration As stated above, the direction of the net force is in the same direction as the acceleration. Thus, if the direction of the acceleration is known, then the direction of the net force is also known. Consider the two oil drop diagrams below for an acceleration of a car. From the diagram, determine the direction of the net force that is acting upon the car. Then click the buttons to view the answers. (If necessary, review acceleration from the previous unit.)
See Answer
See Answer
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In conclusion, Newton's second law provides the explanation for the behavior of objects upon which the forces do not balance. The law states that unbalanced forces cause objects to accelerate with an acceleration that is directly proportional to the net force and inversely proportional to the mass.
Rocket Science! NASA rockets (and others) accelerate upward off the launch pad as they burn a tremendous amount of fuel. As the fuel is burned and exhausted to propel the rocket, the mass of the rocket changes. As such, the same propulsion force can result in increasing acceleration values over time. Use the Rocket Science widget below to explore this effect.
Problem #1: Carbon mass number exact weight percent abundance 12
12.000000
98.90
13
13.003355
1.10
To calculate the average atomic weight, each exact atomic weight is multiplied by its percent abundance (expressed as a decimal). Then, add the results together and round off to an appropriate number of significant figures. This is the solution for carbon: (12.000000) (0.9890) + (13.003355) (0.0110) = 12.011 amu ________________________________________ Problem #2: Nitrogen mass number exact weight percent abundance 14
14.003074
99.63
15
15.000108
0.37
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This is the solution for nitrogen: (14.003074) (0.9963) + (15.000108) (0.0037) = 14.007 amu Video: How to Calculate an Average Atomic Weight. ________________________________________ Problem #3: Chlorine
Problem #4: Silicon
mass number exact weight percent abundance percent abundance
mass number exact weight
35
34.968852
75.77
28
27.976927
92.23
37
36.965903
24.23
29
28.976495
4.67
30
29.973770
The answer for chlorine: 35.453
3.10
The answer for silicon: 28.086
________________________________________ This type of calculation can be done in reverse, where the isotopic abundances can be calculated knowing the average atomic weight. Go to tutorial on reverse direction. ________________________________________ Problem #5: In a sample of 400 lithium atoms, it is found that 30 atoms are lithium-6 (6.015 g/mol) and 370 atoms are lithium-7 (7.016 g/mol). Calculate the average atomic mass of lithium. Solution: 1) Calculate the percent abundance for each isotope: Li-6: 30/400 = 0.075 Li-7: 370/400 = 0.925 2) Calculate the average atomic weight: x = (6.015) (0.075) + (7.016) (0.925)
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x = 6.94 g/mol ________________________________________ Problem #6: A sample of element X contains 100 atoms with a mass of 12.00 and 10 atoms with a mass of 14.00. Calculate the average atomic mass (in amu) of element X. Solution: 1) Calculate the percent abundance for each isotope: X-12: 100/110 = 0.909 X-14: 10/110 = 0.091 2) Calculate the average atomic weight: x = (12.00) (0.909) + (14.00) (0.091) x = 12.18 amu (to four sig figs) 3) Here's another way: 100 atoms with mass 12 = total atom mass of 1200 10 atoms with mass 14 = total atom mass of 140 1200 + 140 = 1340 (total mass of all atoms) Total number of atoms = 100 + 10 = 110 1340/110 = 12.18 amu The first way is the standard technique for solving this type of problem. That's because we do not generally know the specific number of atoms in a given sample. More commonly, we know the percent abundances, which is different from the specific number of atoms in a sample. ________________________________________ Problem #7: Boron has an atomic mass of 10.81 amu according to the periodic table. However, no single atom of boron has a mass of 10.81 amu. How can you explain this difference? Young Ji International School / College
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Solution: 10.81 amu is an average, specifically a weighted average. It turns out that there are two stable isotopes of boron: boron-10 and boron-11. Neither isotope weighs 10.81 amu, but you can arrive at 10.81 amu like this: x = (10.013) (0.199) + (11.009) (0.801) x = 1.99 + 8.82 = 10.81 ________________________________________ Problem #8: Copper occurs naturally as Cu-63 and Cu-65. Which isotope is more abundant? Solution: Look up the atomic weight of copper: 63.546 amu Since our average value is closer to 63 than to 65, we concude that Cu-63 is the more abundant isotope. ________________________________________ Problem #9: Copper has two naturally occuring isotopes. Cu-63 has an atomic mass of 62.9296 amu and an abundance of 69.15%. What is the atomic mass of the second isotope? What is its nuclear symbol? Solution: 1) Look up the atomic weight of copper: 63.546 amu 2) Set up the following and solve: (62.9296) (0.6915) + (x) (0.3085) = 63.546 43.5158 + 0.3085x = 63.546 0.3085x = 20.0302 x = 64.9277 amu
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3) The nuclear symbol is: 29-Cu-65 The correct symbol would have the 29 subscripted left of the Cu and the 65 would be superscripted left of the Cu. ________________________________________ Problem #10: Naturally occurring iodine has an atomic mass of 126.9045. A 12.3849 g sample of iodine is accidentally contaminated with 1.0007 g of I-129, a synthetic radioisotope of iodine used in the treatment of certain diseases of the thyroid gland. The mass of I-129 is 128.9050 amu. Find the apparent "atomic mass" of the contaminated iodine. Solution: 1) Calculate mass of contaminated sample: 12.3849 g + 1.0007g = 13.3856 g 2) Calculate percent abundances of (a) natural iodine and (b) I-129 in the contaminated sample: (a) 12.3849 g / 13.3856 g = 0.92524 (b) 1.0007 g / 13.3856 g = 0.07476 3) Calculate "atomic mass" of contaminated sample: (126.9045) (0.92524) + (128.9050) (0.07476) = x x = 127.0540 amu You have not given enough information to make it possible to answer your question. By "law of inertia" do you mean Newtons first law? That is - any object in motion will continue iin motion or at rest will remain at rest unless acted upon be an unbalanced force. If this is what you mean then it the usual questions you get are more qualatative than quatitiative, things like explain why you tend to move outward when a car goes round a corner. If by law of inertia you mean conservation of momentum then we can get computation easily. This gives a formula p=mv ie momentum equals mass times velocity. If u is the initial velocity and v is the final velocity, m1 is the mass if the first object and m2 is the lass of the secons object then we get a formula m1u1+ m2u2 = m1v1 + m2v2 Young Ji International School / College
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This can be applied to situations like collisions. E;g; A truck weighing 4000 kg moving at 20 m/s south hits a car wieghing 1000 kg moving north at 30 m/s head on. They become entangled during the collision. Find the final velocity of the tangled mess immediately after the collision. Let south be the positive direction, m1 = 4000 kg u1= 20 m/s south =+20 m/s m2 = 1000 kg u2=30 m/s north = - 30 m/s m1u1+ m2u2 = m1v1 + m2v2 m1u1+ m2u2 = (m1+m2)v v=(m1u1+ m2u2)/(m1+m2) =(4000 x 20 + 1000 x -30)/(4000 + 1000) =(80 000 - 30 000)/ 5000 =50 000/5000 = 10 m/s south There are many other possible examples E.g An astronaunt becomes sepatated from his space ship. He is difting in space 20 m away from the ship, at rest relative to the ship. He has a tool bag with him. He throws the tool bg away from the ship causing him to move towards the ship. If he and his space suit etc have a combined mass of 100 kg and the tool bag has a mass of 10 kg and he throws it at a speed of 5.0 m/s, with what speed will he move towards his ship? Since the man is drifting in space his initial momentum is zero. By conservation of momentum the final momentum will also be zero therfore the momenta of the tool bag and the astronaunt must be equal and opposite. ie m1v1 = m2v2
m1 = 100 kg v1 = ? m2 = 10 kg v2 = 5.0 m/s Young Ji International School / College
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m1v1=m2v2 v1 = (m2v2)/m1 =10 x 5.0/100 =0.50 m/s He moves towards his ship at half a meter per second. Any basic physics text book will give many more examples like these. Q: A mass of 5 kg is suspended by a rope of length 2 m from the ceiling. A force of 45 N in the horizontal direction is applied at the midpoint R of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium? (Take g = 10 ms-2). Neglect the mass of the rope. Q: A mass of 3 kg rests on a horizontal plane. The plane is gradually inclined until at an angle θ = 20° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface? Q: A small block B is placed is placed on another block A of mass 7 kg and length 15 cm. Initially the block B is near the right end of block A. A constant horizontal force of 10 N is applied to the block A. All the surfaces are assumed frictionless. Find the time elapsed before the block B separates from A. Q: A ball of mass 5 kg and a block of mass 12 kg are attached by a lightweight cord that passes over a frictionless pulley of negligible mass as shown in the figure. The block lies on a frictionless incline of angle 30o. Find the magnitude of the acceleration of the two objects and the tension in the cord. Take g = 10 ms-2. Q: Two blocks of masses 5 kg and 7 kg are placed in contact with each other on a frictionless horizontal surface. A constant horizontal force 20 N is applied to the block of mass 7 kg. (a) Determine the magnitude of the acceleration of the two-block system. (b) Determine the magnitude of the contact force between the two blocks. Q: A block of mass 5 kg starts to slide down a frictionless plane having an inclination of 25.0° from rest at the top. The length of the incline is 2.00 m, find (a) the acceleration of the block and (b) its speed when it reaches the bottom of the incline. Take g = 10 ms-2. Q: A 75.0 kg man stands on a platform scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.20 m/s in 1.00 s. It travels with this constant speed for the next 10.00 s. The elevator then undergoes a uniform acceleration in the negative y direction for 1.70 s and comes to rest. What does the scale register (a) before the elevator starts to move? (b) during the first 1.00 s? (c) while the elevator is traveling at constant speed? (d) during the time it is slowing down? Take g = 10 ms-2.
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Q: A block of mass 2.50 kg is accelerated across a rough surface by a rope passing over a pulley, as shown in figure. The tension in the rope is 12.0 N, and the pulley is 10.0 cm above the top of the block. The coefficient of kinetic friction is 0.300. (a) Determine the acceleration of the block when x = 0.400 m. (b) Find the value of x at which the acceleration becomes zero. Take g = 10 ms-2. Q: A block is given an initial velocity of 5.00 m/s up a frictionless 20.0° incline. How far up the incline does the block slide before coming to rest? Take g = 10 ms-2. Q: Two blocks of mass 5 kg and 9 kg are connected by a string of negligible mass that passes over a frictionless pulley. The inclines are frictionless. Find (a) the magnitude of the acceleration of each block and (b) the tension in the string. Take g = 10 ms-2. Q: In figure blocks A and B have masses 40 kg and 20 kg respectively. (a) Determine the minimum weight of block C to keep A from sliding if the coefficient of friction, μs between A and the table is 0.18. Block C is suddenly lifted off A. (b) What is the acceleration of block A if μk between A and the table is 0.15. Take g = 10 ms-2. Q: Two masses 5 kg and 7 kg situated on a frictionless, horizontal surface are connected by a light string. A force of 50 N is exerted on one of the masses to the right. Determine the acceleration of the system and the tension T in the string. Q: A block of mass m1 = 5 kg on a frictionless horizontal table is connected to a block of mass m2 = 3 kg by means of a very light pulley P1 and a light fixed pulley P2 as shown in figure. If a1 and a2 are the accelerations of m1 and m2, respectively, (a) what is the relationship between these accelerations? Find (b) the tensions in the strings and (c) the accelerations a1 and a2. Take g = 10 ms-2. Q: A block A of mass 0.5 kg can slide on a frictionless incline of angle 30o and length 0.8 m kept inside an elevator going up with uniform velocity 2m/s. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline. Take g = 10 ms-2. Q: The elevator shown is descending with a constant acceleration of 1.5 ms-2. The mass of the block A is 1 kg. What force is exerted by block A on block B? Take g = 10 ms-2. Q: Consider the three connected objects shown in figure. If the inclined plane is frictionless and the system is in equilibrium, find (in terms of m, g, and θ (a) the mass M and (b) the tensions T1 and T2. If the value of M is double the value found in part (a), find (c) the acceleration of each object, and (d) the tensions T1 and T2. Q: In the above problem, if the coefficient of static friction between m and 2m and the inclined plane is μs, and the system is in equilibrium, find (a) the minimum value of M and (b) the maximum value of M. Q: A mass M = 16 kgis held in place by an applied force F and a pulley system as shown in figure. The pulleys are massless and frictionless. Find (a) the tension in each section of rope, T1, T2, T3, T4, and T5 and (b) the magnitude of F. Take g = 10 ms-2. Young Ji International School / College
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Q: What horizontal force must be applied to the cart shown in figure so that the blocks remain stationary relative to the cart? Assume all surfaces, wheels, and pulley are frictionless. Q: A block slides with constant velocity down an inclined plane that has slope angle θ. The block is then projected up the same plane with an initial speed u. (a) How far up the plane will it move before coming to rest? (b) After the block comes to rest, will it slide down the plane again? Q: A block of mass m1 = 4.0 kg is put on top of a block of mass m2 =5.0 kg. To cause the top block to slip on the bottom one while the bottom one is held fixed, a horizontal force of at least 12 N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table. Find the magnitudes of (a) the maximum horizontal force that can be applied to the lower block so that the blocks will move together and (b) the resulting acceleration of the blocks. Take g = 10 ms-2. Q: Find the acceleration of block of mass in the figure shown. All the surfaces are frictionless and the pulleys and the string are light. Q: Find the acceleration of the 5 kg block in figure. Take g = 10 ms-2 Q: In the given figure, suppose m2 = 2.5 kg and m3 = 3 kg. What should be the mass m1 so that it remains at rest? Take g = 10 ms-2. Q: A constant force F = m2g/3 is applied on the mass m1 as shown in figure. The pulley and the string are light and the surface of the table is smooth. Find the acceleration of m1. Q: Block 1 of mass m1 = 2.0 kg and block 2 of mass m2 = 1.0 kg are connected by a string of negligible mass. Block 2 is pushed by force of magnitude 25 N and angle θ = 35°.The coefficient of kinetic friction between each block and the horizontal surface is 0.25. What is the tension in the string? Take g = 10 ms-2. Q: The two blocks shown in figure are not attached to each other. The coefficient of static friction between the blocks is μs = 0.35, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force required to keep the smaller block from slipping down the larger block? Take g = 10 ms-2. Q: Find the mass of the hanging block in figure which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulley are light. 1.) A four kilogram object is moving across a frictionless surface with a constant velocity of 2 meters per second. Determine the force necessary to maintain the state of motion. Young Ji International School / College
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2.) A net force of 10 Newtons acts on a box which has a mass of 2 kg. What will be the acceleration of the box? 3.)
How much horizontal net force is required to accelerate a 1000 kg car at 2 m/s2?
4.) If an unbalanced force of 600 newtons acts on a body to accelerate it at +15 m/s2, what is the mass of the body? 5.) A body with a mass of 1 kg is accelerated by a force of 2 N. What is the velocity of this body after 5 s of motion?
Solutions 1.) 0, it's moving at a constant velocity. 2.)
5m/s^2
3.)
2000N
4.)
F = ma m=F/a m = 600n/15 m/s2 m= 40 kg
5.)
v = 10 m/s
Check Your Understanding 1. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff. 2. A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. 3. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.60 seconds, what will be his final velocity and how far will he fall? 4. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.
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5. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon. 6. Rocket-powered sleds are used to test the human response to acceleration. If a rocketpowered sled is accelerated to a speed of 444 m/s in 1.83 seconds, then what is the acceleration and what is the distance that the sled travels? 7. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. 8. An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway? 9. A car traveling at 22.4 m/s skids to a stop in 2.55 s. Determine the skidding distance of the car (assume uniform acceleration). 10. A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo. 11. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)? 12. A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (assume a uniform acceleration). 13. A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.) 14. The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below. 15. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.) 16. A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well. Young Ji International School / College
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17. It was once recorded that a Jaguar left skid marks that were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it began to skid. 18. A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed. 19. A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster. 20. With what speed in miles/hr (1 m/s = 2.23 mi/hr) must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance.
Solutions to Above Problems 1. Given: a = +3.2 m/s2
Find: t = 32.8 s
d = ??
vi = 0 m/s
2. d = vi*t + 0.5*a*t2 3. d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2 4. d = 1720 m 5. Return to Problem 1 6. 7. Given: d = 110 m
Find: t = 5.21 s
a = ??
vi = 0 m/s
8. d = vi*t + 0.5*a*t2 9. 110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2 10. 110 m = (13.57 s2)*a 11. a = (110 m)/(13.57 s2) 12. a = 8.10 m/ s2 13. Return to Problem 2 14. 15. Given: Young Ji International School / College
Find: Page 36
a = -9.8 m
t = 2.6 s
d = ??
vi = 0 m/s
vf = ?? 16. d = vi*t + 0.5*a*t2 17. d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s2)*(2.60 s)2 18. d = -33.1 m (- indicates direction) 19. vf = vi + a*t 20. vf = 0 + (-9.8 m/s2)*(2.60 s) 21. vf = -25.5 m/s (- indicates direction) 22. Return to Problem 3 23. 24. Given: vi = 18.5 m/s
Find: vf = 46.1 m/s
d = ??
t = 2.47 s
a = ?? 25. a = (Delta v)/t 26. a = (46.1 m/s - 18.5 m/s)/(2.47 s) 27. a = 11.2 m/s2 28. d = vi*t + 0.5*a*t2 29. d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s2)*(2.47 s)2 30. d = 45.7 m + 34.1 m 31. d = 79.8 m 32. (Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d) 33. Return to Problem 4 34. 35. Given: vi = 0 m/s
Find: d = -1.40 m
a = -1.67 m/s2
t = ??
36. d = vi*t + 0.5*a*t2 37. -1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s2)*(t)2 38. -1.40 m = 0+ (-0.835 m/s2)*(t)2 39. (-1.40 m)/(-0.835 m/s2) = t2 40. 1.68 s2 = t2 41. t = 1.29 s
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42. Return to Problem 5 43. 44. Given: vi = 0 m/s
Find: vf = 44 m/s
a = ??
t = 1.80 s
d = ?? 45. a = (Delta v)/t 46. a = (444 m/s - 0 m/s)/(1.83 s) 47. a = 243 m/s2 48. d = vi*t + 0.5*a*t2 49. d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s2)*(1.83 s)2 50. d = 0 m + 406 m 51. d = 406 m 52. (Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d) 53. Return to Problem 6 54. 55. Given: vi = 0 m/s
Find: vf = 7.10 m/s
a = ??
d = 35.4 m
56. vf2 = vi2 + 2*a*d 57. (7.10 m/s)2 = (0 m/s)2 + 2*(a)*(35.4 m) 58. 50.4 m2/s2 = (0 m/s)2 + (70.8 m)*a 59. (50.4 m2/s2)/(70.8 m) = a 60. a = 0.712 m/s2 61. Return to Problem 7 62. 63. Given: vi = 0 m/s
Find: a = 3 m/s2
vf = 65 m/s
d = ??
64. vf2 = vi2 + 2*a*d 65. (65 m/s)2 = (0 m/s)2 + 2*(3 m/s2)*d 66. 4225 m2/s2 = (0 m/s)2 + (6 m/s2)*d 67. (4225 m2/s2)/(6 m/s2) = d 68. d = 704 m Young Ji International School / College
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69. Return to Problem 8 70. 71. Given:
Find:
vi = 22.4 m/s
vf = 0 m/s
d = ??
t = 2.55 s
72. d = (vi + vf)/2 *t 73. d = (22.4 m/s + 0 m/s)/2 *2.55 s 74. d = (11.2 m/s)*2.55 s 75. d = 28.6 m 76. Return to Problem 9 77. 78. Given:
Find:
a = -9.8 m/s2
vf = 0 m/s
vi = ??
d = 2.62 m
79. vf2 = vi2 + 2*a*d 80. (0 m/s) = vi2 + 2*(-9.8 m/s2)*(2.62 m) 2
81. 0 m2/s2 = vi2 - 51.35 m2/s2 82. 51.35 m2/s2 = vi2 83. vi = 7.17 m/s 84. Return to Problem 10 85. 86. Given:
Find:
a = -9.8 m/s2
vf = 0 m/s
d = 1.29 m
vi = ?? t = ??
87. vf2 = vi2 + 2*a*d 88. (0 m/s) = vi2 + 2*(-9.8 m/s2)*(1.29 m) 2
89. 0 m2/s2 = vi2 - 25.28 m2/s2 90. 25.28 m2/s2 = vi2 91. vi = 5.03 m/s 92. To find hang time, find the time to the peak and then double it. 93. vf = vi + a*t 94. 0 m/s = 5.03 m/s + (-9.8 m/s2)*tup 95. -5.03 m/s = (-9.8 m/s2)*tup Young Ji International School / College
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96. (-5.03 m/s)/(-9.8 m/s2) = tup 97. tup = 0.513 s 98. hang time = 1.03 s 99. Return to Problem 11 100. 101. Given: vi = 0 m/s
Find: vf = 521 m/s
a = ??
d = 0.840 m
102. vf2 = vi2 + 2*a*d (521 m/s)2 = (0 m/s)2 + 2*(a)*(0.840 m)
103. 104.
271441 m2/s2 = (0 m/s)2 + (1.68 m)*a (271441 m2/s2)/(1.68 m) = a
105.
106. 107.
a = 1.62*105 m /s2 Return to Problem 12
108. 109. Given: a = -9.8 m/s2
Find: vf = 0 m/s
t = 3.13 s
d = ??
a. (NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.) First use: vf = vi + a*t 0 m/s = vi + (-9.8 m/s2)*(3.13 s) 0 m/s = vi - 30.7 m/s vi = 30.7 m/s (30.674 m/s) Now use: vf2 = vi2 + 2*a*d (0 m/s)2 = (30.7 m/s)2 + 2*(-9.8 m/s2)*(d) 0 m2/s2 = (940 m2/s2) + (-19.6 m/s2)*d -940 m2/s2 = (-19.6 m/s2)*d (-940 m2/s2)/(-19.6 m/s2) = d d = 48.0 m Return to Problem 13
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110. Given:
Find:
vi = 0 m/s
a = -9.8 m/s2
d = -370 m
t = ??
111. d = vi*t + 0.5*a*t2 -370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s2)*(t)2
112.
-370 m = 0+ (-4.9 m/s2)*(t)2
113.
(-370 m)/(-4.9 m/s2) = t2
114.
115. 116. 117.
75.5 s2 = t2 t = 8.69 s
Return to Problem 14
118. 119. Given:
Find:
vi = 367 m/s
vf = 0 m/s 121.
120. vf2 = vi2 + 2*a*d (0 m/s)2 = (367 m/s)2 + 2*(a)*(0.0621 m)
122.
0 m2/s2 = (134689 m2/s2) + (0.1242 m)*a 123.
-134689 m2/s2 = (0.1242 m)*a
124.
(-134689 m2/s2)/(0.1242 m) = a 125.
126.
a = ??
d = 0.0621 m
a = -1.08*106 m /s2
(The - sign indicates that the bullet slowed down.) 127.
Return to Problem 15
128. 129. Given:
Find:
a = -9.8 m/s2
t = 3.41 s 131.
vi = 0 m/s
d = ??
130. d = vi*t + 0.5*a*t2 d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s2)*(3.41 s)2 132.
d = 0 m+ 0.5*(-9.8 m/s2)*(11.63 s2) 133.
134.
d = -57.0 m
(NOTE: the - sign indicates direction) 135.
Return to Problem 16
136. 137. Young Ji International School / College
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Given:
Find:
a = -3.90 m/s2
vf = 0 m/s
vi = ??
d = 290 m
138. vf2 = vi2 + 2*a*d (0 m/s)2 = vi2 + 2*(-3.90 m/s2)*(290 m)
139.
0 m2/s2 = vi2 - 2262 m2/s2
140.
2262 m2/s2 = vi2
141. 142. 143.
vi = 47.6 m /s
Return to Problem 17
144. 145. Given: vi = 0 m/s
Find: vf = 88.3 m/s
a = ??
d = 1365 m
t = ?? vf2
2
146. = vi + 2*a*d (88.3 m/s)2 = (0 m/s)2 + 2*(a)*(1365 m)
147.
7797 m2/s2 = (0 m2/s2) + (2730 m)*a
148.
149.
7797 m2/s2 = (2730 m)*a
150.
(7797 m2/s2)/(2730 m) = a
153.
151.
a = 2.86 m/s2
152.
vf = vi + a*t
88.3 m/s = 0 m/s + (2.86 m/s2)*t
154.
(88.3 m/s)/(2.86 m/s2) = t 155.
156.
t = 30. 8 s
Return to Problem 18
157. 158. Given: vi = 0 m/s
Find: vf = 112 m/s
d = 398 m
a = ??
159. vf2 = vi2 + 2*a*d (112 m/s)2 = (0 m/s)2 + 2*(a)*(398 m)
160. 161.
12544 m2/s2 = 0 m2/s2 + (796 m)*a 162.
12544 m2/s2 = (796 m)*a
163.
(12544 m2/s2)/(796 m) = a
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a = 15.8 m/s2
164. 165.
Return to Problem 19
166. 167. Given:
Find:
a = -9.8 m/s2
vf = 0 m/s
d = 91.5 m
vi = ?? t = ??
168. 170.
First, find speed in units of m/s: 169. vf2 = vi2 + 2*a*d
(0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(91.5 m) 0 m2/s2 = vi2 - 1793 m2/s2
171.
1793 m2/s2 = vi2
172. 173. 174. 175.
vi = 42.3 m/s
Now convert from m/s to mi/hr: vi = 42.3 m/s * (2.23 mi/hr)/(1 m/s) 176. 177.
vi = 94.4 mi/hr
Return to Problem 20
Newton’s first law of motion This law is really only a definition of force. It says that when a body is acted upon by an external resultant force it will accelerate. If the resultant force is zero, then the body either remains at rest or else it will continue to move at constant velocity (that is with constant speed in a straight line). Consider a parachutist who jumps from a plane travelling horizontally. His initial vertical speed is zero. He will immediately be acted upon by his weight acting vertically downwards and since the external resultant force is not zero he will accelerate. He will not increase in speed indefinitely because as his speed increases so does his frictional drag – this opposes the down force of his weight. Eventually the frictional drag will increase until it equals his weight at this point the resultant force will be zero and he will stop accelerating but continue to fall at a constant (or terminal) speed. For the human body this is about 45-55 m/s or 100-120 mph. When the parachutist releases his parachute the frictional drag is suddenly increased to be greater that his weight and the resultant force is upwards – he will start to decelerate. This Young Ji International School / College
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will continue with the drag force reducing until the forces are again equal and the speed of fall constant. At this point this terminal speed should be only a few m/s. In summary Newton‘s first law can be defined as A body not acted upon by an external resultant force moves with constant velocity or is at rest. Mass The mass of a body is sometime said to be the quantity of matter in a body. This is quite vague because of the use of the word quantity. The mass of a body is a number assigned to it to distinguish it from another which may appear identical. It determines the behaviour of the body when acted upon by a force which causes it to change its motion. The mass can then be considered to be a measure of the resistance to change of motion. The resistance to change in motion is known as inertia. A body with a large mass is said to have a large inertia. Newton‘s first law is sometime knows as the law of inertia. Newton’s second law of motion Before stating this law we will first define linear momentum, or simply momentum. Momentum will be denoted p and is defined as
Momentum is a vector quantity and is expressed in SI units by kg m/s or Ns (note that these units are in fact equivalent). The second law states that the force causing acceleration is proportional to the rate of change of momentum with time and acts in the direction of the change. If a force F changes the velocity of a body with constant mass m uniformly from u to v in time t, then Newton‘s second law states
since acceleration, a = (v-u)/t. k is the constant of proportionality. By definition the SI unit of force, the Newton N, causes an acceleration of 1 m/s2 of a mass of 1 kg. This conveniently gives k=1 and the second law of motion may be summarised as Young Ji International School / College
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Force = mass
acceleration
Newton‘s first law is a special case of his second law with the force equal to zero. Worked Example 2.1 A railway engine pulls a wagon of mass 10 000 kg along a straight track at a steady speed. The pull force in the couplings between the engine and wagon is 1000 N. a. What is the force opposing the motion of the wagon? b. If the pull force is increased to 1200 N and the resistance to movement of the wagon remains constant, what would be the acceleration of the wagon?
Solution a) When the speed is steady, by Newton‘s first law, the resultant force must be zero. The pull on the wagon must equal the resistance to motion. So the force resisting motion is 1000 N. b) The resultant force on the wagon is 1200 – 1000 = 200 N By Equation 2.2
Worked Example 2.2 a) Find the acceleration of a 20 kg crate along a horizontal floor when it is pushed with a resultant force of 10 N parallel to the floor. b) How far will the crate move in 5s (starting from rest)? Solution a)
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b) Distance travelled is given by Equation 1.3
Mass and weight The weight of a body may be defined as the force with which it is attracted to earth. When a body fall freely to earth (strictly speaking in a vacuum – but approximately in air) its acceleration is constant at g = 9.81 m/s2. Since force is mass
Weight is a force – so in SI units it is in Newton‘s N. (Do not confuse weight with mass – this is a very common mistake)
Worked Example 2.3 A 1kg stone fall freely from rest from a bridge. a. What is the force causing it to accelerate? b. What is its speed 4s later? c. How far has it fallen in this time? Solution a) The force causing it to fall is its weight. As it is falling with acceleration due to gravity
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b) From Equation 1.1
c) From Equation 1.3
Newton’s third law of motion This law states that is a body, A, exerts a force, F, on body B then body B exerts an equal but opposite force on body A. This law applies bodies both at rest or in motion. The law is sometimes summarised as Every action has an equal and opposite reaction. A block of mass M resting on a table exerts a downward force Mg on the table. By Newton‘s third law the table exerts an equal force in the vertically upward direction on the block.
Worked Example 2.4 A lift with its load has a mass of 2000 kg. It is supported by a steel cable. Find the tension in he cable when it: a. b. c. d. e.
is at rest accelerates upwards uniformly at 1m/s2 move upwards at a steady speed of 1 m/s moves downwards at a steady speed of 1 m/s accelerates downwards with uniform acceleration of 1 m/s2
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Solution
Figure 2.1 Lift and force direction for Worked Example 2.4 a) When at rest we can use Newton‘s first law which says that the resultant force on the lift is zero. Force acting down is the lifts weight, the force acting up is the tension in the cable. These two must be equal and opposite to give a resultant force of zero. So,
This T acts vertically upwards. b) As the lift is accelerating upwards so T must exceed the weight mg. So the resultant acceleration force
by Newton second law, F = ma, so
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c) As in (a), by Newton‘s first law, the resultant force on the lift must be zero, so
d) As in (c) the tension in the cable will still equal mg since the change in direction of motion does not alter the fact that there is no acceleration.
e) If the lift accelerates downwards, then mg must exceed the tension T. So the resultant accelerating force is
By Newton‘s second law F = ma, so
Motion of connected masses We will look at the motion of two masses connected by a (negligibly) light inextensible cable passing over a light pulley wit frictionless bearings. Under these conditions the tension in the rope is the same throughout it length. As the masses are connected the magnitude of the velocities and the accelerations of the two masses will be equal. The two mass are m1 and m2 and the pulley system is arranged as in Figure 2.2
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Figure 2.2: Connected masses arrangement for Worked Example 2.2 Suppose mass m1 accelerates downwards with acceleration a. mass m2 will accelerate upward at the same rate. Using Newton‘s second law we can find the tension in the cable and acceleration a. The forces acting on m1 are the weight, m1g acting downwards and the tension T acting vertically upwards. As the mass is moving downwards the weight exceeds the tension and the resultant force is
also this force is given by F = m1a.
Using the same considerations for mass m2 the tension must be greater than he weight so the resultant force is
and F = m2a so
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Worked Example 2.5 Mass of weight 1.2kg and 1.0kg hang at the ends of a light rope passing over a light frictionless pulley. Find the acceleration of the mass and the tension in the rope. Solution The 1.2kg mass will move downwards. The pulley and mass arrangement is as shown in Figure 2.3. Let the acceleration be a and the tension T.
Figure 2.3: Connected masses over a pulley: Worked example 2.5 For the 1.2kg mass
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[1] For the 1.0kg mass
[2] Solve [1] and [2] simultaneously Adding [1]and[2]
Substituting for a into [2] gives
Friction The force which prevents or tries to prevent the slipping or sliding of two surfaces in contact is called friction. Several rules (or laws) have been developed from experiment and experience (rather than by theory). These, described below, apply only to dry surfaces. i.
The frictional resistance between two sliding surfaces is directly proportional to the force pressing the two surfaces together.
FS = frictional force resisting sliding motion. N is the force pressing the two surfaces together
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This law fails when the force pressing the surface together is very small or very large. E.g. when very large the surfaces may tend to seize together. ii. iii.
The frictional resistance depends on the nature of the roughness of the surfaces involved The frictional resistance is independent of the area of the surface in contact.
This law fails when the area of the surface is so small that damage to the surface occurs leading to increased friction. iv.
The frictional resistance is independent of speed of sliding.
This law fails when the speed of sliding is very high or very low. When the speed is very high, the temperature of the surfaces may increase and change the frictional properties. Frictional resistance is greatest when the speed of sliding is zero - when motion is about to commence. Clearly the above laws must be applied with caution. At extremes of force and speed careful thought must be given to decide whether the results is acceptable. The laws for lubricated surface are considerably different to those above. We will not be going into those in this module.
Coefficient of friction Consider a block, as shown in Figure 2.4, with mass m resting on a horizontal surface.
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Figure 2.4: A block on a rough surface with frictional resistance to sliding Let the force between the surfaces be N (known often as the normal reaction.) N will equal the weight, by Newton's third law. Also let the external force applied to the block be FA . As FA increases from zero, the frictional resistance to motion F will also increase from zero. When Freaches the maximum value FS the block will be on the point of moving. At this point FA = FS and by law (i)
S
is the coefficient of static friction.
From experiments it has been shown that once the block starts to move, the applied force required to keep it moving steadily is less than FS. That is the frictional resistance F when sliding is less than FS. Or that the force required to move an object from a stationary position is greater than to that required to keep it moving steadily. This then means the we need to have a coefficient of sliding friction block is moving
The values of below:
and
Sdepend
for when the
on the surface in contact. Some typical values are given
Steel on steel Masonry on rock
S
= 0.58
S
= 0.6-0.7
Masonry on clay
S
= 0.30
Wood on brick
S
= 0.6
Rubber sliding on bitumen at 100m/min
= 1.07
Worked example 2.6 to the horizontal. What is the coefficient of (static) friction ? Solution Young Ji International School / College
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The force acting on the crate are: Its weight mg The normal reaction of the ramp N The frictional resistance F These are shown in Figure 2.5
Figure 2.5: A crate sliding down a slope. Worked Example 2.5 Since there is no acceleration down the ramp (the crate isn‘t moving!) the resultant force parallel to the ramp must be zero. Resolving forces parallel to the ramp gives
Also, since there is no acceleration at right angles to the ramp the resultant force at right angles must be zero. Resolving forces at right angles gives
For the coefficient of friction, as
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Circular motion - banked roads or tracks In section one the acceleration a of a body moving round a circle, radius r, moving with uniform speed v, was shown to be (Equation 1.13)
and that this acts towards the centre of the circle. By Newton's second law the force F producing this acceleration on a mass m is
In this case the force is called the centripetal force. The force may be provided in many ways, for example for a car travelling round a curved level road the force is the friction between the tyres and the road. When the curved tract is banked downwards toward the centre of motion then the frictional forces in the case of the car would be less than if the track were level. The reduced dependence on friction to provide a centripetal force gives greater comfort and safety. Consider the four wheeled vehicle travelling round a track banked at an angle to the horizontal, as in Figure 2.6. Let the conditions be such that when the vehicle is moving with a speed of v there is no sideways force. The forces acting are then weight acting at the centre of gravity G of the vehicle, and the normal reaction R1 and R2 at the wheels.
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Figure 2.6: Forces on a vehicle on a banked track Taking moments about G gives
i.e. R1 = R2 - the reaction forces are the same, we will call them both R from now on. Vertically there is no motion so no acceleration so resolving forces in the vertical direction gives
Horizontally, by Equation 2.8
so resolving forces horizontally gives
Dividing Equation 2.10 by 2.9 gives
This is the condition for no sideways force on the vehicle Newton's laws of motion are three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and theforces acting upon it, and its motion in response to said forces. They have been expressed in several different ways over nearly three centuries,[1] and can be summarized as follows: 4. First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3] 5. Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object. 6. Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. Young Ji International School / College
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The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. Newton's laws are applied to objects which are idealized as single point masses,[6] in the sense that the size and shape of the object's body are neglected in order to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealized as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterize the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalization of Newton's laws of motion for rigid bodies called the Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton‘s laws of motion, then Euler‘s laws can be derived from Newton‘s laws. Euler‘s laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law only holds when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light.
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Let us begin our explanation of how Newton changed our understanding of the Universe by enumerating his Three Laws of Motion. Newton's First Law of Motion:
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
This we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia". Newton's Second Law of Motion:
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
This is the most powerful of Newton's three Laws, because it allows quantitative calculations of dynamics: how do velocities change when forces are applied. Notice the fundamental difference between Newton's 2nd Law and the dynamics of Aristotle: according to Newton, a force causes only a change in velocity (an acceleration); it does not maintain the velocity as Aristotle held. This is sometimes summarized by saying that under Newton, F = ma, but under Aristotle F = mv, where v is the velocity. Thus, according to Aristotle there is only a velocity if there is a force, but according to Newton an object with a certain velocity maintains that velocity unless a force acts on it to cause an acceleration (that is, a change in the velocity). As we have noted earlier in conjunction with the discussion of Galileo, Aristotle's view seems to be more in accord with common sense, but that is because of a failure to appreciate the role played by frictional forces. Once account is taken of all forces acting in a given situation it is the dynamics of Galileo and Newton, not of Aristotle, that are found to be in accord with the observations. Newton's Third Law of Motion:
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III. For every action there is an equal and opposite reaction.
Matter is defined as anything that has mass and volume. Mass is a measure of an object's inertia. It is proportional to weight: the more mass an object has, the more weight it has. However, mass is not the same as weight. Weight is a force created by the action of gravity on a substance while mass is a measure of an object's resistance to change in motion. Mass is measured by comparing the substance of interest to a standard kilogram called the International Prototype Kilogram (IPK). The IPK is a metal cylinder where the height and diameter both equal 39.17 millimeters and is made of an alloy of 90% platinum and 10% iridium. Thus, the standard kilogram is defined and all other masses are a comparison to this kilogram. When atom masses are measured in a mass spectrometer, a different internal standard is used. Your take home lesson with regard to mass is that mass is a relative term judged by a comparison. Volume is a measure of the amount of space occupied by an object. Volume can be measured directly with equipment designed using graduations marks or indirectly using length measurements depending on the state (gas, liquid, or solid) of the material. A graduated cylinder, for example, is a tube that can hold a liquid which is marked and labeled at regular intervals, usually every 1 or 10 mL. Once a liquid is placed in the cylinder, one can read the graduation marks and record the volume measurement. Since volume changes with temperature, graduated equipment has limits to the precision with which one can read the measurement. Solid objects that have regular shape can have their volume calculated by measuring their dimensions. In the case of a box, its volume equals length times width times height. It is particularly interesting to note that measuring is different from calculating a specific value. While mass and volume can both be determined directly relative to either a defined standard or line marks on glass, calculating other values from measurements is not considered measuring. For example, once you have measured the mass and volume of a liquid directly, one can then calculate the density of a substance by dividing the mass by the volume. This is considered indirectly determining density. Interestingly enough, one can also measure density directly if an experiment which allows the comparison of density to a standard is set up. Another quantity of matter directly or indirectly determined is the amount of substance. This can either represent a counted quantity of objects (e.g. three mice or a dozen bagels) or the indirectly determined number of particles of a substance being dealt with such as how Young Ji International School / College
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many atoms are contained in a sample of a pure substance. The latter quantity is described in terms of moles. One mole is a specifically defined as the number of particles in 12 grams of the isotope Carbon-12. This number is 6.02214078(18)x 1023 particles. Units of Measure
Mass: the kilogram (kg). Also, the gram (g) and milligram (mg).
1 kg = 1000 g
1000 mg = 1 g.
Volume: the liter (L), milliliter (mL). Also, cubic centimeters (cc) and cubic meters (m3).
1 cc = 1 mL
1000 mL = 1 L
1000 L = 1 m3
Amount: the mole (mol).
1 mol = 6.02214078(18)x 1023 particles
Atoms, Elements, and Compounds The fundamental building block of matter is the atom.
The red dots are protons, the black dots are neutrons, and the blue dots are electrons. Any atom is composed of a little nucleus surrounded by a "cloud" of electrons. In the nucleus there are protons and neutrons.
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However, the term "atom" just refers to a building block of matter; it doesn't specify the identity of the atom. It could be an atom of carbon, or an atom of hydrogen, or any other kind of atom. This is where the term "element" comes into play. When an atom is defined by the number of protons contained in its nucleus, chemists refer to it as an element. All elements have a very specific identity that makes them unique from other elements. For example, an atom with 6 protons in its nucleus is known as the element carbon. When speaking of the element fluorine, chemists mean an atom that contains 9 protons in its nucleus. 
Atom: A fundamental building block of matter composed of protons, neutrons, and electrons.

Element: A uniquely identifiable atom recognized by the number of protons in the nucleus.
Despite the fact that we define an element as a unique identifiable atom, when we speak, for example, 5 elements, we don't usually mean those 5 atoms are of the same type (having the same number of protons in their nucleus). We mean 5 'types' of atoms. It is not necessary there are only 5 atoms. There may be 10, or 100, etc. atoms, but those atoms belong to one of 5 types of atoms. I'd rather define 'element' as 'type of atom'. I think it is more precise. If we'd like to refer to 5 atoms having the same 6 protons in their nucleus, I'd say '5 carbon atoms' or '5 atoms of carbon'. It is important to note that if the number of protons in the nucleus of an atom changes, so does the identity of that element. If we could remove a proton from nitrogen (7 protons), it is no longer nitrogen. We would, in fact, have to identify the atom as carbon (6 protons). Remember, elements are unique and are always defined by the number of protons in the nucleus. The Periodic Table of the Elements shows all known elements organized by the number of protons they have. An element is composed of the same type of atom; elemental carbon contains any number of atoms, all having 6 protons in their nuclei. In contrast, compounds are composed of different type of atoms. More precisely, a compound is a chemical substance that consists of two or more elements. A carbon compound contains some carbon atoms (with 6 protons each) and some other atoms with different numbers of protons. Compounds have properties different from the elements that created them. Water, for example, is composed of hydrogen and oxygen. Hydrogen is an explosive gas and oxygen is a gas that fuels fire. Water has completely different properties, being a liquid that is used to extinguish fires. The smallest representative for a compound (which means it retains characteristics of the compound) is called a molecule. Molecules are composed of atoms that have "bonded" Young Ji International School / College
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together. As an example, the formula of a water molecule is "H2O": two hydrogen atoms and one oxygen atom. Properties of Matter Properties of matter can be divided in two ways: extensive/intensive, or physical/chemical.
Extensive properties depend on the amount of matter that is being measured. These include mass and volume.
Physical properties can be measured without changing the chemical's identity. The freezing point of a substance is physical. When water freezes, it's still H2O.
Intensive properties do not depend on the
Chemical properties deal with how one
amount of matter. These include density and color.
chemical reacts with another. We know that wood is flammable because it becomes heat, ash, and carbon dioxide when heated in the presence of oxygen.
States of Matter One important physical property is the state of matter. Three are common in everyday life: solid, liquid, and gas. The fourth, plasma, is observed in special conditions such as the ones found in the sun and fluorescent lamps. Substances can exist in any of the states. Water is a compound that can be liquid, solid (ice), or gas (steam).
The ice in this picture is a solid. The water in the picture is a liquid. In the air there is water vapor, which is a gas.
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The states of matter depend on the bonding between molecules. Solids Solids have a definite shape and a definite volume. Most everyday objects are solids: rocks, chairs, ice, and anything with a specific shape and size. The molecules in a solid are close together and connected by intermolecular bonds. Solids can be amorphous, meaning that they have no particular structure, or they can be arranged into crystalline structures or networks. For instance, soot, graphite, and diamond are all made of elemental carbon, and they are all solids. What makes them so different? Soot is amorphous, so the atoms are randomly stuck together. Graphite forms parallel layers that can slip past each other. Diamond, however, forms a crystal structure that makes it very strong. Liquids Liquids have a definite volume, but they do not have a definite shape. Instead, they take the shape of their container to the extent they are indeed "contained" by something such as beaker or a cupped hand or even a puddle. If not "contained" by a formal or informal vessel, the shape is determined by other internal (e.g. intermolecular) and external (e.g. gravity, wind, inertial) forces. The molecules are close, but not as close as a solid. The intermolecular bonds are weak, so the molecules are free to slip past each other, flowing smoothly. A property of liquids is viscosity, the measure of "thickness" when flowing. Water is not nearly as viscous as molasses, for example. Gases Gases have no definite volume and no definite shape. They expand to fill the size and shape of their container. The oxygen that we breathe and steam from a pot are both examples of gases. The molecules are very far apart in a gas, and there are minimal intermolecular forces. Each atom is free to move in any direction. Gases undergo effusion and diffusion. Young Ji International School / College
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Effusion occurs when a gas seeps through a small hole, and diffusion occurs when a gas spreads out across a room. If someone leaves a bottle of ammonia on a desk, and there is a hole in it, eventually the entire room will reek of ammonia gas. That is due to the diffusion and effusion. These properties of gas occur because the molecules are not bonded to each other.
Answer the following problems. (5 points each) 1. What is the speed of a rocket that travels 9000 meters in 12.12 seconds? 2. What is the speed of a jet plane that travels 528 meters in 4 seconds?
Forces and Motion: Speed, Velocity, and Acceleration EQUATIONS: Speed:
Velocity:
Acceleration:
Force:
Sample Problems: A girl travels 20 miles on her bicycle. The trip takes 2 hours. Express her speed in miles/hr. 1. First, we identify the variables in our problem: distance (d) = 20 miles time (t) = 2 hours 2. We place the variables in their correct position in the speed formula S = d/t S = 20 mi/2 hour 3. Perform the calculation and express the resulting speed value with the appropriate unit: S = 10 mi/hr
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A car starts from a stoplight and is traveling with a velocity of 10 m/sec east in 20 seconds. What is the acceleration of the car? 1. First we identify the information that we are given in the problem: vf - 10 m/sec vo - 0 m/sec time - 20 seconds 2. Then we insert the given information into the acceleration formula: a = (vf - vo)/t a = (10 m/sec - 0 m/sec)/20 sec 3. Solving the problem gives an acceleration value of 0.5 m/sec2. Now try on your own: 1. What is the speed of a rocket that travels 9000 meters in 12.12 seconds?
2. What is the speed of a jet plane that travels 528 meters in 4 seconds? 3. How long will your trip take (in hours) if you travel 350 km at an average speed of 80 km/hr? 4. How far (in meters) will you travel in 3 minutes running at a rate of 6 m/s? 5. A trip to Cape Canaveral, Florida takes 10 hours. The distance is 816 km. Calculate the average speed. 6. How many seconds will it take for a satellite to travel 450 km at a rate of 120 m/s? 7. What is the speed of a walking person in m/s if the person travels 1000 m in 20 minutes? 8. A ball rolls down a ramp for 15 seconds. If the initial velocity of the ball was 0.8 m/sec and the final velocity was 7 m/sec, what was the acceleration of the ball ? 9. A meteoroid changed velocity from 1.0 km/s to 1.8 km/s in 0.03 seconds. What is the acceleration of the meteoroid?
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10. A car going 50mph accelerates to pass a truck. Five seconds later the car is going 80mph. Calculate the acceleration of the car. 11. The space shuttle releases a space telescope into orbit around the earth. The telescope goes from being stationary to traveling at a speed of 1700 m/s in 25 seconds. What is the acceleration of the satellite? 12. A ball is rolled at a velocity of 12 m/sec. After 36 seconds, it comes to a stop. What is the acceleration of the ball? 13. How much force is needed to accelerate a truck with a mass of 2,000 kg, at a rate of 3 m/s²? 14. A dragster in a race accelerated from stop to 60 m/s by the time it reached the finish line. The dragster moved in a straight line and traveled from the starting line to the finish line in 8.0 sec. What was the acceleration of the dragster? 15. A 300 N force acts on a 25 kg object. The acceleration of the object is
Know ALSO the following vocabulary terms: Constant speed – Speed that does not change Velocity – Speed in a given direction Frame of reference – A background used to judge motion or speed Instantaneous Speed – Speed at a given moment in time Speed – amount of distance traveled in a certain amount of time Average Speed – total distance divided by total time Time-Distance Graph – graph that shows speed of an object Acceleration – change in velocity over time Motion – an object changing position or distance in time Rate of Change – amount of time it takes to change position or motion
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Inertia - tendency of a still object to stay still or moving object to keep moving unless acted on by an unbalanced force Force – push or pull Centripetal Force – force keeping objects moving in a circle Gravity – pull of objects in the universe – pull determined by mass and distance Newton‘s Three Laws of Motion – 1st: Law of Inertia (see Inertia definition); 2nd: Force=mass x acceleration; 3rd: For every action, there is an opposite and equal reaction
Problem 1: From rest, a car accelerated at 8 m/s2 for 10 seconds. a) What is the position of the car at the end of the 10 seconds? b) What is the velocity of the car at the end of the 10 seconds? Solution to Problem 1: a) The car starts from rest therefore the initial speed u = 0. Nothing is said about the initial position and we therefore assume it is equal to 0. Hence the position x is given by the equation x = (1/2) a t 2 where a is the acceleration (=8 m/s2) and t is the period of time between initial and final positions x = (1/2)8 (10)2 = 400 m b) The velocity v of the car at the end of the 10 seconds is given by v = a t = 8 * 10 = 80 m/s
Problem 2: With an initial velocity of 20 km/h, a car accelerated at 8 m/s2 for 10 seconds. a) What is the position of the car at the end of the 10 seconds? b) What is the velocity of the car at the end of the 10 seconds?
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Solution to Problem 2: a) The car has an initial velocity of 20 km/h, therefore the initial speed u = 20 km/h. Nothing is said about the initial position and we therefore assume it is equal to 0. Hence the position x is given by the equation x = (1/2) a t 2 + u t where a is the acceleration (=8 m/s2) and t is period of time between initial and final positions and u is the initial velocity. Since the time is given in seconds, we need to convert 20 km/h into m/s as follows: 20 * 1km 1000 m u = 20 km/h =
1 hour
1 hour
1 km 3600 seconds = 5.6 m/s
We now have x = (1/2) (8) 102 + 5.6*10 = 456 m b) v = at + u = 8*10 + 5.6 = 85.6 m/s
Problem 3: A car accelerates uniformly from 0 to 72 km/h in 11.5 seconds. a) What is the acceleration of the car in m/s2? b) What is the position of the car by the time it reaches the velocity of 72 km/h? Solution to Problem 3: a) The acceleration a is a measure if the rate of change of the velocity within a period of time. Hence change in velocity v - u 72 km/h - 0 u=
change in time
t 11.5 seconds
=
=
We now convert 72 km/h into m/s Young Ji International School / College
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72 * 1km 1000 m u = 72 km/h =
1 hour
1 hour
1 km 3600 seconds = 20 m/s
We now calculate the acceleration a a = (20 m/s) / (11.5 s) = 1.74 m/s2 (approximetd) b) Two ways to find the position x: 1) x = (1/2)(v + u) t
or
2) x = (1/2) a t 2 + u t
1) We first use: x = (1/2)(v + u) t = 0.5*(20 m/s + 0)*11.5 = 115 m 2) We now use: (1/2) a t2 + u t = 0.5*1.74*(11.5) 2 + 0*t = 115 m
Problem 4: An object is thrown straight down from the top of a building at a speed of 20 m/s. It hits the ground with a speed of 40 m/s. a) How high is the building? b) How long was the object in the air? Solution to Problem 4: a) We consider that the direction from ground up is the positive direction of the falling object. We are given the initial (-20 m/s) and final velocities (-40 m/s); the minus sign was added to take into account the fact that the falling object is moving in the negative direction. We know the gravitational acceleration (g = - 9.8 m/s2) acting on the falling object and we are asked to find the height of the building. If we consider the position of the object as being x (wth x = 0 on the ground), then we may use the equation relating the initial and final velocities u and v, the acceleration a and the initial (x0 which the height of the building) and final (x, on the ground) positions as follows: v2 = u2 + 2 a (x - x0) (-40 m/s)2 = (-20 m/s)2 + 2 (-9.8 m/s0) (0 - x0) Solve the above for x0 Young Ji International School / College
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x0 = 1200 / 19.6 = 61.2 m b) x - x0 = (1/2)(u + v)t -61.2 = 0.5(-20 - 40)t t = 61.2 / 30 = 2.04 s
Problem 5: A train brakes from 40 m/s to a stop over a distance of 100 m. a) What is the acceleration of the train? b) How much time does it take the train to stop? Solution to Problem 5: a) We are given the initial velocity u = 40 m/s, the final velocity v = 0 (train stops) and the distance. Hence the formula that relates these 3 quantities and the acceleration is given by v2 = u2 + 2 a x 02 = 402 + 2 a (100) Solve for the acceleration a a = -1600 / 200 = - 8 m/s2 b) There two ways to find the time: 1) Use: x = (1/2)(v + u) t 100 = 0.5(0 + 40) t Solve for t: t = 5 seconds. 2) Use x = (1/2) a t2 + ut 100 = 0.5 ( - 8) t2 + 40t 4 t2 - 40 t + 100 = 0
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4 (t2 - 10 t + 25) = 0 4(t - 5)2 = 0 t = 5 seconds.
Problem 6: A boy on a bicycle increases his velocity from 5 m/s to 20 m/s in 10 seconds. a) What is the acceleration of the bicycle? b) What distance was covered by the bicycle during the 10 seconds? Solution to Problem 6: a) In this problem the initial velocity u = 5 m/s and the final velocity v = 20 m/s. The acceleration a of the bicycle is the rate of change of the velocity and is given as follows 20 m/s - 5 m/s v-u a=
= t
10 seconds = 1.5 m/s2
b) There are two ways to find the distance covered by the bicyle in t = 10 seconds. 1) x = (1/2)(v + u) t = 0.5 (20 + 5) 10 = 125 m 2) x = (1/2) a t2 + u t = 0.5 * 1.5 * 100 + 5 * 10 = 125 m
Problem 7: a) How long does it take an airplane to take off if it needs to reach a speed on the ground of 350 km/h over a distance of 600 meters (assume the plane starts from rest)? b) What is the acceleration of the airplane over the 600 meters? Solution to Problem 7: a) In this problem the initial velocity u = 0 (assumed because it is not given) , the final velocity v = 350 km/h and the distance x = 600 meters = 0.6 km The relationship between the give quantities is: x = (1/2)(v + u) t Young Ji International School / College
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0.6 = 0.5 (350 + 0) t Solve for t t = (0.6 / 175) hours = 12.3 seconds b) The acceleration a of the airplane is given by a = (v - u) / t = 350 km/h / 12.3 s Convert 350 km/h into m/s 350 km/h = 350,000 m / 3,600 s = 97.2 m/s a = 97.2 m/s / 12.3 s = 8 m/s2 (to the nearest unit)
Problem 8: Starting from a distance of 20 meters to the left of the origin and at a velocity of 10 m/s, an object accelerates to the right of the origin for 5 seconds at 4 m/s2. What is the position of the object at the end of the 5 seconds of acceleration? Solution to Problem 8: a) In this problem, we may consider that the direction of the object is the positive direction and the initial position x0 = -20 meters (to the left of the origin), the initial velocity u = 10 m/s, the acceleration a = 4 m/s2 and the time is t = 5 seconds. The position is given by x = (1/2) a t2 + u t + x0 = 0.5 * 4 * (5)2 + 10 * 5 - 20 = 80 meters to the right of the origin.
Problem 9: What is the smallest distance, in meters, needed for an airplane touching the runway with a velocity of 360 km/h and an acceleration of -10 m/s2 to come to rest? Solution to Problem 9: a) In this problem the initial velocity u = 360 km/h, the final velocity v = 0 (rest) and the acceleration a = -10 m/s2. The distance x can be calculated using the formula v2 = u2 + 2 a x Young Ji International School / College
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Convert 360 km/h into m/s: 360 km/h = (360 000 m) /(3600 s) = 100 m/s x = ( v2 - u2 ) / (2 a) = (0 - 10,000) / (-20) = 500 meters
Problem 10: To approximate the height of a water well, Martha and John drop a heavy rock into the well. 8 seconds after the rock is dropped, they hear a splash caused by the impact of the rock on the water. What is the height of the well. (Speed of sound in air is 340 m/s). Solution to Problem 10: a) In this problem we have: 1) a rock was dropped down the well and is uniformly accelerated downward due to gravity. If h is the height of the well and t is the time taken by the rock to reach the bottom of the well, then we have h = (1/2)(9.8) t 2 2) After the splash, the sound travels up the well at a constant speed of 340 m/s. Again the same height h of the well is given by h = 340 *(8 - t) : 8 - t is the time taken for the sount to travel from bottom to top where the sound is heard. The above equations give: (1/2)(9.8) t2 = 340 *(8 - t) 4.9 t2 + 340 t - 2720 = 0 Solve for t, two solutions: t = 7.24 s and the second solution is negative and is not valid. The height h of the well is calculated using one of the above equations: h = 340 *(8 - t) = 340 *(8 - 7.24) = 257 meters (approximated to the the nearest meter)
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Problem 11: A rock is thrown straight up and reaches a height of 10 m. a) How long was the rock in the air? b) What is the initial velocity of the rock? Solution to Problem 11: a) In this problem the rock has an initial velocity u. When the rock reaches a height of 10 m, it returns down to earth and the the velocity v = 0 when x = 10 meters. Hence v = -9.8 t + u 0 = -9.8 t + u u = 9.8 t x = (1/2)(u + v) t 10 = 0.5 (9.8 t + 0) t = 4.9 t2 Solve for t: t = 1.42 seconds b) u = 9.8 t = 9.8 * 1.24 = 14 m/s
Problem 12: A car accelerates from rest at 1.0 m/s2 for 20.0 seconds along a straight road . It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car. Solution to Problem 12: a) The car goes through 3 stages: stage 1: acceleration a = 1, initial velocity = 0, t = 20 s. Hence the distance x is given by x = (1/2) a t2 = (1/2) (1) 202 = 200 meters stage 2: constant speed v is the speed at the end of stage 1. v = a t = 1 * 20 = 20 m/s Young Ji International School / College
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x = v t = 20 m/s * (1/2 hour) = 20 m/s * 1800 s = 36,000 meters stage 3: deceleration to a stop, hence u = 20 m/s and v = 0 (stop) x = (1/2)(u + v) t = (1/2)(20 + 0) 30 = 300 meters total distance = 200 + 36,000 + 300 = 36,500 meters. 1. Q: A car moved 80 km to the South. What is its displacement? A: 20 km South B: 50 km East C: 80 km South D: 160 km North ------------------------------------2. Q: A car moved 60 km East and 90 km West. What is the distance? A: 30 km B: 60 km C: 90 km D: 150 km ------------------------------------3. Q: A car moved 60 km East and 90 km West. What is the displacement? A: 30 km West B: 60 km West C: 30 km East D: 150 km ------------------------------------4. Q: Average velocity can be calculated by dividing displacement over what? A: time B: distance C: mass D: density ------------------------------------5. Q: What is the average velocity of a car that moved 60km in 3 hours? A: 10 km/h B: 20 km/h C: 30 km/h D: 60 km/h ------------------------------------6. Q: What is the average velocity of a car that moved 40 km East and 80 km West in 2 hours? A: 5 km/h B: 10 km/h C: 15 km/h D: 20 km/h ------------------------------------7. Q: How far will a car travel in 25 min at 12 m/s? Young Ji International School / College
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A: 10 km B: 14 km C: 18 km D: 24 km ------------------------------------8. Q: How far will a car travel in 2 hours at 20 m/s? A: 144 km B: 158 km C: 168 km D: 234 km ------------------------------------9. Q: If car A is at 40 km/h and car B is at 10 km/h in the opposite direction, what is the velocity of the car A relative to the car B? A: 10 km/h B: 20 km/h C: 40 km/h D: 50 km/h ------------------------------------10. Q: If you are walking at constant velocity of 8 km/h and a car passed you by at the speed of 30 km/h from behind, what is the car's velocity from your viewpoint? A: 22 km/h B: 30 km/h C: 38 km/h D: 40 km/h ------------------------------------11. Q: If car A is at 70 km/h and car B is at 50 km/h in the same direction, what is the velocity of the car A relative to the car B? A: 10 km/h B: 20 km/h C: 30 km/h D: 40 km/h ------------------------------------12. Q: If a car moves 12 km North, 19 km East, and 12 km South, what is its displacement? A: 12 km B: 19 km C: 31 km D: 43 km ------------------------------------13. Q: Acceleration is the measure of the change in what? A: density B: motion C: velocity D: mass ------------------------------------14. Q: Average acceleration is calculated by: A: velocity change devided by the mass B: mass change devided by elapsed time Young Ji International School / College
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C: velocity change devided by elapsed time D: velocity change devided by gravity ------------------------------------15. Q: If a car accelerates from 3 m/s to 12 m/s in 3 seconds, what is the car's average acceleration? A: 1 m/s2 B: 2 m/s2 C: 3 m/s2 D: 4 m/s2 ------------------------------------16. Q: How long does it take to accelerate an object from rest to 15 m/s if the acceleration was 3 m/s2? A: 2 s B: 4 s C: 5 s D: 15 s ------------------------------------17. Q: You started to run at 10 km/h when you left your house and you arrived at school 30 minutes later. Assuming that your average acceleration was 30 km/h2, how fast were you running when you arrived? A: 15 km/h B: 20 km/h C: 25 km/h D: 30 km/h ------------------------------------18. Q: Acceleration due to gravity is represented by what symbol? A: v B: g C: t D: s ------------------------------------19. Q: What is g? A: 9.8 m/s2 B: 10.7 m/s2 C: 12.6 m/s2 D: 98 m/s2 ------------------------------------20. Q: How long will it take for an apple falling from a 29.4m-tall tree to hit the ground? A: 1.56 s B: 2.04 s C: 2.45 s D: 3.72 s ------------------------------------21. Q: How long does it take for a car to change its velocity from 10 m/s to 25 m/s if the acceleration is 5 m/s2? A: 2 s B: 3 s Young Ji International School / College
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C: 4 s D: 5 s ------------------------------------22. Q: If a car has a constant acceleration of 4 m/s2, starting from rest, how fast is it traveling after 5 seconds? A: 20 m/s2 B: 24 m/s2 C: 30 m/s2 D: 40 m/s2 ------------------------------------23. Q: If a car has a constant acceleration of 4 m/s2, starting from rest, how far has it traveled after 5 seconds? A: 50 m B: 60 m C: 70 m D: 80 m ------------------------------------24. Q: If a car has a constant acceleration of 4 m/s2, starting from rest, how far has it traveled by the time it reaches the speed of 40 m/s? A: 50 m B: 100 m C: 200 m D: 400 m ------------------------------------25. Q: A car is at velocity of 20 km/h. If the car traveled 120 km in 3 hours at constant acceleration, what is its final velocity? A: 50 km/h B: 60 km/h C: 70 km/h D: 80 km/h ------------------------------------26. Q: How long will it take for a falling object to reach 108 m/s if its initial velocity is 10 m/s? A: 6 s B: 8 s C: 10 s D: 12 s ------------------------------------27. Q: What is the final velocity of an apple if it falls from a 100m-tree? A: 43.4 m/s B: 44.3 m/s C: 45.7 m/s D: 46.4 m/s ------------------------------------28. Q: What is the displacement of a car whose initial velocity is 5 m/s and then accelerated 2 m/s2 for 10 seconds? A: 150 m B: 175 m Young Ji International School / College
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C: 200 m D: 250 m ------------------------------------29. Q: What is the final velocity of a car that accelerated 10 m/s2 from rest and traveled 180m? A: 30 m/s B: 40 m/s C: 50 m/s D: 60 m/s ------------------------------------30. Q: If a car accelerated from 5 m/s to 25 m/s in 10 seconds, how far will it travel? A: 100 m B: 150 m C: 200 m D: 250 m Directions: Encircle the correct answer. 1. The significant effect of the passing of the Clean Air Bill is the: a. Lessening of motor vehicles c. reduction of lead and other chemical pollution b. Increase in the price of prime commodities d. sudden decrease of oil supply for vehicular use 2. A change in the composition of a substance resulting in the formation of a new substance is called: a. Nuclear change b. mechanical change c. physical change chemical change 3. At the outset of the rainy season the epidemic of H-fever is feared. Which practice is the best approach to prevent its occurrence in homes? a. Clean the yards of breeding places for mosquitoes like old tires, cans, etc. b. Fumigate the house with smoke and chemicals c. Submit children to vaccination d. Avoid mosquito bites in the afternoon 4. A patient collapsed due to her low sugar level in the blood. What first aid must be applied at once? a. Give glass of coca cola or sprite b. Give a cold glass of coffee with sugar c. Give a hot glass of milk without sugar d. Allow the patient to take hot porridge. 5. After a airplane crash in the mountains, what was the easiest source of identification of the victims? a. Identification of bone structure c. identification of the body length b. Identification of eyes d. series of teeth available 6. Food markets are encouraged to handle cooked food well. One incident in a wedding party sent hundreds of quest to the hospital. It was found out that the food. a. Was half cooked c. had ptomaine poison b. Was contaminated with dysentery bacteria d. was left uncovered Young Ji International School / College
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7. Farmers are asked to change their crops by season. What approach is applied to this case? a. Strip cropping b. crop rotation c. continuous farming d. terracing 8. Heart attack has claimed many live. Out of 380 experimented men and women it was established that those who were less prone to heart attack were tea drinkers. The 44% findings show: a. That caffeine cause more heart ailment b. Tea makes people active c. Tea leads to the reduction of fats d. Tea with tannin is less dangerous 9. Protest from inhabitants close to dumping sites in Metro Manila waste arise from some observable factors, the most serious of which is: a. Noise pollutant from garbage trucks b. Presence of flies and mosquitoes c. presence of human being dumped in the site d. unlimited seepage off waste into the water sheds 10. Seafarers decide to leave the shores when weather bureau declares the signal for travel. Small boats between islands Romblon, Marinduque and Mindoro cannot sail if the signal raised is; a. Signal #3 b. signal #2 c. signal #4 d. signal#1 11. There is a campaign against cholera. How can the pupils get protected from catching the disease? a. Allow children to eat food sold by the peddlers b. Open up a store in the classroom for children’s recess time. c. Teach children to wash their hands with soap and water before and after meals. d. Contact the parents for a meeting. 12. Poisoning of farmers during fertilizing field is traced to: a. Spraying fields at high noon b. Failure to use hand gloves c. Smoking during and after spraying d. Using bottled drinking water 13. A common cause of teacher’s illness is traces to: a. Urinary tract infection b. anemia c. tuberculosis d. tonsillitis 14. Children in the mountain ranges are diagnosed as suffering from goiter. Determine the cause of such disease. a. Lack of iodine in food b. excess of iodine in diet c. cexcess of vitamin in diet d. Lack of iron in diet. 15. One good rule to avoid intestinal disease is: a. Wash your hands before eating b. Wash your feet before going to bed c. Sleep under a mosquito net d. Avoid insects bites Young Ji International School / College
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16. Opening of a cement plants requires getting a DENR clearance. Which of these clearances is required? a. Air Pollution Clearance b. Waste Disposal c. BIR d. Environmental Clearance (ECC) 17. When do doctors declare dengue fever as an epidemic? a. When two are hospitalized from the neighborhood b. When the proportion of patients reaches at least 15% of the population. c. When every household of five house is sick with high fever. d. When everyone is suffering from a cold. 18. One approach to lessen vehicular air pollution is: a. Ban twenty or more year old vehicles from the streets b. Ban diesel-using cars in the highway c. Ask pedestrians to use bicycles d. Utilizing the MRT and LRT 19. There are several advertisements that encourage people to take this supplement so that they can grow 3 to 5 inches more even after the age of 20. a. This is not possible because there is a definite pattern of growth of bones and muscles. b. This true because the ad would not have been allowed. c. This is not true because there are no specific individual mentioned. d. This is true because of the protein content. 20. Environmentalist believe that: a. Opening dump sites will waste disposal best b. Burying plastics will ease clogging of water canals c. Classifying garbage identify biodegradable and non-biodegradable waste d. Burning garbage is the safest approach 21. Food preparations are handled well to avoid spoilage caused by _______ of products. a. Unsanitary condition b. miscalculation c. unlimited preservatives d. mislabeling 22. Rivers in Metro manila are the identified causes of heavy flood. Authorities account this to: a. Waste burning in home yards b. Waste dumping on river banks c. Waste classification d. Waste incineration 23. Earth Day is celebrated on ____. a. April 22 b. May 22 c. June 22 d. July 22 24. Waste from the kitchen is considered useful if properly separated. How are these classified? a. A non-degradable b. biodegradable c. metallic recesses d. degradable 25. The Philippine Air Force took off to scatter salt to the existing clouds. This was an attempt to: a. Encourage earthquake occurrence b. Produce rain over dry fields c. Drive the clouds further to the sea Young Ji International School / College
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2nd Quarter Module (Lesson: Phases and Forms of Matter) State of matter is one of the distinct forms that matter takes on. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many other states are known such as Bose–Einstein condensates and neutron-degenerate matter but these only occur in extreme situations such as ultra-cold or ultra-dense matter. Other states, such as quark–gluon plasmas, are believed to be possible but remain theoretical for now. For a complete list of all exotic states of matter, see the list of states of matter. Historically, the distinction is made based on qualitative differences in properties. Matter in the solid state maintains a fixed volume and shape, with component particles (atoms, moleculesor ions) close together and fixed into place. Matter in the liquid state maintains a fixed volume, but has a variable shape that adapts to fit its container. Its particles are still close together but move freely. Matter in the gaseous state has both variable volume and shape, adapting both to fit its container. Its particles are neither close together nor fixed in place. Matter in the plasma state has variable volume and shape, but as well as neutral atoms, it contains a significant number of ions and electrons, both of which can move around freely. Plasma is the most common form of visible matter in the universe.[1]
The four fundamental states of matter. Clockwise from top left, they are solid, liquid, plasma and gas, represented by an ice sculpture, a drop of water, electrical arcing from a tesla coil, and the air around clouds respectively. The term phase is sometimes used as a synonym for state of matter, but a system can contain several immiscible phases of the same state of matter. Young Ji International School / College
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The four fundamental states Solid
A crystalline solid: atomic resolution image of strontium titanate. Brighter atoms are Sr and darker ones are Ti. Solid In a solid the particles (ions, atoms or molecules) are closely packed together. The forces between particles are strong so that the particles cannot move freely but can only vibrate. As a result, a solid has a stable, definite shape, and a definite volume. Solids can only change their shape by force, as when broken or cut. In crystalline solids, the particles (atoms, molecules, or ions) are packed in a regularly ordered, repeating pattern. There are various differentcrystal structures, and the same substance can have more than one structure (or solid phase). For example, iron has a bodycentred cubicstructure at temperatures below 912 °C, and a face-centred cubic structure between 912 and 1394 °C. Ice has fifteen known crystal structures, or fifteen solid phases, which exist at various temperatures and pressures. Glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states; therefore they are described below as nonclassical states of matter. Solids can be transformed into liquids by melting, and liquids can be transformed into solids by freezing. Solids can also change directly into gases through the process of sublimation. Liquid
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Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present. Liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. The volume is definite if the temperature and pressure are constant. When a solid is heated above its melting point, it becomes liquid, given that the pressure is higher than the triple point of the substance. Intermolecular (or interatomic or interionic) forces are still important, but the molecules have enough energy to move relative to each other and the structure is mobile. This means that the shape of a liquid is not definite but is determined by its container. The volume is usually greater than that of the corresponding solid, the best known exception being water, H2O. The highest temperature at which a given liquid can exist is its critical temperature. Gas
The spaces between gas molecules are very big. Gas molecules have very weak or no bonds at all. The molecules in "gas" can move freely and fast. Gas A gas is a compressible fluid. Not only will a gas conform to the shape of its container but it will also expand to fill the container. In a gas, the molecules have enough kinetic energy so that the effect of intermolecular forces is small (or zero for an ideal gas), and the typical distance between neighboring molecules is much greater than the molecular size. A gas has no definite shape or volume, but occupies the entire container in which it is confined. A liquid may be converted to a gas by heating at constant pressure to the boiling point, or else by reducing the pressure at constant temperature. At temperatures below its critical temperature, a gas is also called a vapor, and can be liquefied by compression alone without cooling. A vapour can exist in equilibrium with a liquid (or solid), in which case the gas pressure equals the vapor pressure of the liquid (or solid).
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A supercritical fluid (SCF) is a gas whose temperature and pressure are above the critical temperature and critical pressure respectively. In this state, the distinction between liquid and gas disappears. A supercritical fluid has the physical properties of a gas, but its high density confers solvent properties in some cases, which leads to useful applications. For example, supercritical carbon dioxide is used to extract caffeine in the manufacture of decaffeinated coffee. Plasma
In a plasma, electrons are ripped away from their nuclei, forming an electron "sea". This gives it the ability to conduct electricity. Plasma (physics) Like a gas, plasma does not have definite shape or volume. Unlike gases, plasmas are electrically conductive, produce magnetic fields and electric currents, and respond strongly to electromagnetic forces. Positively charged nuclei swim in a "sea" of freely-moving disassociated electrons, similar to the way such charges exist in conductive metal. In fact it is this electron "sea" that allows matter in the plasma state to conduct electricity. The plasma state is often misunderstood, but it is actually quite common on Earth, and the majority of people observe it on a regular basis without even realizing it. Lightning, electric sparks, fluorescent lights, neon lights, plasma televisions, some types of flame and the stars are all examples of illuminated matter in the plasma state. A gas is usually converted to a plasma in one of two ways, either from a huge voltage difference between two points, or by exposing it to extremely high temperatures. Heating matter to high temperatures causes electrons to leave the atoms, resulting in the presence of free electrons. At very high temperatures, such as those present in stars, it is assumed that essentially all electrons are "free", and that a very high-energy plasma is essentially bare nuclei swimming in a sea of electrons. Phase transitions Phase transitions
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This diagram illustrates transitions between the four fundamental states of matter. A state of matter is also characterized by phase transitions. A phase transition indicates a change in structure and can be recognized by an abrupt change in properties. A distinct state of matter can be defined as any set of states distinguished from any other set of states by a phase transition. Water can be said to have several distinct solid states. The appearance of superconductivity is associated with a phase transition, so there are superconductive states. Likewise, ferromagnetic states are demarcated by phase transitions and have distinctive properties. When the change of state occurs in stages the intermediate steps are called mesophases. Such phases have been exploited by the introduction of liquid crystal technology. The state or phase of a given set of matter can change depending on pressure and temperature conditions, transitioning to other phases as these conditions change to favor their existence; for example, solid transitions to liquid with an increase in temperature. Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point, boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms. Forms of matter that are not composed of molecules and are organized by different forces can also be considered different states of matter. Superfluids (like Fermionic condensate) and the quark–gluon plasma are examples. Activity Module (Lesson: Phases and Forms of Matter)
Create a Venn Diagram below to compare and contrast solids, liquids and gases. Try to fill in each bullet point with a new idea. Use the summary on the front of this page to help you.
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SOLID
LIQUID
GAS
Explain the following phase changes in your own words:
1. Melting = ___________________________________________________________________________ 2. Freezing = ___________________________________________________________________________ 3. Evaporation = ___________________________________________________________________________ 4. Condensation = ___________________________________________________________________________ 5. Sublimation = ___________________________________________________________________________ Young Ji International School / College
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6. Deposition = ___________________________________________________________________________ Module (Lesson: Pressure)
Pressure Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal, which is a Newton per square meter. For an object sitting on a surface, the force pressing on the surface is the weight of the object, but in different orientations it might have a different area in contact with the surface and therefore exert a different pressure.
Pressure calculation.
There are many physical situations where pressure is the most important variable. If you are peeling an apple, then pressure is the key variable: if the knife is sharp, then the area of contact is small and you can peel with less force exerted on the blade. If you must get an injection, then pressure is the most important variable in getting the needle through your skin: it is better to have a sharp needle than a dull one since the smaller area of contact implies that less force is required to push the needle through the skin. When you deal with the pressure of a liquid at rest, the medium is treated as a continuous distribution of matter. But when you deal with a gas pressure, it must be approached as an average pressure from molecular collisions with the walls. Pressure in a fluid can be seen to be a measure of energy per unit volume by means of the definition of work. This energy is related to other forms of fluid
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energy by theBernoulli equation.
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Pressure as Energy Density Pressure in a fluid may be considered to be a measure of energy per unit volume or energy density. For a force exerted on a fluid, this can be seen from the definition of pressure:
The most obvious application is to the hydrostatic pressure of a fluid, where pressure can be used as energy density alongside kinetic energy density and potential energy density in the Bernoulli equation. The other side of the coin is that energy densities from other causes can be conveniently expressed as an effective "pressure". For example, the energy density of solvent molecules which leads to osmosis is expressed as osmotic pressure. The energy density which keeps a star from collapsing is expressed as radiation pressure.
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Fluid Kinetic Energy The kinetic energy of a moving fluid is more useful in applications like the Bernoulli equation when it is expressed as kinetic energy per unit volume
When the kinetic energy is that of fluid under conditions of laminar flow through a tube, one must take into account the velocity profile to evaluate the kinetic energy. Across the cross-section of flow, the kinetic energy must be calculated using the average of the velocity squared , which is not the same as squaring the average velocity. Expressed in terms of the maximum velocity vm at the center of the flow, the kinetic energy is
Activity (Lesson: Pressure) TO CALCULATE THE PRESSURE (p), USE THE EQUATION p = F / A WHERE ―F‖ EQUALS THE FORCE APPLIED AND ―A‖ EQUALS THE AREA (which is L X W). BE SURE TO WRITE THE EQUATION AND ALL UNITS. 1. Calculate the pressure on a man‘s foot when a woman who weighs 130 lb steps on his foot with her heel which has an area of 0.5 in2 with all her weight. 2. Calculate the pressure exerted on the floor when an elephant who weighs 6000 lb stands on one foot which has an area of 20 in2. 3. Calculate the pressure exerted on the heel of a boy‘s foot if the boy weighs 80 N and he lands on one heel which has an area of 16 cm2. 4. How much must a woman weigh (force) if the pressure she exerts while standing on one foot which has an area of 30 in2 exerts a pressure of 4 lb/ in2 ?
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5. What is the area of a car tire that touches the road if the car‘s weight on that tire is 768 lb and the pressure exerted on the road is 12 lb / in2 ?
Module (Lesson: Density) The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density isρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:
Where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
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Densities of Common Elements and Compounds Substance
Density grams per mL
Pine wood
0.35 -0.50
The formal definition of density is mass per unit volume. Usually the density is expressed in grams per mL or cc. Mathematically a "per" statement is translated as a division. cc is a cubic centimeter and is equal to a mL Therefore, Density= mass = g/mL volume
Mass vs. Weight: Although the terms mass and weight are used almost interchangeably, there is a difference between them. Mass is a measure of the quantity of matter, which is constant all over the universe. Weight is proportional to mass but depends on location in the universe. Weight is the force exerted on a body by gravitational attraction (usually by the earth). Example: The mass of a man is constant. However the man may weigh: 150 lbs on earth, 25 lbs on the moon (because the force of gravity on the moon is 1/6 that of the earth), and be "weightless" in space.
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Water
1.00
Salt, NaCl
2.16
Aluminum, Al
2.70
Iron, Fe
7.80
Gold, Au
19.30
Mercury, Hg
13.5
In order to determine the density of an object, it is necessary to know: the mass, the volume of the substance, and the definition of density. Density = mass (g) volume (mL) Solution: Apply the definition: Example:Calculate the density in g/mL of aluminum if a 50 mL block weighs135 g.
Density =
135 g =
2.70 g/mL
50 mL If the density of a substance and either mass or volume is known, volume or mass, respectively, can be calculated using either simple algebra or dimensional analysis. The density must be translated as a conversion factor. Solution: The density translated as a conversion factor is: Example:Calculate the mass in a 200 cc block of Titanium with a density of 4.51 g. per cc.
4.51 g = 1 cc - "per" is equivalent to an equal sign. 200 cc x 4.51 g = 902 g 1 cc Density (gm/cm^3)
Material Liquids Water at 4 C
1.0000
Water at 20 C
0.998
Gasoline
0.70
Mercury
13.6
Milk
1.03
Material Young Ji International School / College
Density (gm/cm^3) Page 95
Solids Magnesium
1.7
Aluminum
2.7
Copper
8.3-9.0
Gold
19.3
Iron
7.8
Lead
11.3
Platinum
21.4
Uranium
18.7
Osmium
22.5
Ice at 0 C
0.92 Density (gm/cm^3)
Material Gases at STP Air
0.001293
Carbon dioxide
.001977
Carbon monoxide
0.00125
Hydrogen
0.00009
Helium
0.000178
Nitrogen
0.001251 Density Worksheet
In the SI system, volume can be expressed in two ways, one is in liters and the other as a unit of distance ―cubed‖ such as cm3. When using distance the ―cube‖ is because you must multiply a distance times a distance times a distance. It is very important that all three distances are in the same unit such as cm or m or mm. For a cube the formula is length X width X height. Once you have the volume and the mass, it is easy to calculate the density of an object, that is, the amount of stuff in a certain space. To find the density, the formula is mass/volume. Work the following problems for practice; you‘ll need it on an upcoming lab and chapter test. 1. What is the volume of a box measuring 1mX5mX6m? (Remember units) 2. What is the volume of a box measuring 2cmX7cmX3cm? 3. What is the volume of a cube measuring 5cm on each side? 4. What is the volume of a cube measuring 1cm on each side? 5. What is the volume of a box measuring 3cmX6cmX4cm? 6. What is the volume of a box measuring 8mmX10cmX5cm? (Be careful – units!)
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I cm3 is equal to 1mL or another way to put it is 1L = 1,000cm3. Convert your answers as required. 7. What is the volume in ml of a box measuring 2cmX3cmX4cm? 8. What is the volume in ml of a cube measuring 5cm on each side? 9. What is the volume in L of a box measuring 5cmX20cmX5cm? 10. What is the volume in L of a cube measuring 10cm on each side? 11. What is the volume in L of a cube measuring 1m on each side? For the next problems you’ll need to figure density. Remember that density is mass/volume. 12. An iron cube measures 10cmX10cmX10cm. What is its volume? 13. If the same iron cube weighs 7.9kg, what is its density in g/cm3? 14. What is the density of a cube of water measuring 2cmX4cmX1cm, with a mass of 8g? 15. What is the density of a block of wood measuring .9cmX2cmX6cm with a mass of 5.4g 16. What has the greater density, a cube of water measuring 1cmX1cmX1cm and having a mass of 1g, or a block of plastic measuring 2cmX3cmX1cm with a mass of 4g? Water has a density of approximately 1g/cm3. In fact icm3 of water used to be the standard for a gram. Objects will sink if their density is greater that water and will float if their density is less. For the following problems, decide if the block will sink or float. 17. A cube measuring 2cm on each side weights 5g, will it sink or float? 18. A block has a mass of 20g and measures 2cmX4cmX2cm, will it sink or float? 19. A hollow iron cube has measures 5cm on each side and has a mass of 20g. Will the iron cube sink or float? 20. A cube made of very old hard wood, has a mass of 45g and measures 6cm aside, will it sink or float? Module (Lesson: Fluid Pressure and Gravity) Pressure (symbol: p or P) is the ratio of force to the area over which that force is distributed. Pressure is force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure (also spelled gage pressure)[a] is the pressure relative to the local atmospheric or ambient pressure. Pressure is measured in any unit of force divided by any unit of area. The SI unit of pressure is the newton per square metre, which is called the pascal (Pa) after the seventeenth-century philosopher and scientist Blaise Pascal. Thelbf/square inch (PSI) is the traditional unit of pressure in US/UK customary units. A pressure of 1 Pa approximately equals the pressure exerted by a dollar bill resting flat on a table. Everyday pressures are often stated in kilopascals (1 kPa = 1000 Pa) - 1 kPa is approximately one-seventh of a lbf/in2. The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity. The pressure in a static fluid arises from the weight of the fluid and is given by the expression
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ρ = m/V = fluid density Pstatic fluid = ρgh where g = acceleration of gravity h = depth of fluid The pressure from the weight of a column of liquid of area A and height h is
The most remarkable thing about this expression is what it does not include. The fluid pressure at a given depth does not depend upon the total mass or total volume of the liquid. The above pressure expression is easy to see for the straight, unobstructed column, but not obvious for the cases of different geometry which are shown. Because of the ease of visualizing a column height of a known liquid, it has become common practice to state all kinds of pressures in column height units, like mmHg or cm H2O, etc. Pressures are often measured by manometers in terms of a liquid column height.
Fluid column height in the relationship
is often used for the measurement of pressure. After entering the relevant data, any one of the highlighted quantities below can be calculated by clicking on it. Pressure difference = density x g x height Top of Form If the fluid density is ρ= gm/cm3 = and the column height is
kg/m3
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h=
m=
x 10^
m
h= ft then the pressure difference is ΔP =
kPa
ΔP =
lb/in2
ΔP =
mmHg=
ΔP =
atmos
ΔP =
inches water=
inches Hg
cm water
Bottom of Form
Note that this static fluid pressure is dependent on density and depth only; it is independent
Pressure units
V
Technical
Standard
atmosphere
atmosphere
(bar)
(at)
(atm)
(Torr)
(psi)
≡ 1 N/m2
10−5
1.0197×10−5
9.8692×10−6
7.5006×10−3
1.450377×10−4
105
≡ 106 dyn/cm2
1.0197
0.98692
750.06
14.50377
0.980665×105
0.980665
≡ 1 kp/cm2
0.9678411
735.5592
14.22334
1.01325×105
1.01325
1.0332
≡ p0
≡ 760
14.69595
133.3224
1.333224×10−3
1.359551×10−3
1.315789×10−3
≈ 1 mmHg
1.933678×10−2
6.8948×103
6.8948×10−2
7.03069×10−2
6.8046×10−2
51.71493
≡ 1 lbF/in2
Pascal
Bar
(Pa)
T
Torr
Pounds per square inch
E
1 Pa 1 bar 1 at 1 atm 1 Torr 1 psi
of total mass, weight, volume, etc. of the fluid.
Worksheet: Fluid Pressure and Gravity
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1. What is atmospheric pressure in pascals?
In psi?
2. What causes the air pressure? 3. How much force is exerted on the upward facing side of a normal piece of typing paper lying on a table? (This is probably most easily down with psi.) 4. Why can‘t an astronaut on a space walk simply wear a scuba mask to give him air? Why must he have that bulky suit? 5. What is the gauge pressure 1 meter deep in Lake Olathe? 6. What is the absolute pressure 1 meter deep in Lake Olathe? 7. What is the gauge pressure 10 meters deep in Lake Olathe? 8. What is the absolute pressure 10 meters deep in Lake Olathe? Note: The pressure caused by a fluid can be calculated by the equation P = ρgh, but sometimes all we want is the change in pressure between two points in a fluid. This can be calculated by the equation ΔP = ρgΔh. Remember that the absolute pressure in a fluid can be found by adding the atmospheric pressure above the fluid to the pressure caused by the fluid. 9. Mr. Holloway is deep-sea diving in Lake Olathe (recognize the irony?). a. How much deeper would he have to dive to change the pressure on him by 100,000 Pa? b. He dive until the gauge pressure is 300,000 Pa. How deep is he? c.What is the absolute pressure on him in part b? 10. Cities (like Stilwell) build water towers to provide water pressure to homes like yours and mine. Imagine a typical water tower with a height of 50 meters for this problem. A single pipe carries water from the tower straight down to ground level and then out to homes in the area. a. What is the pressure difference in the water pipe from the top of the tower to ground level? b. What is the pressure difference in the water pipe from the top of the tower to a home that is on a hill and is only 20 meters below the top of the tower? Note: This demonstrates how the difference in height between the top of your local water tower and your house determines the amount of water pressure you will have. You‘ll also get more water pressure in the basement then you will upstairs. Some homes have pumps that help supply a greater water pressure.
Module (Lesson: Archimedes’ Principle) Archimedes’ principle, physical law of buoyancy, discovered by the ancient Greek mathematician and inventor Archimedes, stating that anybody completely or partially Young Ji International School / College
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submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface for an object partially submerged in a liquid. The weight of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. The buoyant force on a body floating in a liquid or gas is also equivalent in magnitude to the weight of the floating object and is opposite in direction; the object neither rises nor sinks. For example, a ship that is launched sinks into the ocean until the weight of the water it displaces is just equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo. If the weight of an object is less than that of the displaced fluid, the object rises, as in the case of a block of wood that is released beneath the surface of water or a helium-filled balloon that is let loose in air. An object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced. In fact, in some accurate weighing, a correction must be made in order to compensate for the buoyancy effect of the surrounding air. The buoyant force, which always opposes gravity, is nevertheless caused by gravity. Fluid pressure increases with depth because of the (gravitational) weight of the fluid above. This increasing pressure applies a force on a submerged object that increases with depth. The result is buoyancy. Cube immersed in a fluid, with its sides parallel to the direction of gravity. The fluid will exert a normal force on each face, and therefore only the forces on the top and bottom faces will contribute to buoyancy. The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth). Multiplying the pressure difference by the area of a face gives the net force on the cube - the buoyancy, or the weight of the fluid displaced. By extending this reasoning to irregular shapes, we can see that, whatever the shape of the submerged body, the buoyant force is equal to the weight of the fluid displaced. The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational constant, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.
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Suppose a rock's weight is measured as 10 Newtons when suspended by a string in a vacuum with gravity acting on it. Suppose that when the rock is lowered into water, it displaces water of weight 3 Newtons. The force it then exerts on the string from which it hangs would be 10 Newtons minus the 3 Newtons of buoyant force: 10 − 3 = 7 Newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water. For a fully submerged object, Archimedes' principle can be reformulated as follows,
then inserted into the quotient of weights, which has been expanded by the mutual volume
yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes:
(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.) Example: If you drop wood into water, buoyancy will keep it afloat. Example: A helium balloon in a moving car. When increasing speed or driving in a curve, the air moves in the opposite direction to the car's acceleration. However, due to buoyancy, the balloon is pushed "out of the way" by the air, and will actually drift in the same direction as the car's acceleration. When an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force that is proportional to the weight of the displaced liquid. The sum force acting on the object, then, is proportional to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force), hence equilibrium buoyancy is achieved when these two weights (and thus forces) are equal consider a ball immersed in a liquid. The liquid experiences an up thrust which is the buoyant force.in otherwise is proportional to the weight of the liquid displaced. The total force acting on the object at that b point in time is proportional to the difference between the weight exacted by the object and the weight of the displaced liquid hence equilibrium is attend. the apparent weight of the object = The original weight – the buoyant force exerted.
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For example: If we have a rock which is hanging on a thread in a pool and initially a force of 20 Newton is exerted by it. Now the force of buoyancy exerted back by water is 3 Newton. Then the Net force exerted by the rock is 20 – 3 = 17 Newton. It is noteworthy that it is quite easy to pull an object through water than to actually lift it from the bottom of a water pool. The hot air balloon rises in the air as the density of the warmer air inside the balloon is less than the cooler air outside the balloon. There is a buoyant force acting on the system and so the balloon as well as the basket displaces a fluid that is heavier than both of them. This is the reason balloons tend to fly better in the morning as the surrounding air is cool. This rule is very useful in determining the density and volume of an irregular object. It is done by measuring its mass in the air and also when it is submerged in water.
Worksheet: Archimedes’ Principle In the following diagram, W = weight, m = mass, V = volume, FB = buoyant force, ρ = density.
Floating
DisplacedW ater
Object
Sinking
Water Displaced
Object
WH20 disp FB
WH2Odisp FB Wo
FB
Wo
FB
Vo VH2Odisp
Vo VH2Odisp
Wo WH2Odisp
Wo WH2Odisp
mo mH2Odisp
mo mH2Odisp
ρo ρH2O
ρo ρH2O
1. For a floating object, how does the buoyant force compare to the weight of the object? Why must this be true? Young Ji International School / College
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2. For a floating object, how does the buoyant force compare to the weight of water displaced? Is this always true? 3. For a sinking object, how does the buoyant force compare to the weight of the object? Why must this be true? 4. For a sinking object, how does the buoyant force compare to the weight of water displaced? Is this always true? Sez who? 5. A floating object has a specific gravity of 0.8. How much of it will be below the surface of the water? 6. An object weighs 200 Newtons. When placed in a full bucket of water, 50 Newtons of water spill out over the edge. What is the buoyant force on the object and how much does it seem to weigh when in the water? 7. A 40 Newton log is floating in a Lake. 75 % of the log is below the surface. a. What is the buoyant force on the log? b. What is the weight of water displaced by the log? c. What is the mass of water displaced by the log? d. What is the volume of water displaced by the log? e. What is the specific gravity of the log? 8. A 100-Newton rock only seems to weigh 80 Newtons while under water. a. What is the buoyant force on the rock? b. What is the weight of water displaced by the rock? c. What is the volume of water displaced by the rock? (Hint: first find the mass of the water) d. What is the density of the rock? 9. A particular ship (floating) has a total mass of 3.0 x 106 kg. a. What is the buoyant force on the ship? b. What is the mass of water displaced by the ship? c. What is the volume of water displaced by the ship? d. Does the ship have a volume greater than, equal to or less than the volume of the water it displaces?
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Module (Lesson: First Law of Thermodynamics) First Law of Thermodynamics The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:
The first law makes use of the key concepts of internal energy, heat, andsystem work. It is used extensively in the discussion of heat engines. The standard unit for all these quantities would be the joule, although they are sometimes expressed in calories or BTU. It is typical for chemistry texts to write the first law as ΔU=Q+W. It is the same law, of course - the thermodynamic expression of the conservation of energy principle. It is just that W is defined as the work done on the system instead of work done by the system. In the context of physics, the common scenario is one of adding heat to a volume of gas and using the expansion of that gas to do work, as in the pushing down of a piston in an internal combustion engine. In the context of chemical reactions and process, it may be more common to deal with situations where work is done on the system rather than by it. Enthalpy Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. Enthalpy is defined by H = U + PV where P and V are the pressure and volume, and U is internal energy. Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables. It is somewhat parallel to the first law of thermodynamics for a constant pressure system Q = ΔU + PΔV since in this case Q=ΔH
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It is a useful quantity for tracking chemical reactions. If as a result of an exothermic reaction some energy is released to a system, it has to show up in some measurable form in terms of the state variables. An increase in the enthalpy H = U + PV might be associated with an increase in internal energy which could be measured by calorimetry, or with work done by the system, or a combination of the two. The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But if the process changes the volume, as in a chemical reaction which produces a gaseous product, then work must be done to produce the change in volume. For a constant pressure process the work you must do to produce a volume change ΔV is PΔV. Then the term PV can be interpreted as the work you must do to "create room" for the system if you presume it started at zero volume.
System Work When work is done by a thermodynamic system, it is ususlly a gas that is doing the work. The work done by a gas at constant pressure is:
Example
For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is:
Work done by a system decreases the internal energy of the system, as indicated in the First Law of Thermodynamics. System work is a major focus in the discussion of heat engines. Activity Module (Lesson: First Law of Thermodynamics) 1. Is it possible for a system to lose energy even when heat is flowing into it? If not, why not? If so, explain how such a thing is possible.
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2. As a hot air balloon cools down it is compressed by the air around it. For this process, identify the sign of the heat, the change in internal energy and the work.
3. As a popcorn kernel is warmed, the water inside the kernel vaporizes and then expands and does work For this process, identify the sign of the heat, the change in internal energy and the work.
4. In an automobile engine, after unburned gas is injected into the cylinder, the piston compresses the gas and raises its temperature. In the process, the walls of the cylinder get warmer as well. For this process, identify the sign of the heat, the change in internal energy and the work.
5. When you pump a bicycle pump quickly, the compression is almost adiabatic because there isn‘t much time for the gas to exchange energy with anything. During a single pump, you do 36 J of work on 4.26 x 10-4 kg of air inside the cylinder. a) How much does the internal energy of the air inside the pump change during a single pump?
b) Remember that internal energy simply depends on the specific heat at constant volume. How hot will the air in the pump get after a single pump if it starts at room temperature?
6. On a sunny day, a 5 m3 tank full of 20 kg of helium heats up from 15 °C to 35 °C. How much heat happens to the helium in the tank? [cv = 3115.8 J/(kg K) for helium]
7. A platter of birdseed is mounted on top of a gas-filled piston. As the birdseed on top of the platter is eaten, the gas expands isothermally and does 4.17 J of work. How much heat occurs during this process?
8. A child takes a long, partially inflated, cylindrical balloon, 4 cm in diameter and 50 cm long, into the bathtub with them. As the balloon floats on the surface, the air in the balloon receives 34.9 J of energy in the form of heat and expands isobarically until it is 58 cm long (and still the same width). How much does the internal energy of the balloon increase? [Hint: what determines the pressure of the air inside the balloon?]
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9. When you place a room temperature (20 °C) soda bottle in the fridge, the 0.0022 kg of carbon dioxide gas in the bottle cools isometrically by losing 23.5 J of energy as heat. a) How much does the internal energy of the carbon dioxide gas change?
b) If the specific heat at constant volume is cV = 658 J/(kg K) for carbon dioxide, at what temperature does the gas end up?
10. When you release 0.05 kg of air [cv = 785.7 J/(kg K)] from a compressed air tank, the high pressure air expands adiabatically as it pushes outward on the low pressure air around it. In the process, the temperature drops from 20 °C to 5 °C
a) How much does the internal energy of the air change as it cools down?
b) How much work does the compressed air do during the process? Module (Lesson: Heat Transfer)
Heat Transfer The transfer of heat is normally from a high temperature object to a lower temperature object. Heat transfer changes the internal energy of both systems involved according to the First Law of Thermodynamics.
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Heat Conduction Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is:
Calculation
= heat transferred in time = = thermal conductivity of the barrier = area = temperature = thickness of barrier
Heat Convection Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises (see Ideal Gas Law). Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.
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Convection can also lead to circulation in a liquid, as in the heating of a pot of water over a flame. Heated water expands and becomes more buoyant. Cooler, more dense water near the surface descends and patterns of circulation can be formed, though they will not be as regular as suggested in the drawing.
Convection cells are visible in the heated cooking oil in the pot at left. Heating the oil produces changes in the index of refraction of the oil, making the cell boundaries visible. Circulation patterns form, and presumably the wall-like structures visible are the boundaries between the circulation patterns.
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Convection is thought to play a major role in transporting energy from the center of the Sun to the surface, and in movements of the hot magma beneath the surface of the earth. The visible surface of the Sun (the photosphere) has a granular appearance with a typical dimension of a granule being 1000 kilometers. The image at right is from the NASA Solar Physics website and is credited to G. Scharmer and the Swedish Vacuum Solar Telescope. The granules are described as convection cellswhich transport heat from the interior of the Sun to the surface.
In ordinary heat transfer on the Earth, it is difficult to quantify the effects of convection since it inherently depends upon small nonuniformities in an otherwise fairly homogeneous medium. In modeling things like the cooling of the human body, we usually just lump it in with conduction. How is heat transferred? Heat can travel from one place to another in three ways: Conduction, Convection and Radiation. Both conduction and convection require matter to transfer heat. If there is a temperature difference between two systems heat will always find a way to transfer from the higher to lower system. CONDUCTION-Conduction is the transfer of heat between substances that are in direct contact with each other. The better the conductor, the more rapidly heat will be transferred. Metal is a good conduction of heat. Conduction occurs when a substance is heated, particles will gain more energy, and vibrate more. These molecules then bump into nearby particles and transfer some of their energy to them. This then continues and passes the energy from the hot end down to the colder end of the substance. CONVECTION-Thermal energy is transferred from hot places to cold places by convection. Convection occurs when warmer areas of a liquid or gas rise to cooler areas in the liquid or gas. Cooler liquid or gas then takes the place of the warmer areas which have risen higher. This results in a continous circulation pattern. Water boiling in a pan is a good example of these convection currents. Another good example of convection is in the atmosphere. The earth's surface is warmed by the sun, the warm air rises and cool air moves in. Young Ji International School / College
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RADIATION-Radiation is a method of heat transfer that does not rely upon any contact between the heat source and the heated object as is the case with conduction and convection. Heat can be transmitted though empty space by thermal radiation often called infrared radiation. This is a type electromagnetic radiation . No mass is exchanged and no medium is required in the process of radiation. Examples of radiation is the heat from the sun, or heat released from the filament of a light bulb. Heat Transfer Worksheet Fill in the blanks using the correct form of heat transfer 1. The transfer of heat through material by direct contact is 2.
_________.
_________________is the transfer of heat in a fluid (gas or liquid) as a result of the movement of the fluid itself.
3. What kind of heat transfer does the sun use? (hint: it transfers heat via electromagnetic waves through space). Identify the method of heat transfer that takes place in each illustration. Some illustrations may show more than one form of heat transfer.
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Module (Lesson: Specific Heat) Specific Heat The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. The relationship between heat and temperature change is usually expressed in the form shown below where c is the specific heat. The relationship does not apply if a phase change is encountered, because the heat added or removed during a phase change does not change the temperature.
The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C which is higher than any other common substance. As a result, water plays a very important role in temperature regulation. The specific heat per gram for water is much higher than that for a metal, as described in the water-metal example. For most purposes, it is more meaningful to compare the molar specific heats of substances. This worked example problem demonstrates how to calculate the specific heat of a substance when given the amount of energy used to change the substance's temperature. Problem: It takes 487.5 J to heat 25 grams of copper from 25 °C to 75 °C. What is the specific heat in Joules/g·°C? Solution: Use the formula: Q = mcΔT where Q = heat energy m = mass c = specific heat ΔT = change in temperature 487.5 J = (25 g) c(75 °C - 25 °C) 487.5 J = (25 g)c(50 °C)
Solve for c: c = 487.5 J/(25g)(50 °C) Young Ji International School / College
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c = 0.39 J/g·°C Answer: The specific heat of copper is 0.39 J/g·°C.
Specific Heat and Heat Capacity Worksheet
1
The temperature of 335 g of water changed from 24.5oC to 26.4oC. How much heat did this sample absorb? c for water = 4.18 J/goC
2.
How much heat in kilojoules has to be removed from 225g of water to lower its temperature from 25.0oC to 10.0oC?
3.
To bring 1.0kg of water from 25oC to 99oC takes how much heat input?
4.
An insulated cup contains 75.0g of water at 24.00oC. A 26.00g sample of metal at 82.25oC is added. The final temperature of the water and metal is 28.34oC. What is the specific heat of the metal?
5.
A calorimeter has a heat capacity of 1265 J/oC. A reaction causes the temperature of the calorimeter to change from 22.34oC to 25.12oC. How many joules of heat were released in this process?
6.
What is the specific heat of silicon if it takes 192J to raise the temperature of 45.0g of Si by 6.0oC?
7.
Aqueous silver ion reacts with aqueous chloride ion to yield a white precipitate of solid silver chloride. When 10.0 mL of 1.00M AgNO3 solution is added to 10.0mL of 1.00 M NaCl solution at 25oC in a calorimeter a white precipitate of AgCl forms and the temperature of the aqueous mixture increases to 32.6oC. Assuming that the specific heat of the aqueous mixture is 4.18 J/goC, that the density of the mixture is 1.00 g/mL, and that the calorimeter itself absorbs a negligible amount of heat, calculate the amount of heat absorbed in kJ/mol of Ag+.
8.
Assuming that Coca Cola has the same specific heat as water ( 4.18 J/goC), calculate the amount of heat in kJ transferred when one can ( about 350g) is cooled from 25oC to 3oC .
9.
What is the specific heat of lead if it takes 96J to raise the temperature of a 75g block by 10oC?
10.
When 25 mL of 1.0M H2SO4 is added to 50 mL of 1.0 M NaOH at 25oC in a calorimeter, the temperature of the aqueous solution increases to 33.9 oC. Assuming that the specific heat of the solution is 4.18 J/gC, that its density is 1.00 /mL, and
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that the calorimeter itself absorbs a negligible amount of heat, calculate the amount of heat absorbed for the reaction. Module (Lesson: Phase Transition) A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another one by heat transfer. The term is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium certain properties of the medium change, often discontinuously, as a result of the change of some external condition, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions are common in nature and used today in many technologies.
Humidity is the amount of water vapor in the air. Water vapor is the gaseous state of water and is invisible. Relative Humidity is the humidity expressed as a percentage of the saturation density.
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Calculation of Relative Humidity Relative humidity is the ratio of the amount of moisture actually in the air to the maximum amount of moisture that the air could hold at a given temperature. Temperature determines how much moisture the air can hold. Warm air can hold a lot of moisture. Cold air can hold very little. The maximum amount is also called the saturation value or saturation humidity. The actual amount is called the absolute humidity. These values are measured in grams per cubic meter (g/m3).
o
F 23 32 41 50 59 68 77 86 95 104
o
C ‐5 0 5 10 15 20 25 30 35 40
SATURATION VALUES Temp H2O Vapor – Max Humidity (g/m3) 3.3 4.8 6.8 9.4 12.8 17.3 23.0 30.4 39.6 51.1
If air at 25oC (77oF) contains 15 gm at H2O vapor per cubic meter, then Absolute Humidity = 15 gm Relative Humidity = Absolute Humidity = 15 = 65% Saturation Value 23
Relative Humidity Worksheet Solve the Problems. 1. On a winter day, the temperature is -15 oC, and the humidity is 0.001 kg/m3. a. What is the relative humidity?
b. When this air is brought inside a building, it is heated to 20 oC. If the humidity isn‘t change, what is the relative humidity inside the building?
2. The temperature of the air in thermals decreases about 10 oC for each 1000m they rise. If a thermal leaves the groung with a temperature of 30 oC and a relative humidity of 31 %, at what altitude will the air become saturated and the water vapor
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begin to condense to form a cloud? ( In other words, at what altitude does the temperature equal the dew point?)
3. Inside a building, the temperature is 20 oC, and the relative humidity is 40%. How much water vapor is in each cubic meter of air?
Module (Lesson: Second Law of Thermodynamics)
Second Law of Thermodynamics The second law of thermodynamics is a general principle which places constraints upon the direction of heat transfer and the attainable efficiencies of heat engines. In so doing, it goes beyond the limitations imposed by the first law of thermodynamics. It's implications may be visualized in terms of the waterfall analogy.
The maximum efficiency which can be achieved is the Carnot efficiency. Second Law: Heat Engines Second Law of Thermodynamics: It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir. This precludes a perfect heat engine.
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This is sometimes called the "first form" of the second law, and is referred to as the KelvinPlanck statement of the second law.
Second Law: Refrigerator Second Law of Thermodynamics: It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object. This precludes a perfect refrigerator. The statements about refrigerators apply to air conditioners and heat pumps, which embody the same principles. This is the "second form" or Clausius statement of the second law.
Second Law: Entropy Second Law of Thermodynamics: In any cyclic process the entropy will either increase or remain the same.
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Entropy:
a state variable whose change is defined for a reversible process at T where Q is the heat absorbed.
Entropy:
a measure of the amount of energy which is unavailable to do work.
Entropy: a measure of the disorder of a system. Entropy: a measure of the multiplicity of a system.
Since entropy gives information about the evolution of an isolated system with time, it is said to give us the direction of "time's arrow" . If snapshots of a system at two different times shows one state which is more disordered, then it could be implied that this state came later in time. For an isolated system, the natural course of events takes the system to a more disordered (higher entropy) state.
Second Law of Thermodynamics Worksheet
Problems Multiple Choice: 1. To increase the diameter of an aluminum ring from 50.0 mm to 50.1 mm, the temperature of the ring must increase by 80°C. What temperature change would be necessary to increase the diameter of an aluminum ring from 100.0 mm to 100.1 mm? a. 20°C b. 40°C c. 80°C d. 110°C e. 160°C 2. A gas is enclosed in a metal container with a moveable piston on top. Heat is added to the gas by placing a candle flame in contact with the container's bottom. Which of the following is true about the temperature of the gas? a. The temperature must go up if the piston remains stationary. b. The temperature must go up if the piston is pulled out dramatically. c. The temperature must go up no matter what happens to the piston. d. The temperature must go down no matter what happens to the piston. e. The temperature must go down if the piston is compressed dramatically. Young Ji International School / College
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3. A small heat engine operates using a pan of 100°C boiling water as the high temperature reservoir and the atmosphere as a low temperature reservoir. Assuming ideal behavior, how much more efficient is the engine on a cold, 0°C day than on a warm, 20°C day? a. 1.2 times as efficient b. 2 times as efficient c. 20 times as efficient d. infinitely more efficient e. just as efficient 4. A 1-m3 container contains 10 moles of ideal gas at room temperature. At what fraction of atmospheric pressure is the gas inside the container? a. 1/40 atm b. 1/20 atm c. 1/10 atm d. 1/4 atm e. 1/2 atm Module (Lesson: Wave- Types and Properties) A wave is disturbance or oscillation that travels through matter or space, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations. Waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this equation varies depending on the type of wave. There are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed. The deformation reverses itself owing to restoring forces resulting from its deformation. For example, sound waves propagate via air molecules colliding with their neighbors. When air molecules collide, they also bounce away from each other (a restoring force). This keeps the molecules from continuing to travel in the direction of the wave. The second main type of wave, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles, and can therefore travel through a vacuum. These types of waves vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.
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Further, the behavior of particles in quantum mechanics are described by waves. In addition, gravitational waves also travel through space, which are a result of a vibration or movement in gravitational fields. A wave can be transverse or longitudinal depending on the direction of its oscillation. Transverse waves occur when a disturbance creates oscillations perpendicular (at right angles) to the propagation (the direction of energy transfer). Longitudinal waves occur when the oscillations are parallel to the direction of propagation. While mechanical waves can be both transverse and longitudinal, all electromagnetic waves are transverse. Transverse Waves For transverse waves the displacement of the medium is perpendicular to the direction of propagation of the wave. A ripple on a pond and a wave on a string are easily visualized transverse waves.
Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.
Longitudinal Waves In longitudinal waves the displacement of the medium is parallel to the propagation of the wave. A wave in a "slinky" is a good visualization. Sound waves in air are longitudinal waves.
Sound Waves in Air Young Ji International School / College
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A single-frequency sound wave traveling through air will cause a sinusoidal pressure variation in the air. The air motion which accompanies the passage of the sound wave will be back and forth in the direction of the propagation of the sound, a characteristic of longitudinal waves.
Physics professor Clint Sprott of the University of Wisconsin shows one way to visualize these longitudinal pressure waves in his "Wonders of Physics" demonstration show. A loudspeaker is driven by a tone generator to produce single frequency sounds in a pipe which is filled with natural gas (methane). A series of holes is drilled in the pipe to release a small amount of gas. Igniting the gas produces flames for which the height increases with the pressure in the pipe. The pattern of the flames shows the pressure variation and can be used to roughly measure the wavelength of the pressure wave in the pipe.
Low frequency
High frequency
Shown below is more detail on the attachment of the loudspeaker to the pipe. The loudspeaker is driven by the amplified output of a tunable oscillator.
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A series of small holes were drilled at regular intervals in the pipe. They appeared to be about 8 mm apart.
A Wave Transports Energy and not Matter When a wave is present in a medium (that is, when there is a disturbance moving through a medium), the individual particles of the medium are only temporarily displaced from their rest position. There is always a force acting upon the particles that restores them to their original position. In a slinky wave, each coil of the slinky ultimately returns to its original position. It is for this reason, that a wave is said to involve the movement of a disturbance without the movement of matter. Waves are said to transport energy. As a disturbance moves through a medium from one particle to its adjacent particle, energy is being transported from one end of the medium to the other. In a slinky wave, a person imparts energy to the first coil by doing work upon it. The first coil receives a large amount of energy that it subsequently transfers to the second coil. When the first coil returns to its original position, it possesses the same amount of energy as it had before it was displaced. The first coil transferred its energy to the second coil. The second coil then has a large amount of energy that it subsequently transfers to the third coil. When the second coil returns to its original position, it possesses the same amount of energy as it had before it was displaced. The third coil has received the energy of the second coil. This process of energy transfer continues as each coil interacts with its neighbor. In this manner, energy is transported from one end of the slinky to the other, from its source to another location. A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil up and down. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced upwards and downwards. In this case, the particles of the medium move perpendicular to the direction that the pulse moves.
A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Suppose that a slinky is stretched out in a Young Ji International School / College
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horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil left and right. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced leftwards and rightwards. In this case, the particles of the medium move parallel to the direction that the pulse moves.
Any wave moving through a medium has a source. Somewhere along the medium, there was an initial displacement of one of the particles. For a slinky wave, it is usually the first coil that becomes displaced by the hand of a person. So if you wish to create a transverse wave in a slinky, then the first coil of the slinky must be displaced in a direction perpendicular to the entire slinky. Similarly, if you wish to create a longitudinal wave in a slinky, then the first coil of the slinky must be displaced in a direction parallel to the entire slinky.
The Anatomy of a Wave Consider the transverse waveform below. If a snapshot of such a transverse wave could be taken so as to freeze the shape of the rope in time, then it would look like the following diagram.
The dashed line drawn through the center of the diagram represents the equilibrium or rest position of the slinky. This is the position that the string would assume if there were no disturbance moving through it. Once a disturbance is introduced into the slinky, the particles of the string begin to vibrate upwards and downwards. At any given moment in time, a particle on the medium could be above or below the rest position. Points A, E and H on the diagram represent the crests of this wave. The crest of a wave is the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position. Points C and J on the diagram represent the troughs of this wave. The trough of a wave is the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position. Young Ji International School / College
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The wave shown above can be described by a variety of properties. One such property is amplitude. The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from equilibrium to crest. The wavelength is another property of a wave that is portrayed in the diagram above. The wavelength (Îť) of a wave is simply the length of one complete wave cycle. If you were to trace your finger across the wave in the diagram above, you would notice that your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic and regular fashion over both time and space. And the length of one such spatial repetition (known as awave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In the diagram above, the wavelength is the horizontal distance from A to E, or the horizontal distance from B to F, or the horizontal distance from D to G, or the horizontal distance from E to H. If a snapshot of such a longitudinal wave could be taken so as to freeze the shape of the slinky in time, then it would look like the following diagram.
Because the coils of the slinky are vibrating longitudinally, there are regions where they become pressed together and other regions where they are spread apart. A region where the coils are pressed together in a small amount of space is known as a compression. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. Points A, C and E on the diagram above represent compressions and points B, D, and F represent rarefactions. While a transverse wave has an alternating pattern of crests and troughs, a longitudinal wave has an alternating pattern of compressions and rarefactions. For a transverse wave, the wavelength is determined by measuring from crest to crest. In the case of a longitudinal wave, a wavelength measurement is made by measuring the distance from a compression to the next compression or from a rarefaction to the next rarefaction. On the diagram above, the distance from point A to point C or from point B to point D would be representative of the wavelength. Frequency and Period of a Wave A single back-and-forth vibration of the first coil of a slinky introduces a pulse into the slinky. But the act of continually vibrating the first coil with a back-and-forth motion in periodic fashion introduces a wave into the slinky. Suppose that a hand holding the first coil of a slinky is moved back-and-forth two complete cycles in one second. The rate of the hand's motion would be 2 cycles/second. In turn, every coil of the slinky would vibrate at this rate of 2 cycles/second. This rate of 2 cycles/second is referred to as the frequency (f) of the wave. The unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. The quantity frequency is often confused with the quantity period. Period refers to the time that it takes to do something. The period (T) of a wave is the time for a particle on a Young Ji International School / College
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medium to make one complete vibrational cycle. Period, being a time, is measured in units of seconds. So, frequency is the number of cycles per second, and the period is the number of seconds per cycle. They are inverses of each other. f = 1/T T = 1/f The Velocity of a Wave The velocity of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a wave crest in a given interval of time. In equation form, v = d/t If the crest of a slinky wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2 m/s. Because wavelength (λ) and period (T) are units of distance and time, the above equation may be written as follows: v=λf By this, you can see the wavelength and frequency are inverses of each other. For a given velocity, if you increase the frequency, the wavelength will be shortened. The velocity of the wave is dependent on several factors, including the tension in the slinky (FT) and the linear mass density (μ) of the slinky, where μ is found by dividing the mass by the length.. This relationship is as follows: v = √(FT/μ) Standing Waves Standing wave patterns are wave patterns produced in a medium when two waves of identical frequencies (such as a slinky wave and its bounce-back reflection) interfere in such a manner to produce points along the medium that always appear to be standing still. These points that have the appearance of standing still are referred to as nodes. The points of maximum displacement are called antinodes. The simplest standing wave pattern that could be produced within a slinky is one that has nodes at the two ends of the slinky and one antinode in the middle. The animation below depicts the vibrational pattern observed when the medium is seen vibrating in this manner.
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The above pattern is called the first harmonic. Other wave patterns can be observed within the slinky when it is vibrated at greater frequencies. For instance, if you vibrate the end with twice the frequency as that associated with the first harmonic, then a second standing wave pattern can be achieved. This standing wave pattern is characterized by nodes on the two ends of the slinky and an additional node in the exact center of the slinky. As in all standing wave patterns, every node is separated by an antinode. This pattern with three nodes and two antinodes is referred to as the second harmonic and is depicted in the animation shown below.
If the slinky frequency is increased even more, then the third harmonic wave pattern can be produced within the slinky. The standing wave pattern for the third harmonic has an additional node and antinode between the ends of theslinky. The pattern is depicted in the animation shown below.
Observe that each consecutive harmonic is characterized by having one additional node and antinode compared to the previous one. The table below summarizes the features of the standing wave patterns for the first several harmonics.
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Harmonic
# of Nodes
# of Antinodes
1st
2
1
2nd
3
2
3rd
4
3
4th
5
4
5th
6
5
6th
7
6
nth
n+1
n
Pattern
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WAVES AND THE VIBRATING STRING Worksheet OBJECTIVE: To study waves. TERMINOLOGY: wave
frequency (f)
wavelength (ď Ź)
interference
constructive
destructive
node
anti-node
linear mass density (ď )
THEORY: Waves are a common phenomena. We are all aware that when a rock is thrown into water, it creates a wave that travels out from the source (the splash). For water waves, the wave moves rather slowly so that it is easily seen. Most other waves move rather fast and so are hard to see.
In Parts 1 and 2 we will use just any old "pulse" as a wave on a slinky in this experiment (since the wave on a slinky moves relatively slowly) to see how the wave moves and then how it reflects (bounces).
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In part 3 we will use a vibrator to create a "nice" wave, a sine wave, on a string. We will not be able to see the wave itself move since it moves so fast, but we will be able to have it reflect back and forth and INTERFERE with itself so that it sets up what are called standing waves (for reasons that should become evident) that we can see.
The speed of a wave depends quite naturally on what the wave is moving in. For a wave along a stretched string the speed of the wave depends on the tension in the string and the string's linear mass density, i.e. its mass per length, and is given by the equation:
v F / (1)
where v is the speed of the wave, F is the tension in the string, and is the mass per unit length or linear mass density ( = m / L) of the string.
For "nice" waves (sine waves), the wave repeats itself in both space and time. The distance over which it repeats itself is called the wavelength (); the time over which it repeats itself is called the period (T). Instead of period, however, we often talk about the frequency (f) of a wave which is defined simply as 1/T. [Note: period has units of seconds/cycle, while frequency has units of cycles/second.] By definition, the speed of a wave (v) is the distance traveled divided by the time it takes to cover that distance:
v = /T = f
.
(2)
Note that the speed depends on the tension and the mass density of the string (Eq. (1)) and the speed relates the wavelength to the frequency (Eq. (2)). The tension and the mass density determine the speed, and the speed and frequency then determine the wavelength (or the speed and wavelength determine the frequency).
If one end of a string is held fixed and the other end is attached to a vibrator so its direction of vibration is at right angles to the direction of the string, wave disturbances will travel along the string with the speed v of Eq (1). At the fixed end the waves will be reflected back along the string. In general, the reflected waves will interfere with the incoming waves to produce a rather jumbled pattern on the string. But if the tension and the length are adjusted so that the number of half-wavelengths on the string is an integer, then the initial Young Ji International School / College
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and reflected waves will add together to set up a stationary wave pattern. NOTE: for standing waves, the theory predicts that the wavelength should be twice the distance between the nodes.
Part 1: Waves on a slinky
PROCEDURE: 1. Stretch the slinky to some distance and try to measure the speed of a pulse that you put on the slinky. Remember that speed is simply the distance traveled divided by the time it takes to go that distance. Try to estimate the speed of the pulse as best you can. 2. Stretch the slinky to some other distance and again try to measure the speed of the pulse that you put on the slinky. Did the speed change when you changed the conditions on the slinky? REPORT: Record your measurements and observations as described in the Procedure.
Part 2: Reflection of waves PROCEDURE: 1. Stretch the slinky to some distance and put a pulse on the slinky so that the pulse is up. Then watch to see if the pulse reflects (bounces) off of a fixed end (your partner?). If it does reflect, notice whether the pulse stays up or becomes inverted (pulse is down). 2. Now stand on something high (the desk?) and hold the slinky up so that the other end does NOT touch the ground (the end is free). Now put a pulse on the slinky (pulse is away from you). Notice whether there is a reflection in this case, and if so whether the pulse stays away from you or becomes inverted (points toward you) on reflection. REPORT: Record your observations as described in the Procedure.
Part 3: Interference and standing waves on a string
PROCEDURE: 1. Note that the frequency of the vibrator is 120 cycles/sec (also called Hertz). This is determined by the construction of the vibrator. Young Ji International School / College
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2. Measure the total length of the string with a meter stick, and weigh it on a balance. (The string should be at least 2 meters long.) Calculate the linear density (ď ). 3. Connect one end of the string to the vibrator and the other end to a weight hanger hung over a pulley. 4. Start the vibrator, and increase the tension (F) in the string by adding weights until there are six or seven loops in the string. When in proper adjustment the amplitude of vibration will be a maximum. The place where the maxima occur are called anti-nodes; the places where the string does not vibrate are called nodes. Record the tension, number of loops, and the length of the string from vibrator to pulley. 5. Repeat the above procedure, each time increasing the tension so as to reduce the number of loops, until at least three sets of measurements have been obtained. 6. Calculate the speed of the wave from Eq. (1) and then wavelength of the wave from Eq. (2) for each set. REPORT: 1. Record all of your data and show your calculations as described in the Procedure. 2. Compare your calculated wavelengths from step 6 above to the length of the string (from vibrator to pulley). The wavelengths should be such that an integer number of wavelengths equals twice the length. Is this true in all your cases? What could account for any slight discrepancies? Application: For a guitar, the speed of the wave on a guitar string is determined by the mass density of the string (notice on a guitar that the six strings have different diameters) and by the tension in the string (notice that to tune a guitar you must adjust the tension in the strings). When you play a certain note on a guitar string, you must press the guitar string at a certain position. This position then determines the length of the string, and hence the possible wavelengths that will sound (resonate). Then from Eq. (2), there will be only certain frequencies coming from the string, and these certain frequencies combine to form that certain note on the guitar.
Young Ji International School/College Module (Lesson: Wave- Types and Properties)
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Propagation of Waves The process of communication involves the transmission of information from one location to another. As we have seen, modulation is used to encode the information onto a carrier wave, and may involve analog or digital methods. It is only the characteristics of the carrier wave which determine how the signal will propagate over any significant distance. This chapter describes the different ways that electromagnetic waves propagate. Basics An electromagnetic wave is created by a local disturbance in the electric and magnetic fields. From its origin, the wave will propagate outwards in all directions. If the medium in which it is propagating (air for example) is the same everywhere, the wave will spread out uniformly in all directions.
Figure 1 Far from its origin, it will have spread out enough that it will appear have the same amplitude everywhere on the plane perpendicular to its direction of travel (in the near vicinity of the observer). This type of wave is called a plane wave. A plane wave is an idealization that allows one to think of the entire wave traveling in a single direction, instead of spreading out in all directions.
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Figure 2 Electromagnetic waves propagate at the speed of light in a vacuum. In other mediums, like air or glass, the speed of propagation is slower. If the speed of light in a vacuum is given the symbol c0, and the speed in some a medium is c, we can define the index of refraction, n as:
n = c0 / c Here's a short table of the indices of refraction for common media: substance index of refraction vacuum 1 air 1.0003 water 1.33 glass 1.55
Reflection When a plane wave encounters a change in medium, some or all of it may propagate into the new medium or be reflected from it. The part that enters the new medium is called the transmitted portion and the other the reflected portion. The part which is reflected has a very simple rule governing its behavior. Make the following construction:
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Figure 3 Angle of Incidence = the angle between the direction of propagation and a line perpendicular to the boundary, on the same side of the surface. Angle of Reflection = the angle between the direction of propagation of the reflected wave and a line perpendicular to the boundary, also on the same side of the surface. Then the rule for reflection is simply stated as:
The angle of reflection = The angle of incidence
Figure 4 If the incident medium has a lower index of refraction then the reflected wave has a 1800 phase shift upon reflection. Conversely, if the incident medium has a larger index of refraction the reflected wave has no phase shift.
Refraction When the wave enters the new medium, the speed of propagation will change. In order to match the incident and transmitted wave at the boundary, the transmitted wave will change its direction of propagation. For example, if the new medium has a higher index of refraction, which means the speed of propagation is lower, the wavelength will become shorter (frequency must stay the same because of the boundary conditions). For the transmitted wave to match the incident wave at the boundary, the direction of propagation of the transmitted wave must be closer to perpendicular. The relationship between the angles and indices of refraction is given by Snell's Law: Young Ji International School / College
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ni sinqI = nt sinqt When the direction of propagation changes, the wave is said to refract. It is most useful to know in which direction the wave will refract, not necessarily by how much.
Figure 5 The transmitted wave will bend more towards the perpendicular when entering a medium with higher index of refraction (slower speed of propagation). Example: Why a pool is deeper than it looks. When you look into a pool, the light from the bottom is refracted away from the perpendicular, because the index of refraction in air is less than in water. To the observer at the side of the pool, the light appears to come from a shallower depth. For the same reason, when you look at objects underwater through a mask, they will appear to be larger than they really are. The light from the object is spread outwards at the water-air interface of your mask. To you it will appear the object is closer or larger.
Interference All electromagnetic waves can be superimposed upon each other without limit. The electric and magnetic fields simply add at each point. If two waves with the same frequency are combined there will a be a constant interference pattern caused by their superposition. Interference can either be constructive, meaning the strength increases as result, or destructive where the strength is reduced. The amount of interference depends of the phase difference at a particular point. Young Ji International School / College
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It can be shown that constructive interference occurs for phase differences of 0-1200, and 240-3600. Thus destructive interference occurs from 120-2400. For two identical waves, no phase shift results in total constructive interference, where the strength is maximum and 1800 phase shift will create total destructive interference (no signal at all). Df = 2pDx/l Df = 2pDt/T The phase shift that causes the interference can occur either due to a difference in path length, Dx, or a difference in the arrival time, Dt. The amount of phase shift, Df, can be computed for these two cases by: Example: Omega is a radio navigation system that used the phase difference in the same signal from two fixed transmitters to determine a line-ofposition. The same phase difference corresponded to multiple lines of position separated by a distance equivalent to 3600 of phase shift. Since the frequency was 10.2 kHz, the wavelength corresponding to 3600 phase shift was 16 miles, which was the lane width on an Omega overprinted chart. Loran-C also has a phase-difference mode with a lane width of only 3000 m since it operates at 100 kHz.
Diffraction Recall that the idealized plane wave is actually infinite in extent. If this wave passes through an opening, called an aperture, it will diffract, or spread out, from the opening. The degree to which the cropped wave will spread out depends on the size of the aperture relative to the wavelength. In the extreme case where the aperture is very large compared to the wavelength, the wave will see no effect and will not diffract at all. At the other extreme, if the opening is very small, the wave will behave as if it were at its origin and spread out uniformly in all directions from the aperture. In between, there will be some degree of diffraction.
Figure 6 Young Ji International School / College
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First consider a circular aperture. If a wave with wavelength l encounters an opening with diameter D, the amount of diffraction as measured by the angle, q ,at which the new wave diverges from the opening, measured from edge to edge, will be approximated by ASPECT OF WAVE PROPAGATION Worksheet
1. Determine the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of 0.600 m. 2. What is the wavelength of a water wave that has a frequency of 2.50 Hz and a speed of 4.0 m/s? 3. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance with a wavelength of 1.25 m, what is the frequency of the wave? 4. The period of a sound wave from a piano is 1.18 x 10-3 s. If the speed of the wave in air is 3.4 x 102 m/s, what is its wavelength? 5. If an FM radio station transmits radio signals that have a wavelength of 3.2 m, and radio waves travel at the speed of light, where would you have to adjust your tuner in order to pick up its music? Check your formula sheet to find the speed of light, and note that FM waves are measured in MHz (106 Hz) 6. A given crest of a water wave requires 5.2 s to travel between two points on a fishing pier located 19 m apart. It is noted in a series of waves that 20 crests pass the first point in 17 s.
a) What is the speed of the waves? b) What is the wave frequency? c) What is the wavelength of the waves?
7. Five pulses are generated every 0.100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 8. You are creating waves in a rope by shaking your hand back and forth. Without changing the distance your hand moves, you begin to shake it faster and faster. What happens to each of the following aspects of the wave: a) amplitude. b) frequency. c) period. d) velocity. Young Ji International School / College
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Module (Lesson: Sound) Sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a medium such as air or water. In physiology and psychology, sound is the reception of such waves and their perception by the brain.
A drum produces sound via a vibrating membrane. Acoustics is the interdisciplinary science that deals with the study of mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound, and infrasound. A scientist who works in the field of acoustics is an acoustician, while someone working in the field of acoustical engineering may be called an acoustical engineer. An audio engineer, on the other hand is concerned with the recording, manipulation, mixing, and reproduction of sound. Applications of acoustics are found in almost all aspects of modern society, sub disciplines include aero acoustics, audio signal processing, architectural acoustics, bioacoustics, electro-acoustics, environmental noise, musical acoustics, noise control, psychoacoustics, speech, ultrasound, underwater acoustics, and vibration. Sound can propagate through compressible media such as air, water and solids as longitudinal waves and also as a transverse waves in solids (see Longitudinal and transverse waves, below). The sound waves are generated by a sound source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding Young Ji International School / College
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medium. As the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound, thus forming the sound wave. At a fixed distance from the source, the pressure, velocity, and displacement of the medium vary in time. At an instant in time, the pressure, velocity, and displacement vary in space. Note that the particles of the medium do not travel with the sound wave. This is intuitively obvious for a solid, and the same is true for liquids and gases (that is, the vibrations of particles in the gas or liquid transport the vibrations, while the average position of the particles over time does not change). During propagation, waves can be reflected, refracted, or attenuated by the medium. The behavior of sound propagation is generally affected by three things:  

A relationship between density and pressure. This relationship, affected by temperature, determines the speed of sound within the medium. The propagation is also affected by the motion of the medium itself. For example, sound moving through wind. Independent of the motion of sound through the medium, if the medium is moving, the sound is further transported. The viscosity of the medium also affects the motion of sound waves. It determines the rate at which sound is attenuated. For many media, such as air or water, attenuation due to viscosity is negligible.
When sound is moving through a medium that does not have constant physical properties, it may be refracted (either dispersed or focused).
Spherical compression (longitudinal) waves The mechanical vibrations that can be interpreted as sound are able to travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through a vacuum.
Longitudinal and transverse waves
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Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves. Through solids, however, it can be transmitted as both longitudinal waves and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves (in solids) are waves of alternating shear stress at right angle to the direction of propagation. Additionally, sound waves may be viewed simply by parabolic mirrors and objects that produce sound. The energy carried by an oscillating sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter, and the kinetic energy of the displacement velocity of particles of the medium.
Sound wave properties and characteristics
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time. Sound waves are often simplified to a description in terms of sinusoidal plane waves, which are characterized by these generic properties:
Frequency, or its inverse, the period
Wavelength Wave number Amplitude
Sound pressure Sound intensity Speed of sound Direction
Sound that is perceptible by humans has frequencies from about 20 Hz to 20,000 Hz. In air at standard temperature and pressure, the corresponding wavelengths of sound waves range from 17 m to 17 mm. Sometimes speed and direction are combined as a velocity vector; wave number and direction are combined as a wave vector. Transverse waves, also known as shear waves, have the additional property, polarization, and are not a characteristic of sound waves. Young Ji International School / College
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Speed of sound
U.S. Navy F/A-18 approaching the sound barrier. The white halo is formed by condensed water droplets thought to result from a drop in air pressure around the aircraft (see PrandtlGlauert Singularity). The speed of sound depends on the medium that the waves pass through, and is a fundamental property of the material. The first significant effort towards the measure of the speed of sound was made by Newton. He believed that the speed of sound in a particular substance was equal to the square root of the pressure acting on it (STP) divided by its density.
This was later proven wrong when found to incorrectly derive the speed. French mathematician Laplace corrected the formula by deducing that the phenomenon of sound traveling is not isothermal, as believed by Newton, but adiabatic. He added another factor to
the equation-gamma-and multiplied
equation
. Since
to
, thus coming up with the
the final equation came up to
be which is also known as the Newton-Laplace equation. In this equation, K = elastic modulus, c = velocity of sound, and = density. Thus, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium to its density. Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature. In 20 °C (68 °F) air at sea level, the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph) using the formula "v = (331 + 0.6 T) m/s". In fresh water, also at 20 °C, the speed of sound is approximately 1,482 m/s (5,335 km/h; 3,315 mph). In steel, the speed of sound is about Young Ji International School / College
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5,960 m/s (21,460 km/h; 13,330 mph).[8] The speed of sound is also slightly sensitive (a second-orderanharmonic effect) to the sound amplitude, which means that there are nonlinear propagation effects, such as the production of harmonics and mixed tones not present in the original sound (seep arametric array). Perception of sound
Human ear A distinct use of the term sound from its use in physics is that in physiology and psychology, where the term refers to the subject of perception by the brain. The field of psychoacoustics is dedicated to such studies. The physical reception of sound in any hearing organism is limited to a range of frequencies. Humans normally hear sound frequencies between approximately 20 Hz and 20,000 Hz (20 kHz), Both limits, especially the upper limit, decrease with age. Other species have a different range of hearing. For example, dogs can perceive vibrations higher than 20 kHz, but are deaf below 40 Hz. As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication. Earth's atmosphere, water, and virtually any physical phenomenon, such as fire, rain, wind, surf, or earthquake, produces (and is characterized by) its unique sounds. Many species, such as frogs, birds, marine and terrestrial mammals, have also developed special organs to produce sound. In some species, these produce song and speech. Furthermore, humans have developed culture and technology (such as music, telephone and radio) that allows them to generate, record, transmit, and broadcast sound. Sometimes sound refers to only those vibrations with frequencies that are within the hearing range for humans[10] or for a particular animal. Young Ji International School / College
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Noise Noise is a term often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal. Sound pressure level
Sound measurements Characteristic
Symbol
Sound pressure
p · SPL
Particle velocity
v · SVL
Particle displacement
ξ
Sound intensity
I · SIL
Sound power
Pac
Sound power level
SWL
Sound energy Sound exposure
E
Sound exposure level
SEL
Sound energy density
E
Sound energy flux
q
Acoustic impedance
Z
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Speed of sound Audio frequency
AF
Sound pressure is the difference, in a given medium, between average local pressure and the pressure in the sound wave. A square of this difference (i.e., a square of the deviation from the equilibrium pressure) is usually averaged over time and/or space, and a square root of this average provides a root mean square(RMS) value. For example, 1 Pa RMS sound pressure (94 dBSPL) in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm Pa) and (1 atm Pa), that is between 101323.6 and 101326.4 Pa. As the human ear can detect sounds with a wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale. The sound pressure level (SPL) or Lp is defined as
where p is the root-mean-square sound pressure and is a reference sound pressure. Commonly used reference sound pressures, defined in the standard ANSI S1.11994, are 20 ÂľPa in air and 1 ÂľPa in water. Without a specified reference sound pressure, a value expressed in decibels cannot represent a sound pressure level. Since the human ear does not have a flat spectral response, sound pressures are often frequency weighted so that the measured level matches perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.
WAVES and SOUND Worksheet 1. When an automobile moves towards a listener, the sound of its horn seems relatively a. low pitched b. high pitched c. normal 2. When the automobile moves away from the listener, its horn seems a. low pitched b. high pitched c. normal 3. The changed pitch of the Doppler effect is due to changes in Young Ji International School / College
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a. wave speed
b. wave frequency
4. Circle the letter of each statement about the Doppler Effect that is true. a. It occurs when a wave source moves towards an observer. b. It occurs when an observer moves towards a wave source. c. It occurs when a wave source moves away from an observer. d. It occurs when an observer moves away from a wave source. 5. True / False: A moving wave source does not affect the frequency of the wave encountered by the observer. 6. True / False: A higher frequency results when a wave source moves towards an observer. 7. Two fire trucks with sirens on speed towards and away from an observer as shown below.
a) Which truck produces a higher than normal siren frequency? b) Which truck produces a lower than normal siren frequency? 8. What is the frequency heard by a person driving at 15 m/s toward a blowing factory whistle (800. Hz) if the speed of sound is 340.6 m/s? 9. From the previous problem, what frequency would he hear after passing the factory if he continues at the same speed? 10. A car approaching a stationary observer emits 450. Hz from its horn. If the observer detects a frequency of 470. Hz, how fast is the car moving? The speed of sound is 343 m/s. 11. While standing near a railroad crossing, a person hears a distant train horn. According to the train's engineer, the frequency emitted by the horn is 440 Hz. The train is traveling at 20.0 m/s and the speed of sound is 346 m/s. a) What would be the frequency of the train's horn if the train were at rest? b) What is the adjusted frequency that reaches the bystander as the train approaches the crossing? c) What is the adjusted frequency that reaches the bystander once the train has passed the crossing? 12. Determine the speed of sound at 45.0 ยบC. 13. A burglar alarm is wailing with a frequency of 1200. hertz. What frequency does a cop hear who is driving towards the alarm at a speed of 40.0 m/s? The air temperature is 35.0 ยบC.
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14. With reference to the previous problem, what frequency would the burglar hear, if he was running away from the alarm at a speed of 10 m/s? 15. A cop car‘s siren has a frequency of 700. Hz. If you are standing on the sidewalk as the cop car approaches you at a speed of 15.0 m/s, what frequency would you hear? The speed of sound is 343 m/s.
16. In the previous problem, what frequency would you hear if the cop were driving away from you at a speed of 25 m/s? 17. An alarm clock is dropped off the edge of a tall building. You, standing directly under it, hear a tone of 1350. Hz coming from the clock at the instant it hits the ground. Since you know the building is 25.0 m tall, you can find out what the frequency of the alarm would be if you had just held it in your hands. What would that frequency be? The speed of sound is 343 m/s. 18. Two identical cars are driving toward one another and sounding their horns. You‘re the driver of one of the cars. You measure your car‘s horn to be sounding at 512 Hz, but you measure the horn of the other car to be sounding at 600. Hz. The speed of sound is 345 m/s. If you are traveling at 26.8 m/s (60 mph), how fast is the other car traveling? 19. Out in the ocean, a wave crest 3.2 m high meets a wave trough from another direction which is 2.6 m deep. How high is the resulting wave? 20. A physics student sitting on the beach notices that a wave hits the beach every 5.0 seconds, and the waves seem to be about 15 m apart. What is the speed of these waves? 21. Sally and her lab partner held the ends of their spring 6.00 meters apart. There were 6 nodes in the standing wave produced. Sally moved her hand from the rest position back and forth along the floor 16 times in 4.00 s. Sketch the situation and determine the following: a) the wavelength of the wave Sally sent b) the frequency of the wave produced c) the speed of the wave
Module (Lesson: Electricity)
Electricity
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Lightning is one of the most dramatic effects of electricity.
Electricity is the set of physical phenomena associated with the presence and flow of electric charge. Electricity gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and electrical current. In addition, electricity permits the creation and reception of electromagnetic radiation such as radio waves. In electricity, charges produce electromagnetic fields which act on other charges. Electricity occurs due to several types of physics:
electric charge: a property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields. electric field : an especially simple type of electromagnetic field produced by an electric charge even when it is not moving Electromagnetism (i.e., there is no electric current). The electric field produces a force on other charges in its vicinity. electric potential: the capacity of an electric field to do work on an electric charge, typically measured in volts. electric current: a movement or flow of electrically charged particles, typically measured in amperes. electromagnets: Moving charges produce a magnetic field. Electrical currents generate magnetic fields, and changing magnetic fields generate electrical currents.
In electrical engineering,
electricity is used for:
electric current is used to
electric power where energize equipment; electronics which
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circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies. Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries. Even then, practical applications for electricity were few, and it would not be until the late nineteenth century that engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society. Electricity's extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. Electrical power is now the backbone of modern industrial society. History
Thales, the earliest known researcher into electricity Long before any knowledge of electricity existed people were aware of shocks from electric fish. Ancient Egyptian texts dating from 2750 BC referred to these fish as the "Thundered of the Nile", and described them as the "protectors" of all other fish. Electric fish were again reported millennia later by ancient Greek, Romanand Arabic naturalists and physicians. Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocksdelivered by catfish and torpedo rays, and knew that such shocks could travel along conducting objects.Patients suffering from ailments such as gout or headachewere directed to touch electric fish in the hope that the powerful jolt might cure them. Possibly the earliest and nearest approach to the discovery of the identity of lightning, and electricity from any other source, is to be attributed to the Arabs, who before the 15th century had the Arabic word for lightning (raad) applied to theelectric ray. Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BC, from which he believed that Young Ji International School / College
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friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing.Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. According to a controversial theory, the Parthians may have had knowledge of electroplating, based on the 1936 discovery of the Baghdad Battery, which resembles a galvanic cell, though it is uncertain whether the artifact was electrical in nature.
Benjamin Franklin conducted extensive research on electricity in the 18th century, as documented by Joseph Priestley(1767) History and Present Status of Electricity, with whom Franklin carried on extended correspondence. Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber. He coined the New Latin word electricus ("of amber" or "like amber", from elektron, the Greek word for "amber") to refer to the property of attracting small objects after being rubbed. This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646. Further work was conducted by Otto von Guericke, Robert Boyle, Stephen Gray and C. F. du Fay. In the 18th century, Benjamin Franklin conducted extensive research in electricity, selling his possessions to fund his work. In June 1752 he is reputed to have attached a metal key to the bottom of a dampened kite string and flown the kite in a storm-threatened sky. A succession of sparks jumping from the key to the back of his hand showed that lightning was indeed electrical in nature. He also explained the apparently paradoxical behavior of the Leyden jar as a device for storing large amounts of electrical charge in terms of electricity consisting of both positive and negative charges.
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Michael Faraday's discoveries formed the foundation of electric motor technology In 1791, Luigi Galvani published his discovery of bioelectricity, demonstrating that electricity was the medium by which nerve cells passed signals to the muscles. Alessandro Volta's battery, or voltaic pile, of 1800, made from alternating layers of zinc and copper, provided scientists with a more reliable source of electrical energy than the electrostatic machines previously used.The recognition of electromagnetism, the unity of electric and magnetic phenomena, is due to Hans Christian Ørsted and AndréMarie Ampère in 1819-1820; Michael Faraday invented the electric motor in 1821, and Georg Ohm mathematically analyzed the electrical circuit in 1827. Electricity and magnetism (and light) were definitively linked by James Clerk Maxwell, in particular in his "On Physical Lines of Force" in 1861 and 1862. While the early 19th century had seen rapid progress in electrical science, the late 19th century would see the greatest progress inelectrical engineering. Through such people as Alexander Graham Bell, Ottó Bláthy, Thomas Edison, Galileo Ferraris, Oliver Heaviside, Ányos Jedlik, Lord Kelvin,Sir Charles Parsons, Ernst Werner von Siemens, Joseph Swan, Nikola Tesla and George Westinghouse, electricity turned from a scientific curiosity into an essential tool for modern life, becoming a driving force of the Second Industrial Revolution. In 1887, Heinrich Hertzdiscovered that electrodes illuminated with ultraviolet light create electric sparks more easily. In 1905 Albert Einsteinpublished a paper that explained experimental data from the photoelectric effect as being the result of light energy being carried in discrete quantized packets, energizing electrons. This discovery led to the quantum revolution. Einstein was awarded the Nobel Prize in 1921 for "his discovery of the law of the photoelectric effect". The photoelectric effect is also employed in photocells such as can be found in solar panels and this is frequently used to make electricity commercially.
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The first solid-state device was the "cat's whisker" detector, first used in 1930s radio receivers. A whisker-like wire is placed lightly in contact with a solid crystal (such as a germanium crystal) in order to detect a radio signal by the contact junction effect. In a solid-state component, the current is confined to solid elements and compounds engineered specifically to switch and amplify it. Current flow can be understood in two forms: as negatively charged electrons, and as positively charged electron deficiencies called holes. These charges and holes are understood in terms of quantum physics. The building material is most often a crystalline semiconductor. The solid-state device came into its own with the invention of the transistor in 1947. Common solid-state devices include transistors, microprocessor chips, and RAM. A specialized type of RAM called flash RAM is used in flash drives and more recently, solid state drives to replace mechanically rotating magnetic disc hard drives. Solid state devices became prevalent in the 1950s and the 1960s, during the transition from vacuum tubes to semiconductor diodes, transistors, integrated circuit (IC) and the light-emitting diode (LED).
Electric charge
Charge on a gold-leaf electroscope causes the leaves to visibly repel each other The presence of charge gives rise to an electrostatic force: charges exert a force on each other, an effect that was known, though not understood, in antiquity.A lightweight ball suspended from a string can be charged by touching it with a glass rod that has itself been charged by rubbing with a cloth. If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart. Two balls that are charged with a rubbed amber rod also repel each other. However, if one ball is charged by the glass rod, and the other by an amber rod, the two balls are found to attract each other. Young Ji International School / College
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These phenomena were investigated in the late eighteenth century by Charles-Augustin de Coulomb, who deduced that charge manifests itself in two opposing forms. This discovery led to the well-known axiom: like-charged objects repel and opposite-charged objects attract. The force acts on the charged particles themselves, hence charge has a tendency to spread itself as evenly as possible over a conducting surface. The magnitude of the electromagnetic force, whether attractive or repulsive, is given by Coulomb's law, which relates the force to the product of the charges and has an inverse-squarerelation to the distance between them. The electromagnetic force is very strong, second only in strength to the strong interaction, but unlike that force it operates over all distances. In comparison with the much weaker gravitational force, the electromagnetic force pushing two electrons apart is 1042 times that of the gravitational attraction pulling them together. Study has shown that the origin of charge is from certain types of subatomic particles which have the property of electric charge. Electric charge gives rise to and interacts with the electromagnetic force, one of the four fundamental forces of nature. The most familiar carriers of electrical charge are the electron and proton. Experiment has shown charge to be a conserved quantity, that is, the net charge within an isolated system will always remain constant regardless of any changes taking place within that system. Within the system, charge may be transferred between bodies, either by direct contact, or by passing along a conducting material, such as a wire.The informal term static electricity refers to the net presence (or 'imbalance') of charge on a body, usually caused when dissimilar materials are rubbed together, transferring charge from one to the other. The charge on electrons and protons is opposite in sign, hence an amount of charge may be expressed as being either negative or positive. By convention, the charge carried by electrons is deemed negative, and that by protons positive, a custom that originated with the work of Benjamin Franklin.The amount of charge is usually given the symbol Q and expressed in coulombs; each electron carries the same charge of approximately −1.6022×10−19 coulomb. The proton has a charge that is equal and opposite, and thus +1.6022×10−19 coulomb. Charge is possessed not just by matter, but also by antimatter, each antiparticle bearing an equal and opposite charge to its corresponding particle. Charge can be measured by a number of means, an early instrument being the gold-leaf electroscope, which although still in use for classroom demonstrations, has been superseded by the electronic electrometer.
Electric current
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The movement of electric charge is known as an electric current, the intensity of which is usually measured in amperes. Current can consist of any moving charged particles; most commonly these are electrons, but any charge in motion constitutes a current. By historical convention, a positive current is defined as having the same direction of flow as any positive charge it contains, or to flow from the most positive part of a circuit to the most negative part. Current defined in this manner is called conventional current. The motion of negatively charged electrons around an electric circuit, one of the most familiar forms of current, is thus deemed positive in the opposite direction to that of the electrons. However, depending on the conditions, an electric current can consist of a flow of charged particles in either direction, or even in both directions at once. The positive-tonegative convention is widely used to simplify this situation.
An electric arc provides an energetic demonstration of electric current The process by which electric current passes through a material is termed electrical conduction, and its nature varies with that of the charged particles and the material through which they are travelling. Examples of electric currents include metallic conduction, where electrons flow through a conductor such as metal, and electrolysis, where ions (charged atoms) flow through liquids, or through plasmas such as electrical sparks. While the particles themselves can move quite slowly, sometimes with an average drift velocity only fractions of a millimetre per second, the electric field that drives them itself propagates at close to the speed of light, enabling electrical signals to pass rapidly along wires. Current causes several observable effects, which historically were the means of recognizing its presence. That water could be decomposed by the current from a voltaic pile was discovered by Nicholson and Carlisle in 1800, a process now known as electrolysis. Their work was greatly expanded upon by Michael Faraday in 1833. Current through a resistance causes localised heating, an effect James Prescott Joule studied mathematically in 1840.One of the most important discoveries relating to current was made accidentally by Hans Christian Ă˜rsted in 1820, when, while preparing a lecture, he witnessed the current Young Ji International School / College
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in a wire disturbing the needle of a magnetic compass.He had discovered electromagnetism, a fundamental interaction between electricity and magnetics. The level of electromagnetic emissions generated by electric arcing is high enough to produce electromagnetic interference, which can be detrimental to the workings of adjacent equipment. In engineering or household applications, current is often described as being either direct current (DC) or alternating current (AC). These terms refer to how the current varies in time. Direct current, as produced by example from a battery and required by most electronic devices, is a unidirectional flow from the positive part of a circuit to the negative. If, as is most common, this flow is carried by electrons, they will be travelling in the opposite direction. Alternating current is any current that reverses direction repeatedly; almost always this takes the form of a sine wave.Alternating current thus pulses back and forth within a conductor without the charge moving any net distance over time. The timeaveraged value of an alternating current is zero, but it delivers energy in first one direction, and then the reverse. Alternating current is affected by electrical properties that are not observed under steady state direct current, such as inductance and capacitance.These properties however can become important when circuitry is subjected to transients, such as when first energized.
Electric field The concept of the electric field was introduced by Michael Faraday. An electric field is created by a charged body in the space that surrounds it, and results in a force exerted on any other charges placed within the field. The electric field acts between two charges in a similar manner to the way that the gravitational field acts between two masses, and like it, extends towards infinity and shows an inverse square relationship with distance.[26] However, there is an important difference. Gravity always acts in attraction, drawing two masses together, while the electric field can result in either attraction or repulsion. Since large bodies such as planets generally carry no net charge, the electric field at a distance is usually zero. Thus gravity is the dominant force at distance in the universe, despite being much weaker.[27]
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Field lines emanating from a positive charge above a plane conductor An electric field generally varies in space, and its strength at any one point is defined as the force (per unit charge) that would be felt by a stationary, negligible charge if placed at that point. The conceptual charge, termed a 'test charge', must be vanishingly small to prevent its own electric field disturbing the main field and must also be stationary to prevent the effect of magnetic fields. As the electric field is defined in terms of force, and force is a vector, so it follows that an electric field is also a vector, having both magnitude and direction. Specifically, it is a vector field. The study of electric fields created by stationary charges is called electrostatics. The field may be visualized by a set of imaginary lines whose direction at any point is the same as that of the field. This concept was introduced by Faraday, whose term 'lines of force' still sometimes sees use. The field lines are the paths that a point positive charge would seek to make as it was forced to move within the field; they are however an imaginary concept with no physical existence, and the field permeates all the intervening space between the lines. Field lines emanating from stationary charges have several key properties: first, that they originate at positive charges and terminate at negative charges; second, that they must enter any good conductor at right angles, and third, that they may never cross nor close in on themselves. A hollow conducting body carries all its charge on its outer surface. The field is therefore zero at all places inside the body. This is the operating principal of the Faraday cage, a conducting metal shell which isolates its interior from outside electrical effects. The principles of electrostatics are important when designing items of highvoltage equipment. There is a finite limit to the electric field strength that may be withstood by any medium. Beyond this point, electrical breakdown occurs and an electric arc causes flashover between the charged parts. Air, for example, tends to arc across small gaps at electric field strengths which exceed 30 kV per centimetre. Over larger gaps, its breakdown strength is weaker, perhaps 1 kV per centimeter. The most visible natural occurrence of this is lightning, caused when charge becomes separated in the clouds by rising columns of air, and raises the electric field in the air to greater than it can withstand. The voltage of a large lightning cloud may be as high as 100 MV and have discharge energies as great as 250 kWh. The field strength is greatly affected by nearby conducting objects, and it is particularly intense when it is forced to curve around sharply pointed objects. This principle is exploited in the lightning conductor, the sharp spike of which acts to encourage the lightning stroke to develop there, rather than to the building it serves to protect.
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A pair of AA cells. The + sign indicates the polarity of the potential difference between the battery terminals. The concept of electric potential is closely linked to that of the electric field. A small charge placed within an electric field experiences a force, and to have brought that charge to that point against the force requires work. The electric potential at any point is defined as the energy required to bring a unit test charge from an infinite distance slowly to that point. It is usually measured in volts, and one volt is the potential for which one joule of work must be expended to bring a charge of one coulomb from infinity. This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points. An electric field has the special property that it is conservative, which means that the path taken by the test charge is irrelevant: all paths between two specified points expend the same energy, and thus a unique value for potential difference may be stated. The volt is so strongly identified as the unit of choice for measurement and description of electric potential difference that the term voltage sees greater everyday usage. For practical purposes, it is useful to define a common reference point to which potentials may be expressed and compared. While this could be at infinity, a much more useful reference is the Earth itself, which is assumed to be at the same potential everywhere. This reference point naturally takes the name earth or ground. Earth is assumed to be an infinite source of equal amounts of positive and negative charge, and is therefore electrically uncharged—and unchargeable. Electric potential is a scalar quantity, that is, it has only magnitude and not direction. It may be viewed as analogous to height: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field. As relief maps show contour lines marking points of equal height, a set of lines marking points of equal potential (known as equipotential) may be drawn around an Young Ji International School / College
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electrostatically charged object. The equipotential cross all lines of force at right angles. They must also lie parallel to a conductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface. The electric field was formally defined as the force exerted per unit charge, but the concept of potential allows for a more useful and equivalent definition: the electric field is the local gradient of the electric potential. Usually expressed in volts per metre, the vector direction of the field is the line of greatest slope of potential, and where the equipotentials lie closest together.
Electromagnets
Magnetic field circles around a current Ørsted's discovery in 1821 that a magnetic field existed around all sides of a wire carrying an electric current indicated that there was a direct relationship between electricity and magnetism. Moreover, the interaction seemed different from gravitational and electrostatic forces, the two forces of nature then known. The force on the compass needle did not direct it to or away from the current-carrying wire, but acted at right angles to it. Ørsted's slightly obscure words were that "the electric conflict acts in a revolving manner." The force also depended on the direction of the current, for if the flow was reversed, then the force did too. Ørsted did not fully understand his discovery, but he observed the effect was reciprocal: a current exerts a force on a magnet, and a magnetic field exerts a force on a current. The phenomenon was further investigated by Ampère, who discovered that two parallel currentcarrying wires exerted a force upon each other: two wires conducting currents in the same direction are attracted to each other, while wires containing currents in opposite directions
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are forced apart. The interaction is mediated by the magnetic field each current produces and forms the basis for the international definition of the ampere.
The electric motor exploits an important effect of electromagnetism: a current through a magnetic field experiences a force at right angles to both the field and current This relationship between magnetic fields and currents is extremely important, for it led to Michael Faraday's invention of the electric motor in 1821. Faraday's homopolar motor consisted of a permanent magnet sitting in a pool of mercury. A current was allowed through a wire suspended from a pivot above the magnet and dipped into the mercury. The magnet exerted a tangential force on the wire, making it circle around the magnet for as long as the current was maintained. Experimentation by Faraday in 1831 revealed that a wire moving perpendicular to a magnetic field developed a potential difference between its ends. Further analysis of this process, known as electromagnetic induction, enabled him to state the principle, now known as Faraday's law of induction, that the potential difference induced in a closed circuit is proportional to the rate of change of magnetic flux through the loop. Exploitation of this discovery enabled him to invent the first electrical generator in 1831, in which he converted the mechanical energy of a rotating copper disc to electrical energy. Faraday's disc was inefficient and of no use as a practical generator, but it showed the possibility of generating electric power using magnetism, a possibility that would be taken up by those that followed on from his work.
Electrochemistry
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Italian physicist Alessandro Voltashowing his "battery" to French emperorNapoleon Bonaparte in the early 19th century. The ability of chemical reactions to produce electricity, and conversely the ability of electricity to drive chemical reactions has a wide array of uses. Electrochemistry has always been an important part of electricity. From the initial invention of the Voltaic pile, electrochemical cells have evolved into the many different types of batteries, electroplating and electrolysis cells. Aluminium is produced in vast quantities this way, and many portable devices are electrically powered using rechargeable cells.
Electric circuits
A basic electric circuit. The voltage source V on the left drives a current I around the circuit, delivering electrical energy into the resistor R. From the resistor, the current returns to the source, completing the circuit. An electric circuit is an interconnection of electric components such that electric charge is made to flow along a closed path (a circuit), usually to perform some useful task. The components in an electric circuit can take many forms, which can include elements such as resistors, capacitors, switches, transformers and electronics.Electronic circuits contain active components, usually semiconductors, and typically exhibit nonlinear behavior, requiring complex analysis. The simplest electric components are those that are termed passive and linear: while they may temporarily store energy, they contain no sources of it, and exhibit linear responses to stimuli. The resistor is perhaps the simplest of passive circuit elements: as its name suggests, it resists the current through it, dissipating its energy as heat. The resistance is a Young Ji International School / College
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consequence of the motion of charge through a conductor: in metals, for example, resistance is primarily due to collisions between electrons and ions. Ohm's law is a basic law of circuit theory, stating that the current passing through a resistance is directly proportional to the potential difference across it. The resistance of most materials is relatively constant over a range of temperatures and currents; materials under these conditions are known as 'ohmic'. The ohm, the unit of resistance, was named in honor of Georg Ohm, and is symbolised by the Greek letter Ί. 1 Ί is the resistance that will produce a potential difference of one volt in response to a current of one amp. The capacitor is a development of the Leyden jar and is a device that can store charge, and thereby storing electrical energy in the resulting field. It consists of two conducting plates separated by a thin insulating dielectric layer; in practice, thin metal foils are coiled together, increasing the surface area per unit volume and therefore the capacitance. The unit of capacitance is the farad, named after Michael Faraday, and given the symbol F: one farad is the capacitance that develops a potential difference of one volt when it stores a charge of one coulomb. A capacitor connected to a voltage supply initially causes a current as it accumulates charge; this current will however decay in time as the capacitor fills, eventually falling to zero. A capacitor will therefore not permit a steady state current, but instead blocks it. The inductor is a conductor, usually a coil of wire,that stores energy in a magnetic field in response to the current through it. When the current changes, the magnetic field does too, inducing a voltage between the ends of the conductor. The induced voltage is proportional to the time rate of change of the current. The constant of proportionality is termed the inductance. The unit of inductance is the henry, named after Joseph Henry, a contemporary of Faraday. One henry is the inductance that will induce a potential difference of one volt if the current through it changes at a rate of one ampere per second. The inductor's behaviour is in some regards converse to that of the capacitor: it will freely allow an unchanging current, but opposes a rapidly changing one.
Electric power Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is
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where Q is electric charge in coulombs t is time in seconds I is electric current in amperes V is electric potential or voltage in volts Electricity generation is often done with electric generators, but can also be supplied by chemical sources such as electric batteries or by other means from a wide variety of sources of energy. Electric power is generally supplied to businesses and homes by the electric power industry. Electricity is usually sold by the kilowatt hour (3.6 MJ) which is the product of power in kilowatts multiplied by running time in hours. Electric utilities measure power using electricity meters, which keep a running total of the electric energy delivered to a customer.
Electronics
Surface mount electronic components Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies. The nonlinear behavior of active components and their ability to control electron flows makes amplification of weak signals possible and electronics is widely used in information processing, telecommunications, and signal processing. The ability of electronic devices to act as switches makes digital information processing possible. Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system. Today, most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a branch of solid
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state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering.
Electromagnetic wave Faraday's and Ampère's work showed that a time-varying magnetic field acted as a source of an electric field, and a time-varying electric field was a source of a magnetic field. Thus, when either field is changing in time, then a field of the other is necessarily induced. Such a phenomenon has the properties of a wave, and is naturally referred to as an electromagnetic wave. Electromagnetic waves were analyzed theoretically by James Clerk Maxwell in 1864. Maxwell developed a set of equations that could unambiguously describe the interrelationship between electric field, magnetic field, electric charge, and electric current. He could moreover prove that such a wave would necessarily travel at the speed of light, and thus light itself was a form of electromagnetic radiation. Maxwell's Laws, which unify light, fields, and charge are one of the great milestones of theoretical physics. Thus, the work of many researchers enabled the use of electronics to convert signals into high frequency oscillating currents, and via suitably shaped conductors, electricity permits the transmission and reception of these signals via radio waves over very long distances.
Generation and transmission
Early 20th-century alternator made in Budapest,Hungary, in the power generating hall of a hydroelectricstation (photograph by Prokudin-Gorsky, 1905–1915).
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Thales' experiments with amber rods were the first studies into the production of electrical energy. While this method, now known as thetriboelectric effect, can lift light objects and generate sparks, it is extremely inefficient. It was not until the invention of the voltaic pile in the eighteenth century that a viable source of electricity became available. The voltaic pile, and its modern descendant, the electrical battery, store energy chemically and make it available on demand in the form of electrical energy. The battery is a versatile and very common power source which is ideally suited to many applications, but its energy storage is finite, and once discharged it must be disposed of or recharged. For large electrical demands electrical energy must be generated and transmitted continuously over conductive transmission lines. Electrical power is usually generated by electro-mechanical generators driven by steam produced from fossil fuel combustion, or the heat released from nuclear reactions; or from other sources such as kinetic energy extracted from wind or flowing water. The modern steam turbine invented by Sir Charles Parsons in 1884 today generates about 80 percent of the electric power in the world using a variety of heat sources. Such generators bear no resemblance to Faraday's homopolar disc generator of 1831, but they still rely on his electromagnetic principle that a conductor linking a changing magnetic field induces a potential difference across its ends. The invention in the late nineteenth century of the transformer meant that electrical power could be transmitted more efficiently at a higher voltage but lower current. Efficient electrical transmission meant in turn that electricity could be generated at centralized power stations, where it benefited from economies of scale, and then be dispatched relatively long distances to where it was needed.
Wind power is of increasing importance in many countries Since electrical energy cannot easily be stored in quantities large enough to meet demands on a national scale, at all times exactly as much must be produced as is required. This requires electricity utilities to make careful predictions of their electrical loads, and maintain constant co-ordination with their power stations. A certain amount of generation must Young Ji International School / College
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always be held in reserve to cushion an electrical grid against inevitable disturbances and losses. Demand for electricity grows with great rapidity as a nation modernizes and its economy develops. The United States showed a 12% increase in demand during each year of the first three decades of the twentieth century, a rate of growth that is now being experienced by emerging economies such as those of India or ChinaHistorically, the growth rate for electricity demand has outstripped that for other forms of energy. Environmental concerns with electricity generation have led to an increased focus on generation from renewable sources, in particular from wind and hydropower. While debate can be expected to continue over the environmental impact of different means of electricity production, its final form is relatively clean
Applications
The light bulb, an early application of electricity, operates by Joule heating: the passage of current through resistance generating heat. Electricity is a very convenient way to transfer energy, and it has been adapted to a huge, and growing, number of uses.The invention of a practical incandescent light bulb in the 1870s led to lighting becoming one of the first publicly available applications of electrical power. Although electrification brought with it its own dangers, replacing the naked flames of gas lighting greatly reduced fire hazards within homes and factories. Public utilities were set up in many cities targeting the burgeoning market for electrical lighting.
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The Joule heating effect employed in the light bulb also sees more direct use in electric heating. While this is versatile and controllable, it can be seen as wasteful, since most electrical generation has already required the production of heat at a power station. A number of countries, such as Denmark, have issued legislation restricting or banning the use of electric heating in new buildings. Electricity is however a highly practical energy source for refrigeration, with air conditioning representing a growing sector for electricity demand, the effects of which electricity utilities are increasingly obliged to accommodate. Electricity is used within telecommunications, and indeed the electrical telegraph, demonstrated commercially in 1837 by Cooke and Wheatstone, was one of its earliest applications. With the construction of first intercontinental, and then transatlantic, telegraph systems in the 1860s, electricity had enabled communications in minutes across the globe. Optical fibre and satellite communication have taken a share of the market for communications systems, but electricity can be expected to remain an essential part of the process. The effects of electromagnetism are most visibly employed in the electric motor, which provides a clean and efficient means of motive power. A stationary motor such as a winch is easily provided with a supply of power, but a motor that moves with its application, such as an electric vehicle, is obliged to either carry along a power source such as a battery, or to collect current from a sliding contact such as a pantograph. Electronic devices make use of the transistor, perhaps one of the most important inventions of the twentieth century,and a fundamental building block of all modern circuitry. A modern integrated circuit may contain several billion miniaturized transistors in a region only a few centimetres square. Electricity is also used to fuel public transportation, including electric buses and trains.
Electric shock A voltage applied to a human body causes an electric current through the tissues, and although the relationship is non-linear, the greater the voltage, the greater the current. The threshold for perception varies with the supply frequency and with the path of the current, but is about 0.1 mA to 1 mA for mains-frequency electricity, though a current as low as a microamp can be detected as an electrovibration effect under certain conditions. If the current is sufficiently high, it will cause muscle contraction, fibrillation of the heart, and tissue burns. The lack of any visible sign that a conductor is electrified makes electricity a particular hazard. The pain caused by an electric shock can be intense, leading electricity at times to be employed as a method of torture. Death caused by an electric shock is referred
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to as electrocution. Electrocution is still the means of judicial execution in some jurisdictions, though its use has become rarer in recent times.
Electrical phenomena in nature
Electricity is not a human invention, and may be observed in several forms in nature, a prominent manifestation of which is lightning. Many interactions familiar at the macroscopic level, such as touch, friction or chemical bonding, are due to interactions between electric fields on the atomic scale. TheEarth's magnetic field is thought to arise from a natural dynamo of circulating currents in the planet's core.[68] Certain crystals, such as quartz, or even sugar, generate a potential difference across their faces when subjected to external pressure.This phenomenon is known as piezoelectricity, from the Greek piezein meaning to press, and was discovered in 1880 by Pierre and Jacques Curie. The effect is reciprocal, and when a piezoelectric material is subjected to an electric field, a small change in physical dimensions takes place. Some organisms, such as sharks, are able to detect and respond to changes in electric fields, an ability known as electroreception, while others, termed electrogenic, are able to generate voltages themselves to serve as a predatory or defensive weapon. The order Gymnotiformes, of which the best known example is the electric eel, detect or stun their prey via high voltages generated from modified muscle cells called electrocytes. All animals transmit information along their cell membranes with voltage pulses called action potentials, whose functions include communication by the nervous system between neurons and muscles. An electric shock stimulates this system, and causes muscles to contract. Action potentials are also responsible for coordinating activities in certain plants.
Cultural Perception
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In 1850, William Gladstone asked the scientist Michael Faraday why electricity was valuable. Faraday answered, ―One day sir, you may tax it.‖ In the 19th and early 20th century, electricity was not part of the everyday life of many people, even in the industrialized Western world. The popular culture of the time accordingly often depicts it as a mysterious, quasi-magical force that can slay the living, revive the dead or otherwise bend the laws of nature. This attitude began with the 1771 experiments of Luigi Galvani in which the legs of dead frogs were shown to twitch on application of animal electricity. "Revitalization" or resuscitation of apparently dead or drowned persons was reported in the medical literature shortly after Galvani's work. These results were known to Mary Shelley when she authored Frankenstein (1819), although she does not name the method of revitalization of the monster. The revitalization of monsters with electricity later became a stock theme in horror films. As the public familiarity with electricity as the lifeblood of the Second Industrial Revolution grew, its wielders were more often cast in a positive light, such as the workers who "finger death at their gloves' end as they piece and repiece the living wires" in Rudyard Kipling's 1907 poem Sons of Martha. Electrically powered vehicles of every sort featured large in adventure stories such as those of Jules Verne and the Tom Swift books. The masters of electricity, whether fictional or real—including scientists such as Thomas Edison, Charles Steinmetz or Nikola Tesla—were popularly conceived of as having wizardlike powers. With electricity ceasing to be a novelty and becoming a necessity of everyday life in the later half of the 20th century, it required particular attention by popular culture only when it stops flowing, an event that usually signals disaster. The people who keep it flowing, such as the nameless hero of Jimmy Webb‘s song "Wichita Lineman" (1968), are still often cast as heroic, wizard-like figures. Electric Circuits and Ohm’s Law
An electric circuit is formed when a conductive path is created to allow free electrons to continuously move. This continuous movement of free electrons through the conductors of a circuit is called a current, and it is often referred to in terms of "flow," just like the flow of a liquid through a hollow pipe. The force motivating electrons to "flow" in a circuit is called voltage. Voltage is a specific measure of potential energy that is always relative between two points. When we speak of a certain amount of voltage being present in a circuit, we are referring to the measurement of how much potential energy exists to move electrons from one particular point in that circuit to another particular point. Without reference to two particular points, the term "voltage" has no meaning. Young Ji International School / College
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Free electrons tend to move through conductors with some degree of friction, or opposition to motion. This opposition to motion is more properly called resistance. The amount of current in a circuit depends on the amount of voltage available to motivate the electrons, and also the amount of resistance in the circuit to oppose electron flow. Just like voltage, resistance is a quantity relative between two points. For this reason, the quantities of voltage and resistance are often stated as being "between" or "across" two points in a circuit. To be able to make meaningful statements about these quantities in circuits, we need to be able to describe their quantities in the same way that we might quantify mass, temperature, volume, length, or any other kind of physical quantity. For mass we might use the units of "kilogram" or "gram." For temperature we might use degrees Fahrenheit or degrees Celsius. Here are the standard units of measurement for electrical current, voltage, and resistance:
The "symbol" given for each quantity is the standard alphabetical letter used to represent that quantity in an algebraic equation. Standardized letters like these are common in the disciplines of physics and engineering, and are internationally recognized. The "unit abbreviation" for each quantity represents the alphabetical symbol used as a shorthand notation for its particular unit of measurement. And, yes, that strange-looking "horseshoe" symbol is the capital Greek letter Ί, just a character in a foreign alphabet (apologies to any Greek readers here). Each unit of measurement is named after a famous experimenter in electricity: The amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Volta, and the ohm after the German Georg Simon Ohm. The mathematical symbol for each quantity is meaningful as well. The "R" for resistance and the "V" for voltage are both self-explanatory, whereas "I" for current seems a bit weird. The "I" is thought to have been meant to represent "Intensity" (of electron flow), and the other symbol for voltage, "E," stands for "Electromotive force." From what research I've been able to do, there seems to be some dispute over the meaning of "I." The symbols "E" and "V" are interchangeable for the most part, although some texts reserve "E" to represent voltage across a source (such as a battery or generator) and "V" to represent voltage across anything else. All of these symbols are expressed using capital letters, except in cases where a quantity (especially voltage or current) is described in terms of a brief period of time (called an "instantaneous" value). For example, the voltage of a battery, which is stable over a long period of time, will be symbolized with a capital letter "E," while the voltage peak of a lightning strike at the very instant it hits a power line would most likely be symbolized with a lower-case letter "e" (or lower-case "v") to designate that value as being at a single moment in time. This same lower-case convention holds true for current as well, the lowerYoung Ji International School / College
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case letter "i" representing current at some instant in time. Most direct-current (DC) measurements, however, being stable over time, will be symbolized with capital letters. One foundational unit of electrical measurement, often taught in the beginnings of electronics courses but used infrequently afterwards, is the unit of the coulomb, which is a measure of electric charge proportional to the number of electrons in an imbalanced state. One coulomb of charge is equal to 6,250,000,000,000,000,000 electrons. The symbol for electric charge quantity is the capital letter "Q," with the unit of coulombs abbreviated by the capital letter "C." It so happens that the unit for electron flow, the amp, is equal to 1 coulomb of electrons passing by a given point in a circuit in 1 second of time. Cast in these terms, current is the rate of electric charge motion through a conductor. As stated before, voltage is the measure of potential energy per unit charge available to motivate electrons from one point to another. Before we can precisely define what a "volt" is, we must understand how to measure this quantity we call "potential energy." The general metric unit for energy of any kind is the joule, equal to the amount of work performed by a force of 1 newton exerted through a motion of 1 meter (in the same direction). In British units, this is slightly less than 3/4 pound of force exerted over a distance of 1 foot. Put in common terms, it takes about 1 joule of energy to lift a 3/4 pound weight 1 foot off the ground, or to drag something a distance of 1 foot using a parallel pulling force of 3/4 pound. Defined in these scientific terms, 1 volt is equal to 1 joule of electric potential energy per (divided by) 1 coulomb of charge. Thus, a 9 volt battery releases 9 joules of energy for every coulomb of electrons moved through a circuit. These units and symbols for electrical quantities will become very important to know as we begin to explore the relationships between them in circuits. The first, and perhaps most important, relationship between current, voltage, and resistance is called Ohm's Law, discovered by Georg Simon Ohm and published in his 1827 paper, The Galvanic Circuit Investigated Mathematically. Ohm's principal discovery was that the amount of electric current through a metal conductor in a circuit is directly proportional to the voltage impressed across it, for any given temperature. Ohm expressed his discovery in the form of a simple equation, describing how voltage, current, and resistance interrelate:
In this algebraic expression, voltage (E) is equal to current (I) multiplied by resistance (R). Using algebra techniques, we can manipulate this equation into two variations, solving for I and for R, respectively:
Let's see how these equations might work to help us analyze simple circuits:
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In the above circuit, there is only one source of voltage (the battery, on the left) and only one source of resistance to current (the lamp, on the right). This makes it very easy to apply Ohm's Law. If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third. In this first example, we will calculate the amount of current (I) in a circuit, given values of voltage (E) and resistance (R):
What is the amount of current (I) in this circuit?
In this second example, we will calculate the amount of resistance (R) in a circuit, given values of voltage (E) and current (I):
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What is the amount of resistance (R) offered by the lamp?
In the last example, we will calculate the amount of voltage supplied by a battery, given values of current (I) and resistance (R):
What is the amount of voltage provided by the battery?
Ohm's Law is a very simple and useful tool for analyzing electric circuits. It is used so often in the study of electricity and electronics that it needs to be committed to memory by the serious student. For those who are not yet comfortable with algebra, there's a trick to remembering how to solve for any one quantity, given the other two. First, arrange the letters E, I, and R in a triangle like this:
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If you know E and I, and wish to determine R, just eliminate R from the picture and see what's left:
If you know E and R, and wish to determine I, eliminate I and see what's left
Lastly, if you know I and R, and wish to determine E, eliminate E and see what's left:
Eventually, you'll have to be familiar with algebra to seriously study electricity and electronics, but this tip can make your first calculations a little easier to remember. If you are comfortable with algebra, all you need to do is commit E=IR to memory and derive the other two formulae from that when you need them!
REVIEW: Voltage measured in volts, symbolized by the letters "E" or "V". Current measured in amps, symbolized by the letter "I". Resistance measured in ohms, symbolized by the letter "R". Ohm's Law: E = IR ; I = E/R ; R = E/I
Ohms Law Worksheet Basic Circuits
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Lamps in Parallel - Build and Measure Build the circuit below and then measure the current and voltage for Measured Calculated each lamp. Label the circuit below with the measure values adding the polarity and direction of the current. Fill in the measured values below the circuit
% Difference (See Page 2)
-
Voltage Lamp 1 (VL1) Current Lamp 1 (IL1) Power Lamp 1 (PL1) Voltage Lamp 2 (VL2) Current Lamp 2 (IL2) Power Lamp 2 (PL2)\
How well did you estimate the power and current through each lamp? What are things that you could do to improve the prediction or calculated values? Young Ji International School / College
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What are things that you could do to improve the measured values?
What Was Observed? Which were brighter the lamps in parallel or the lamps in series?
Explain the circuit you came up with when trying to make the lamps shine the brightest?
Can you now quantify the brightness by associating it with the power dissipation?
How accurate is it to associate the brightness with the power dissipation?
Fill in the table below using the power measured in the series and parallel circuits Power Lamp 1
Power Lamp 2
Total Power Lamp 1 + Lamp 2
Series Circuit Parallel Circuit Factor (Parallel/Series)
Series circuit brighter, > 1 parallel circuit brighter) and why?
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How to analyze circuits with more than two components Build this circuit and measure the current through each lamp. Enter the measured values in the spaces below. (Groups may need to join in order to have enough lamps.) -
Voltage across Vlamp 1 = _____________________ (V) Voltage across Vlamp 2 = _____________________ (V) Voltage across Vlamp 3 = _____________________ (V) Current Through Lamp 1 Ilamp 1 = _____________________ (A)
Current Through Lamp 2 Ilamp 2 = _____________________ (A)
Current Through Lamp 3 Ilamp 3 = _____________________ (A) How close is 1 Ilamp 1 to Iequiv ? If the percent difference is more than 5% calculate the resistance for each lamp and compare the resistance for each lamp. Current through Iequiv: = ______________ (A) %Difference = ______________________ (%)
Does the current through lamp 1 equal the sum of the current through lamp 2 and lamp
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Module (Lesson: Electromagnetism and EM waves)
Maxwell’s equations for EM fields far from sources James Clerk Maxwell first formally postulated electromagnetic waves. These were subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. According to Maxwell's equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a spatially varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the electric field are always accompanied by a wave in the magnetic field in one direction, and vice versa. This relationship between the two occurs without either type field causing the other; rather, they occur together in the same way that time and space changes occur together and are interlinked in special relativity. In fact, magnetic fields may be viewed as relativistic distortions of electric fields, so the close relationship between space and time changes here is more than an analogy. Together, these fields form a propagating electromagnetic wave, which moves out into space and need never again affect the source. The distant EM field formed in this way by the acceleration of a charge carries energy with it that "radiates" away through space, hence the term for it.
LiÊnard–Wiechert potential
In electromagnetic radiation (such as microwaves from an antenna, shown here) the term applies only to the parts of the electromagnetic field that radiate into infinite space and decrease in intensity by an inverse-square law of power, so that the total radiation energy that crosses through an imaginary spherical surface is the same, no matter how far away from the antenna the spherical surface is drawn. Electromagnetic radiation thus includes the far field part of the Young Ji International School / College
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electromagnetic field around a transmitter. A part of the "near-field" close to the transmitter, forms part of the changing electromagnetic field, but does not count as electromagnetic radiation. Maxwell's equations established that some charges and currents ("sources") produce a local type of electromagnetic field near them that does not have the behavior of EMR. In particular, according to Maxwell, currents directly produce a magnetic field, but it is of a magnetic dipoletype which dies out rapidly with distance from the current. In a similar manner, moving charges being separated from each other in a conductor by a changing electrical potential (such as in an antenna) produce an electric dipole type electrical field, but this also dies away very quickly with distance. Both of these fields make up the near-field near the EMR source. Neither of these behaviors are responsible for EM radiation. Instead, they cause electromagnetic field behavior that only efficiently transfers power to a receiver very close to the source, such as the magnetic induction inside a transformer, or the feedback behavior that happens close to the coil of a metal detector. Typically, near-fields have a powerful effect on their own sources, causing an increased ―load‖ (decreased electrical reactance) in the source or transmitter, whenever energy is withdrawn from the EM field by a receiver. Otherwise, these fields do not ―propagate‖ freely out into space, carrying their energy away without distance-limit, but rather oscillate back and forth, returning their energy to the transmitter if it is not received by a receiver. By contrast, the EM far-field is composed of radiation that is free of the transmitter in the sense that (unlike the case in an electrical transformer) the transmitter requires the same power to send these changes in the fields out, whether the signal is immediately picked up, or not. This distant part of the electromagnetic field is "electromagnetic radiation" (also called the far-field). The farfields propagate (radiate) without ability for the transmitter to affect them, and this causes them to be independent in the sense that their existence and their energy, after they have left the transmitter, is completely independent of both transmitter and receiver. Because such waves conserve the amount of energy they transmit through any spherical boundary surface drawn around their source, and because such surfaces have an area that is defined by the square of the distance from the source, the power of EM radiation always varies according to an inversesquare law. This is in contrast to dipole parts of the EM field close to the source (the near-field), which varies in power according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances, but instead dies away rapidly with distance, with its energy (as noted) either rapidly returning to the transmitter, or else absorbed by a nearby receiver (such as a transformer secondary coil). The far-field (EMR) depends on a different mechanism for its production than the near-field, and upon different terms in Maxwell‘s equations. Whereas the magnetic part of the near-field is due to currents in the source, the magnetic field in EMR is due only to the local change in the electric field. In a similar way, while the electric field in the near-field is due directly to the charges and Young Ji International School / College
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charge-separation in the source, the electric field in EMR is due to a change in the local magnetic field. Both of these processes for producing electric and magnetic EMR fields have a different dependence on distance than do near-field dipole electric and magnetic fields, and that is why the EMR type of EM field becomes dominant in power ―far‖ from sources. The term ―far from sources‖ refers to how far from the source (moving at the speed of light) any portion of the outward-moving EM field is located, by the time that source currents are changed by the varying source potential, and the source has therefore begun to generate an outwardly moving EM field of a different phase. A more compact view of EMR is that the far-field that composes EMR is generally that part of the EM field that has traveled sufficient distance from the source, that it has become completely disconnected from any feedback to the charges and currents that were originally responsible for it. Now independent of the source charges, the EM field, as it moves farther away, is dependent only upon the accelerations of the charges that produced it. It no longer has a strong connection to the direct fields of the charges, or to the velocity of the charges (currents). In the Liénard–Wiechert potential formulation of the electric and magnetic fields due to motion of a single particle (according to Maxwell's equations), the terms associated with acceleration of the particle are those that are responsible for the part of the field that is regarded as electromagnetic radiation. By contrast, the term associated with the changing static electric field of the particle and the magnetic term that results from the particle's uniform velocity, are both seen to be associated with the electromagnetic near-field, and do not comprise EM radiation
Properties
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are inphase with each other, reaching minima and maxima together Young Ji International School / College
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An alternate view of the wave shown above. The physics of electromagnetic radiation is electrodynamics. Electromagnetism is the physical phenomenon associated with the theory of electrodynamics. Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For example, in optics two or more coherent light waves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual light waves. Since light is an oscillation it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. However, in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the Faraday effect and the Kerr effect. In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light of composite wavelengths (natural sunlight) disperses into a visible spectrum passing through a prism, because of the wavelength dependent refractive index of the prism material (dispersion); that is, each component wave within the composite light is bent a different amount. EM radiation exhibits both wave properties and particle properties at the same time (see waveparticle duality). Both wave and particle characteristics have been confirmed in a large number of experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. It is not too difficult to Young Ji International School / College
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experimentally observe non-uniform deposition of energy when light is absorbed, however this alone is not evidence of "particulate" behavior of light. Rather, it reflects the quantum nature of matter.Demonstrating that the light itself is quantized, not merely its interaction with matter, is a more subtle problem. There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the self-interference of a single photon. True single-photon experiments (in a quantum optical sense) can be done today in undergraduate-level labs. When a single photon is sent through an interferometer, it passes through both paths, interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once. A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.
Wave model Electromagnetic radiation is a transverse wave, meaning that the oscillations of the waves are perpendicular to the direction of energy transfer and travel. The electric and magnetic parts of the field stand in a fixed ratio of strengths in order to satisfy the two Maxwell equations that specify how one is produced from the other. These E and B fields are also in phase, with both reaching maxima and minima at the same points in space .A common misconception is that the E and B fields in electromagnetic radiation are out of phase because a change in one produces the other, and this would produce a phase difference between them as sinusoidal functions (as indeed happens in electromagnetic induction, and in the near-field close to antennas). However, in the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a more correct description is that a time-change in one type of field is proportional to a space-change in the other. These derivatives require that the E and B fields in EMR are in-phase. An important aspect of the nature of light is frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has a spectrum of frequencies that sum to form the resultant wave. Different frequencies undergo different angles of refraction, a phenomenon known as dispersion. A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation: Young Ji International School / College
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where v is the speed of the wave (c in a vacuum, or less in other media), f is the frequency and Îť is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant. Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation. Two main classes of solutions are known, namely plane waves and spherical waves. The plane waves may be viewed as the limiting case of spherical waves at a very large (ideally infinite) distance from the source. Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation). As with any time function, this can be decomposed by means of Fourier analysis into its frequency spectrum, or individual sinusoidal components, each of which contains a single frequency, amplitude, and phase. Such a component wave is said to be monochromatic. A monochromatic electromagnetic wave can be characterized by its frequency or wavelength, its peak amplitude, its phase relative to some reference phase, its direction of propagation, and its polarization. Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference. An example of interference caused by EMR is electromagnetic interference (EMI) or as it is more commonly known as, radio-frequency interference (RFI). The energy in electromagnetic waves is sometimes called radiant energy.
Particle model and quantum theory An anomaly arose in the late 19th century involving a contradiction between the wave theory of light on the one hand, and on the other, observers' actual measurements of the electromagnetic spectra that were being emitted by thermal radiators known as black bodies. Physicists struggled with this problem, which later became known as the ultraviolet catastrophe, unsuccessfully for many years. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta. Later, Albert Einstein proposed that the quanta of light might be regarded as real particles, and (still later) the particle of light was given the name photon, to correspond with other particles being
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described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by
where h is Planck's constant, is the wavelength and c is the speed of light. This is sometimes known as the Planck–Einstein equation.In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency of the EMR wave. Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:
The source of Einstein's proposal that light was composed of particles (or could act as particles in some circumstances) was an experimental anomaly not explained by the wave theory: the photoelectric effect, in which light striking a metal surface ejected electrons from the surface, causing an electric current to flow across an applied voltage. Experimental measurements demonstrated that the energy of individual ejected electrons was proportional to the frequency, rather than the intensity, of the light. Furthermore, below a certain minimum frequency, which depended on the particular metal, no current would flow regardless of the intensity. These observations appeared to contradict the wave theory, and for years physicists tried in vain to find an explanation. In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect. Because of the preponderance of evidence in favor of the wave theory, however, Einstein's ideas were met initially with great skepticism among established physicists. Eventually Einstein's explanation was accepted as new particle-like behavior of light was observed, such as the Compton effect. As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level (on average, one that is farther from the nucleus). When an electron in an excited molecule or atom descends to a lower energy level, it emits a photon of light equal to the energy difference. Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies. When the emission of the photon is immediate, this phenomenon is called fluorescence, a type of photoluminescence. An example is visible light emitted from fluorescent paints, in response to ultraviolet (black light). Many other fluorescent emissions are known in spectral bands other than visible light. When the emission of the photon is delayed, the phenomenon is called phosphorescence.
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Wave–particle duality The modern theory that explains the nature of light includes the notion of wave–particle duality. More generally, the theory states that everything has both a particle nature and a wave nature, and various experiments can be done to bring out one or the other. The particle nature is more easily discerned if an object has a large mass, and it was not until a bold proposition by Louis de Broglie in 1924 that the scientific community realised that electrons also exhibited wave–particle duality.
Wave and particle effects of electromagnetic radiation. Together, wave and particle effects explain the emission and absorption spectra of EM radiation, wherever it is seen. The matter-composition of the medium through which the light travels determines the nature of the absorption and emission spectrum. These bands correspond to the allowed energy levels in the atoms. Dark bands in the absorption spectrum are due to the atoms in an intervening medium between source and observer, absorbing certain frequencies of the light between emitter and detector/eye, then emitting them in all directions, so that a dark band appears to the detector, due to the radiation scattered out of the beam. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere. A similar phenomenon occurs for emission, which is seen when the emitting gas is glowing due to excitation of the atoms from any mechanism, including heat. As electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons, but lines are seen because again emission happens only at particular energies after excitation. An example is the emission spectrum ofnebulae.[citation needed] Rapidly moving electrons are most sharply accelerated when they encounter a region of force, so they are responsible for producing much of the highest frequency electromagnetic radiation observed in nature. Today, scientists use these phenomena to perform various chemical determinations for the composition of gases lit from behind (absorption spectra) and for glowing gases (emission spectra). Spectroscopy (for example) determines what chemical elements a star is composed of. Spectroscopy is also used in the determination of the distance of a star, using the red shift.
Speed of propagation Any electric charge that accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is not physically possible in light of causality), which adds to the expressions for the Young Ji International School / College
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electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. In many such situations it is possible to identify an electrical dipole moment that arises from separation of charges due to the exciting electrical potential, and this dipole moment oscillates in time, as the charges move back and forth. This oscillation at a given frequency gives rise to changing electric and magnetic fields, which then set the electromagnetic radiation in motion. At the quantum level, electromagnetic radiation is produced when the wave packet of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in transition state which has an electric dipole moment that oscillates in time. This oscillating dipole moment is responsible for the phenomenon of radiative transition between quantum states of a charged particle. Such states occur (for example) in atoms when photons are radiated as the atom shifts from one stationary state to another. Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν, where E is the energy of the photon, h = 6.626 × 10−34 J·s is Planck's constant, and ν is the frequency of the wave. One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer, regardless of the observer's velocity. (This observation led to Albert Einstein's development of the theory of special relativity.) In a medium (other than vacuum), velocity factor or refractive index are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.
Special theory of relativity By the late nineteenth century, however, a handful of experimental anomalies remained that could not be explained by the simple wave theory. One of these anomalies involved a controversy over the speed of light. The speed of light and other EMR predicted by Maxwell's equations did not appear unless the equations were modified in a way first suggested by FitzGerald and Lorentz, or else otherwise it would depend on the speed of observer relative to the "medium" (called luminiferous aether) which supposedly "carried" the electromagnetic wave Young Ji International School / College
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(in a manner analogous to the way air carries sound waves). Experiments failed to find any observer effect, however. In 1905, Albert Einstein proposed that space and time appeared to be velocity-changeable entities, not only for light propagation, but all other processes and laws as well. These changes then automatically accounted for the constancy of the speed of light and all electromagnetic radiation, from the viewpoints of all observers—even those in relative motion. History of Discovery Electromagnetic radiation of wavelengths other than those of visible light were discovered in the early 19th century. The discovery of infrared radiation is ascribed to William Herschel, the astronomer. Herschel published his results in 1800 before the Royal Society of London. Herschel used a glass prism to refract light from the Sun and detected invisible rays that caused heating beyond the redpart of the spectrum, through an increase in the temperature recorded with a thermometer. These "calorific rays" were later termed infrared. In 1801, the German physicist Johann Wilhelm Ritter made the discovery of ultraviolet in an experiment similar to Hershel's, using sunlight and a glass prism. Ritter noted that invisible rays near the violet edge of a solar spectrum dispersed by a triangular prism darkened silver chloride preparations more quickly than did the nearby violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the ultraviolet rays (which at first were called "chemical rays") were capable of causing chemical reactions. In 1862-4 James Clerk Maxwell developed equations for the electromagnetic field which suggested that waves in the field would travel with a speed that was very close to the known speed of light. Maxwell therefore suggested that visible light (as well as invisible infrared and ultraviolet rays by inference) all consisted of propagating disturbances (or radiation) in the electromagnetic field. Radio waves were not first detected from a natural source, but were rather produced deliberately and artificially by the German scientist Heinrich Hertz in 1887, using electrical circuits calculated to produce oscillations at a much lower frequency than that of visible light, following recipes for producing oscillating charges and currents suggested by Maxwell's equations. Hertz also developed ways to detect these waves, and produced and characterized what were later termed radio waves and microwaves. Wilhelm RÜntgen discovered and named X-rays. After experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed a fluorescence on a nearby plate of coated glass. In one month, he discovered the main properties of X-rays that we understand to this day. The last portion of the EM spectrum was discovered associated with radioactivity. Henri Becquerel found that uranium salts caused fogging of an unexposed photographic plate through a covering paper in a manner similar to X-rays, and Marie Curie discovered that only certain elements gave off these rays of energy, soon discovering the intense radiation of radium. The radiation from pitchblende was differentiated into alpha rays (alpha particles) and beta rays (beta Young Ji International School / College
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particles) by Ernest Rutherford through simple experimentation in 1899, but these proved to be charged particulate types of radiation. However, in 1900 the French scientist Paul Villard discovered a third neutrally charged and especially penetrating type of radiation from radium, and after he described it, Rutherford realized it must be yet a third type of radiation, which in 1903 Rutherford named gamma rays. In 1910 British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles, and in 1914 Rutherford and Edward Andrade measured their wavelengths, and found that they were similar to X-rays but with shorter wavelengths and higher frequency, although there is a 'cross-over' between X and gamma rays so it's possible to have X-rays with a higher energy (and hence shorter wavelength) than gamma rays and vice-versa. It is the origin of the ray that differentiates them, gamma rays tend to be a natural phenomena originating from the unstable nucleus of an atom and X-rays are electrically generated (and hence man-made) unless they are as a result of bremsstrahlung X-radiation caused by the interaction of fast moving particles (such as beta particles) colliding with certain materials, usually of higher atomic numbers.
Electromagnetic Spectrum
Electromagnetic spectrum with visible light highlighted
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Legend: Îł = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme-ultraviolet NUV = Near-ultraviolet Visible light (colored bands) NIR = Near-infrared MIR = Moderate-infrared FIR = Far-infrared EHF = Extremely high frequency (microwaves) SHF = Super-high frequency (microwaves) Young Ji International School / College
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UHF = Ultrahigh frequency (radio waves) VHF = Very high frequency (radio) HF = High frequency (radio) MF = Medium frequency (radio) LF = Low frequency (radio) VLF = Very low frequency (radio) VF = Voice frequency ULF = Ultra-low frequency (radio) SLF = Super-low frequency (radio) ELF = Extremely low frequency(radio) In general, EM radiation (the designation 'radiation' excludes static electric and magnetic and near fields) is classified by wavelength into radio, microwave, infrared, visible, ultraviolet, X-rays, and gamma rays. Arbitrary electromagnetic waves can always be expressed by Fourier analysis in terms of sinusoidal monochromatic waves, which in turn can each be classified into these regions of the EMR spectrum. For certain classes of EM waves, the waveform is most usefully treated as random, and then spectral analysis must be done by slightly different mathematical techniques appropriate to random or stochastic processes. In such cases, the individual frequency components are represented in terms of their power content, and the phase information is not preserved. Such a representation is called the power spectral density of the random process. Random electromagnetic radiation requiring this kind of analysis is, for example, encountered in the interior of stars, and in certain other very wideband forms of radiation such as the Zero-Point wave field of the electromagnetic vacuum. The behavior of EM radiation depends on its frequency. Lower frequencies have longer wavelengths, and higher frequencies have shorter wavelengths, and are associated with photons of higher energy. There is no fundamental limit known to these wavelengths or energies, at either end of the spectrum, although photons with energies near the Planck energy or exceeding it (far too high to have ever been observed) will require new physical theories to describe. Sound waves are not electromagnetic radiation. At the lower end of the electromagnetic spectrum, about 20 Hz to about 20 kHz, are frequencies that might be considered in the audio range. However, electromagnetic waves cannot be directly perceived by human ears. Sound waves are the oscillating compression of molecules. To be heard, electromagnetic radiation must be converted to pressure waves of the fluid in which the ear is located (whether the fluid is air, water or something else).
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Radio and microwave heating and currents, and infrared heating When EM radiation interacts with matter, its behavior changes qualitatively as its frequency changes. At radio and microwave frequencies, EMR interacts with matter largely as a bulk collection of charges which are spread out over large numbers of affected atoms. In electrical conductors, such induced bulk movement of charges (electric currents) results in absorption of the EMR, or else separations of charges that cause generation of new EMR (effective reflection of the EMR). An example is absorption or emission of radio waves by antennas, or absorption of microwaves by water or other molecules with an electric dipole moment, as for example inside a microwave oven. These interactions produce either electric currents or heat, or both. Infrared EMR interacts with dipoles present in single molecules, which change as atoms vibrate at the ends of a single chemical bond. For this reason, infrared is reflected by metals (as is most EMR into the ultraviolet) but is absorbed by a wide range of substances, causing them to increase in temperature as the vibrations dissipate as heat. In the same process, bulk substances radiate in the infrared spontaneously.
Reversible and nonreversible molecular changes from visible light As frequency increases into the visible range, photons of EMR have enough energy to change the bond structure of some individual molecules. It is not a coincidence that this happens in the "visible range," as the mechanism of vision involves the change in bonding of a single molecule (retinal) which absorbs light in the rhodopsin the retina of the human eye. Photosynthesis becomes possible in this range as well, for similar reasons, as a single molecule of chlorophyll is excited by a single photon. Animals which detect infrared do not use such single molecule processes, but are forced to make use of small packets of water which change temperature, in an essentially thermal process that involves many photons. For this reason, infrared, microwaves, and radio waves are thought to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation (however, there does remain controversy about possible non-thermal biological damage from low frequency EM radiation, see below). Visible light is able to affect a few molecules with single photons, but usually not in a permanent or damaging way, in the absence of power high enough to increase temperature to damaging levels. However, in plant tissues that carry on photosynthesis, carotenoids act to quench electronically excited chlorophyll produced by visible light in a process called nonphotochemical quenching, in order to prevent reactions which would otherwise interfere with photosynthesis at high light levels. There is also some limited evidence that some reactive
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oxygen species are created by visible light in skin, and that these may have some role in photo aging, in the same manner as ultraviolet a does.
Molecular damage from ultraviolet As a photon interacts with single atoms and molecules, the effect depends on the amount of energy the photon carries. As frequency increases beyond visible into the ultraviolet, photons now carry enough energy (about three electron volts or more) to excite certain doubly bonded molecules into permanent chemical rearrangement. If these molecules are biological molecules in DNA, this causes lasting damage. DNA is also indirectly damaged by reactive oxygen species produced by ultraviolet A (UVA), which has energy too low to damage DNA directly. This is why ultraviolet at all wavelengths can damage DNA, and is capable of causing cancer, and (for UVB) skin burns (sunburn) which are far worse than would be produced by simple heating (temperature increase) effects. This property of causing molecular damage that is far out of proportion to all temperature-changing (i.e., heating) effects, is characteristic of all EMR with frequencies at the visible light range and above. These properties of high-frequency EMR are due to quantum effects which cause permanent damage to materials and tissues at the single molecular level.
Ionization and extreme types of molecular damage from X-rays and gamma rays At the higher end of the ultraviolet range, the energy of photons becomes large enough to impart enough energy to electrons to cause them to be liberated from the atom, in a process called photoionization. The energy required for this is always larger than about 10 electron volts (eV) corresponding with wavelengths smaller than 124 nm (some sources suggest a more realistic cutoff of 33 eV, which is the energy required to ionize water). This high end of the ultraviolet spectrum with energies in the approximate ionization range, is sometimes called "extreme UV." (Most of this is filtered by the Earth's atmosphere). Electromagnetic radiation composed of photons that carry minimum-ionization energy, or more, (which includes the entire spectrum with shorter wavelengths), is therefore termed ionizing radiation. (There are also many other kinds of ionizing radiation made of non-EM particles). Electromagnetic-type ionizing radiation extends from the extreme ultraviolet to all higher frequencies and shorter wavelengths, which means that all X-rays and gamma rays are ionizing radiation. These are capable of the most severe types of molecular damage, which can happen in biology to any type of biomolecule, including mutation and cancer, and often at great depths from the skin, since the higher end of the X-ray spectrum, and all of the gamma ray spectrum, Young Ji International School / College
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are penetrating to matter. It is this type of damage which causes these types of radiation to be especially carefully monitored, due to their hazard, even at comparatively low-energies, to all living organisms.
ozone layer, shortwave radio, sky wave and ionosphere
Rough plot of Earth's atmospheric absorption and scattering (or opacity) of various wavelengthsof electromagnetic radiation Most electromagnetic waves of higher frequency than visible light (UV and X-rays) are blocked by absorption first from molecular nitrogen, and then (for wavelengths in the upper UV) from the electronic excitation of dioxygen, and finally ozone at the mid-range of UV. Only 30% of the Sun's ultraviolet light reaches the ground, and almost all of this is at the end of the UV spectrum near visible light, which is not blocked by ozone, and is transmitted well. Visible light is also well transmitted in air, as it is not energetic enough to excite nitrogen, oxygen, or ozone, but too energetic to excite molecular vibrational frequencies of water molecules in air. Below visible light, a number of absorption bands in the infrared are due to modes of vibrational excitation in water vapor. However, at energies too low to excite water vapor the atmosphere becomes transparent again, allowing free transmission of most microwave and radio waves. Finally, at radio wavelengths longer than 10 meters or so (about 30 MHz), the air in the lower atmosphere remains transparent to radio, but plasma in certain layers of the ionosphere of upper Earth atmosphere begins to interact with radio waves. This property allows some longer wavelengths (100 meters or 3 MHz) to be reflected and results in farther shortwave radio than can be obtained by line-of-sight. However, certain ionospheric effects begin to block incoming radio waves from space, when their frequency is less than about 10 MHz (wavelength longer than about 30 meters). Young Ji International School / College
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Radio waves When EM radiation at the frequencies for which it is referred to as "radio waves" impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of the conductor by moving the electrons of the conducting material in correlated bunches of charge. Such effects can cover macroscopic distances in conductors (including as radio antennas), since the wavelength of radiowaves is long, by human scales. Radio waves thus have the most overtly "wave-like" characteristics of all the types of EMR, since their waves are so long. Natural sources produce EM radiation across the spectrum. EM radiation with a wavelength between approximately 400 nm nd 700 nm is directly detected by the human eye and perceived as visible light. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light, especially when visibility to humans is not relevant.
Thermal radiation and electromagnetic radiation as a form of heat The basic structure of matter involves charged particles bound together in many different ways. When electromagnetic radiation is incident on matter, it causes the charged particles to oscillate and gain energy. The ultimate fate of this energy depends on the situation. It could be immediately re-radiated and appear as scattered, reflected, or transmitted radiation. It may also get dissipated into other microscopic motions within the matter, coming to thermal equilibrium and manifesting itself as thermal energy in the material. With a few exceptions related to high-energy photons (such asfluorescence, harmonic generation, photochemical reactions, the photovoltaic effect for ionizing radiations at far ultraviolet, X-ray, and gamma radiation), absorbed electromagnetic radiation simply deposits its energy by heating the material. This happens both for infrared, microwave, and radio wave radiation. Intense radio waves can thermally burn living tissue and can cook food. In addition to infrared lasers, sufficiently intense visible and ultraviolet lasers can also easily set paper afire. Ionizing electromagnetic radiation creates high-speed electrons in a material and breaks chemical bonds, but after these electrons collide many times with other atoms in the material eventually most of the energy is downgraded to thermal energy; this whole process happens in a tiny fraction of a second. This process makes ionizing radiation far more dangerous per unit of energy than non-ionizing radiation. This caveat also applies to the ultraviolet (UV) spectrum, even though almost all of it is not ionizing, because UV can damage molecules due to electronic excitation which is far greater per unit energy than heating effects produce. Infrared radiation in the spectral distribution of a black body is usually considered a form of heat, since it has an equivalent temperature, and is associated with an entropy change per unit of Young Ji International School / College
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thermal energy. However, the word "heat" is a highly technical term in physics and thermodynamics, and is often confused with thermal energy. Any type of electromagnetic energy can be transformed into thermal energy in interaction with matter. Thus, any electromagnetic radiation can "heat" (in the sense of increase the thermal energy termperature of) a material, when it is absorbed. The inverse or time-reversed process of absorption is responsible for thermal radiation. Much of the thermal energy in matter consists of random motion of charged particles, and this energy can be radiated away from the matter. The resulting radiation may subsequently be absorbed by another piece of matter, with the deposited energy heating the material. Thermal radiation is an important mechanism of heat transfer. The electromagnetic radiation in an opaque cavity at thermal equilibrium is effectively a form of thermal energy, having maximum Electromagnetic radiation and health and Mobile phone radiation and health The effects of electromagnetic radiation upon living cells, including those in humans, depends upon the power and the frequency of the radiation. For low-frequency radiation (radio waves to visible light) the best-understood effects are those due to radiation power alone, acting through the effect of simple heating when the radiation is absorbed by the cell. For these thermal effects, the frequency of the radiation is important only as it affects radiation penetration into the organism (for example microwaves penetrate better than infrared). Initially, it was believed that low frequency fields that were too weak to cause significant heating could not possibly have any biological effect. Despite this opinion among researchers, evidence has accumulated that supports the existence of complex biological effects of weaker non-thermal electromagnetic fields, (including weak ELF magnetic fields, although the latter does not strictly qualify as EM radiationand modulated RF and microwave fields.Fundamental mechanisms of the interaction between biological material and electromagnetic fields at non-thermal levels are not fully understood. Bio electromagnetics is the study of these interactions and effects. The World Health Organization has classified radiofrequency electromagnetic radiation as a possible group 2b carcinogen. This group contains possible carcinogens with weaker evidence, at the same level as coffee and automobile exhaust. For example, there have been a number of epidemiological studies of looking for a relationship between cell phone use and brain cancer development, which have been largely inconclusive, save to demonstrate that the effect, if it exists, cannot be a large one. At higher frequencies (visible and beyond), the effects of individual photons of the radiation begin to become important, as these now have enough energy individually directly or indirectly Young Ji International School / College
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to damage biological molecules. All frequencies of UV radiation have been classed as Group 1 carcinogens by the World Health Organization. Ultraviolet radiation from sun exposure is the primary cause of skin cancer. Thus, at UV frequencies and higher (and probably somewhat also in the visible range),electromagnetic radiation does far more damage to biological systems than simple heating predicts. This is most obvious in the "far" (or "extreme") ultraviolet, and also X-ray and gamma radiation, are referred to as ionizing radiation due to the ability of photons of this radiation to produce ions and free radicals in materials (including living tissue). Since such radiation can produce severe damage to life at powers that produce very little heating, it is considered far more dangerous (in terms of damage-produced per unit of energy, or power) than the rest of the electromagnetic spectrum. electromagnetic wave equation Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. Inspection of Maxwell's equations without sources (charges or currents) results in, along with the possibility of nothing happening, nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell's equations in free space:
where is a vector differential operator One solution,
is trivial. For a more useful solution, we utilize vector identities, which work for any vector, as follows:
To see how we can use this, take the curl of equation (2):
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Evaluating the left hand side: where we simplified the above by using equation (1). Evaluate the right hand side:
Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely
Applying a similar pattern results in similar differential equation for the magnetic field:
These differential equations are equivalent to the wave equation:
where c0 is the speed of the wave in free space and f describes a displacement Or more simply: where
is d'Alembertian:
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Notice that, in the case of the electric and magnetic fields, the speed is:
This is the speed of light in vacuum. Maxwell's equations unified the vacuum permittivity , the vacuum permeability , and the speed of light itself, c0. This relationship had been discovered by Wilhelm Eduard Weber and Rudolf Kohlrausch prior to the development of Maxwell's electrodynamics, however Maxwell was the first to produce a field theory consistent with waves traveling at the speed of light. But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. Let's consider a generic vector wave for the electric field.
Here,
is the constant amplitude,
is any second differentiable function,
the direction of propagation, and is a position vector. We observe that generic solution to the wave equation. In other words
for a generic wave traveling in the
is a unit vector in is a
direction.
This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?
The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.
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The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of . Not only are the electric and magnetic field waves in the far-field traveling at the speed of light, but they always have a special restricted orientation and proportional magnitudes, , which can be seen immediately from the Pointing vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as . Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are always in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order special derivatives of the wave solution, while the timederivative on the other side of the equations, which gives the other field, is first order in time, resulting in the same phase shift for both fields in each mathematical operation. From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as polarization. On a quantum level, it is described as photon polarization. The direction of the polarization is defined as the direction of the electric field. More general forms of the second-order wave equations given above are available, allowing for both non-vacuum propagation media and sources. A great many competing derivations exist, all with varying levels of approximation and intended applications. One very general example is a form of the electric field equation, which was factorized into a pair of explicitly directional wave equations, and then efficiently reduced into a single uni-directional wave equation by means of a simple slow-evolution approximation.
ELECTROMAGNETIC WAVES Worksheet 1. What is the source of all electromagnetic waves? 2. What determines the frequency of an electromagnetic wave? 3. What is the wavelength of an electromagnetic wave having a frequency of 1 hertz? Of 100,000 hertz? (remember - you know thespeed of light) 4. Distinguish between AM and FM radio waves. 5. Are the wavelengths of radio waves longer or shorter than those detectable by your eyes? Young Ji International School / College
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6. Use the idea of resonance to explain how microwave ovens are able to cook food. 7. About how many more times greater is the frequency of a 100- megahertz-carrier radio wave than a medium-range sound wave? (Remember, you know the frequencies of sound that humans can hear.) 8. Electromagnetic radiation has been detected with a frequency as low as 0.01 hertz. What is the wavelength of such a wave? What type of wave might this be? 9. What is the wavelength of the carrier wave received at FM station 100 megahertz on your radio dial? 10. What is the frequency of an electromagnetic wave that has a wavelength of 300,000 kilometers? 11. If you charge a comb by rubbing through your hair, and then shake it up and down, are you producing electromagnetic waves? In theory, could you shake the comb to produce visible light? 12. If all objects radiate energy, why can't we see objects in a darkened room? 13. An ordinary light bulb gives off visible white light. If you were moving toward it at nearly the speed of light, it would appear to be emitting X rays, while if you moving away from it at the same high speed, it would appear to be emitting radio waves. This is an example of what wave phenomenon? In both cases you could not see the bulb‘s ―light‖ with your eyes. Why? The ozone layer or ozone shield refers to a region of Earth's stratosphere that absorbs most of the Sun's UV radiation. It contains high concentrations of ozone (O3) relative to other parts of the atmosphere, although it is still very small relative to other gases in the stratosphere. The ozone layer contains less than ten parts per million of ozone, while the average ozone concentration in Earth's atmosphere as a whole is only about 0.3 parts per million. The ozone layer is mainly found in the lower portion of the stratosphere, from approximately 20 to 30 kilometres (12 to 19 mi) above Earth, though the thickness varies seasonally and geographically. The ozone layer was discovered in 1913 by the French physicists Charles Fabry and Henri Buisson. Its properties were explored in detail by the British meteorologist G. M. B. Dobson, who developed a simple spectrophotometer (the Dobsonmeter) that could be used to measure stratospheric ozone from the ground. Between 1928 and 1958 Dobson established a worldwide network of ozone monitoring stations, which continue to operate to this day. The "Dobson unit", a convenient measure of the amount of ozone overhead, is named in his honor. The ozone layer absorbs 97–99% of the Sun's medium-frequency ultraviolet light (from about 200 nm to 315 nm wavelength), which otherwise would potentially damage exposed life forms near the surface. United Nations General Assembly has designated September 16 as the International Day for the Preservation of the Ozone Layer. Young Ji International School / College
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The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases. Solar radiation at the frequencies of visible light largely passes through the atmosphere to warm the planetary surface, which then emits this energy at the lower frequencies of infrared thermal radiation. Infrared radiation is absorbed by greenhouse gases, which in turn re-radiate much of the energy to the surface and lower atmosphere. The mechanism is named after the effect of solar radiation passing through glass and warming a greenhouse, but the way it retains heat is fundamentally different as a greenhouse works by reducing airflow, isolating the warm air inside the structure so that heat is not lost by convection. If an ideal thermally conductive blackbody were the same distance from the Sun as the Earth is, it would have a temperature of about 5.3 °C. However, since the Earth reflects about 30% of the incoming sunlight, this idealized planet's effective temperature (the temperature of a blackbody that would emit the same amount of radiation) would be about −18 °C. The surface temperature of this hypothetical planet is 33 °C below Earth's actual surface temperature of approximately 14 °C. The mechanism that produces this difference between the actual surface temperature and the effective temperature is due to the atmosphere and is known as the greenhouse effect.
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Earth‘s natural greenhouse effect makes life as we know it possible. However, human activities, primarily the burning of fossil fuels and clearing of forests, have intensified the natural greenhouse effect, causing global warming.
A representation of the exchanges of energy between the source (the Sun), the Earth's surface, the Earth's atmosphere, and the ultimate sink outer space. The ability of the atmosphere to capture and recycle energy emitted by the Earth surface is the defining characteristic of the greenhouse effect.
The ionosphere is a region of the upper atmosphere, from about 85 km (53 mi) to 600 km (370 mi) altitude, and includes the thermosphere and parts of the mesosphere and exosphere. It is distinguished because it is ionized by solar radiation. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere. It has practical importance because, among other functions, it influences radio propagation to distant places on the Earth.
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Astronomy is a natural science which is the study of celestial objects (such as stars, galaxies, planets, moons, and nebulae), the physics, chemistry, and evolution of such objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explosions, gamma ray bursts, and cosmic microwave background radiation. A related but distinct subject, cosmology, is concerned with studying the universe as a whole. Astronomy is one of the oldest sciences. Prehistoric cultures have left astronomical artifacts such as the Egyptian monuments and Nubian monuments, and early civilizations such as the Babylonians, Greeks, Chinese, Indians, Iranians and Maya performed methodical observations of the night sky. However, the invention of the telescope was required before astronomy was able to develop into a modern science. Historically, astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy and the making of calendars, but professional astronomy is nowadays often considered to be synonymous with astrophysics. Young Ji International School / College
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During the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, which is then analyzed using basic principles of physics. Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can still play an active role, especially in the discovery and observation of transient phenomena and Amateur astronomers have made and contributed to many important astronomical discoveries. Astronomy is a natural science which is the study of celestial objects (such as stars, galaxies, planets, moons, and nebulae), the physics, chemistry, and evolution of such objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explosions, gamma ray bursts, and cosmic microwave background radiation. A related but distinct subject, cosmology, is concerned with studying the universe as a whole. Astronomy is one of the oldest sciences. Prehistoric cultures have left astronomical artifacts such as the Egyptian monuments and Nubian monuments, and early civilizations such as the Babylonians, Greeks, Chinese, Indians, Iranians and Maya performed methodical observations of the night sky. However, the invention of the telescope was required before astronomy was able to develop into a modern science. Historically, astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy and the making of calendars, but professional astronomy is nowadays often considered to be synonymous with astrophysics. During the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, which is then analyzed using basic principles of physics. Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can still play an active role, especially in the discovery and observation of transient phenomena and Amateur astronomers have made and contributed to many important astronomical discoveries.
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Atmosphere Activity 1. Which layer of the Earth‘s atmosphere is the lowest? 2. Which layer of the Earth‘s atmosphere is the highest?
3. At what height is the Ozone Layer? 4. Which layer contains the largest concentration of water vapour? 5. At what height is the Aurora? 6. What Element makes up 78% of the Earths lower atmosphere? 7. What 2 elements made up the Earths ‗first atmosphere‘? 8. What element was missing from the Earths ‗second atmosphere‘? 9. During the second atmosphere why didn‘t the Earth freeze? 10. Global Warming a. Explain why we call it the ‗Greenhouse Effect‘ b. What effects on Earth does Global Warming have? c. What is the name of the Protocol that many countries signed to combat Global warming?
Module (Lesson: Optics)
Optics includes study of dispersion of light. Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually Young Ji International School / College
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describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics. When considering light's particle-like properties, the light is modelled as a collection of particles called "photons". Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, and medicine(particularly ophthalmology and optometry). Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Classical Optics Classical optics is divided into two main branches: geometrical optics and physical optics. In geometrical, or ray optics, light is considered to travel in straight lines, and in physical, or wave optics, light is considered to be an electromagnetic wave. Geometrical optics can be viewed as an approximation of physical optics which can be applied when the wavelength of the light used is much smaller than the size of the optical elements or system being modelled.
Geometrical optics
Geometry of reflection and refraction of light rays Young Ji International School / College
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Geometrical optics, or ray optics, describes the propagation of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media. These laws were discovered empirically as far back as 984 AD and have been used in the design of optical components and instruments from then until the present day. They can be summarized as follows: When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray. The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence. The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of refraction divided by the sine of the angle of incidence is a constant.
where n is a constant for any two materials and a given colour of light. It is known as the refractive index. The laws of reflection and refraction can be derived from Fermat's principle which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. Approximations Geometric optics is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications. Reflections
Diagram of specular reflection Young Ji International School / College
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Reflections can be divided into two types: specular reflection and diffuse reflection. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for production of reflected images that can be associated with an actual (real) or extrapolated (virtual) location in space. Diffuse reflection describes opaque, non limpid materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law, which describes surfaces that have equal luminance when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection. In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the surface normal, a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal. This is known as the Law of Reflection. For flat mirrors, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror images are parity inverted, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflectors retro reflect light, producing reflected rays that travel back in the direction from which the incident rays came. Mirrors with curved surfaces can be modelled by ray-tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common focus. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration. Curved mirrors can form images with magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.
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Refractions
Illustration of Snell's Law for the case n1 < n2, such as air/water interface Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction and another medium with index of refraction . In such situations, Snell's Law describes the resulting deflection of the light ray:
where and are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:
where
and
are the wave velocities through the respective media.
Various consequences of Snell's Law include the fact that for light rays travelling from a material with a high index of refraction to a material with a low index of refraction, it is possible for the interaction with the interface to result in zero transmission. This phenomenon is calledtotal internal reflection and allows for fibre optics technology. As light signals travel down a fibre optic cable, it undergoes total internal reflection allowing for essentially no light lost over the length of the cable. It is also possible to produce polarised light rays using a combination of reflection and refraction: When a refracted ray and the reflected ray form a right angle, the reflected ray has the property of "plane polarization". The angle of incidence required for such a scenario is known as Brewster's angle. Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion
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spectra that appear as rainbows. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. Some media have an index of refraction which varies gradually with position and, thus, light rays curve through the medium rather than travel in straight lines. This effect is what is responsible for mirages seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Material that has a varying index of refraction is called a gradient-index (GRIN) material and has many useful properties used in modern optical scanning technologies including photocopiersand scanners. The phenomenon is studied in the field of gradient-index optics.
A ray tracing diagram for a converging lens. A device which produces converging or diverging light rays due to refraction is known as a lens. Thin lenses produce focal points on either side that can be modelled using the lens maker's equation. In general, two types of lenses exist: convex lenses, which cause parallel light rays to converge, and concave lenses, which cause parallel light rays to diverge. The detailed prediction of how images are produced by these lenses can be made using ray-tracing similar to curved mirrors. Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length ( ) and object distance ( ):
where is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens. The focal length f is considered negative for concave lenses.
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Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an upright virtual image one focal length from the lens, on the same side of the lens that the parallel rays are approaching on. Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal length, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. Likewise, the magnification of a lens is given by
where the negative sign is given, by convention, to indicate an upright object for positive values and an inverted object for negative values. Similar to mirrors, upright images produced by single lenses are virtual while inverted images are real. Lenses suffer from aberrations that distort images and focal points. These are due to both to geometrical imperfections and due to the changing index of refraction for different wavelengths of light (chromatic aberration).
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Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f/2) has a doublesize, virtual and upright image.
Physical optics In physical optics, light is considered to propagate as a wave. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The speed of lightwaves in air is approximately 3.0×108 m/s (exactly 299,792,458 m/s in vacuum). The wavelength of visible light waves varies between 400 and 700 nm, but the term "light" is also often applied toinfrared (0.7–300 μm) and ultraviolet radiation (10–400 nm). The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated. The existence of electromagnetic waves was predicted in 1865 by Maxwell's equations. These waves propagate at the speed of light and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered.
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Modelling and design of optical systems using physical optics Many simplified approximations are available for analyzing and designing optical systems. Most of these use a single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors. The Huygensâ&#x20AC;&#x201C; Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wave front generates a secondary spherical wave front, which Fresnel combined with the principle of superposition of waves. The Kirchhoff diffraction equation, which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygensâ&#x20AC;&#x201C;Fresnel principle can be found in the sections on diffraction and Fraunhofer diffraction. More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with the detailed interaction of light with materials where the interaction depends on their electric and magnetic properties. For instance, the behavior of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarized light. Numerical modeling techniques such as the finite element method, the boundary element method and the transmission-line matrix method can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions. All of the results from geometrical optics can be recovered using the techniques of Fourier optics which apply many of the same mathematical and analytical techniques used in acoustic engineeringand signal processing. Gaussian beam propagation is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics. Superposition and interference
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In the absence of nonlinear effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are in phase, both the wave crests and wave troughs align. This results in constructive interference and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice-versa. This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect.[49]
combined waveform wave 1 wave 2 Two waves in phase
Two waves 180° out of phase
When oil or fuel is spilled, colourful patterns are formed by thin-film interference. Since the Huygensâ&#x20AC;&#x201C;Fresnel principle states that every point of a wave front is associated with the production of a new disturbance, it is possible for a wave front to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns. Interferometry is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolutions. The Michelson interferometer was a famous instrument which used interference effects to accurately measure the speed of light. The appearance of thin films and coatings is directly affected by interference effects. Antireflective coatings use destructive interference to reduce the reflectivity of the Young Ji International School / College
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surfaces they coat, and can be used to minimize glare and unwanted reflections. The simplest case is a single layer with thickness one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength. Constructive interference in thin films can create strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirrors, interference filters, heat reflectors, and filters for color separation in color television cameras. This interference effect is also what causes the colorful rainbow patterns seen in oil slicks. Diffraction and optical resolution
Diffraction on two slits separated by distance . The bright fringes occur along lines where black lines intersect with black lines and white lines intersect with white lines. These fringes are separated by angle and are numbered as order .
Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by Francesco Maria Grimaldi, who also coined the term from the Latin diffringere, 'to break into pieces'. Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in Newton's rings while James Gregory recorded his observations of diffraction patterns from bird feathers. The first physical optics model of diffraction that relied on the Huygensâ&#x20AC;&#x201C;Fresnel principle was developed in 1803 by Thomas Young in his interference experiments with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles. In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction. Young Ji International School / College
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The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (Îť). In general, the equation takes the form
where is the separation between two wavefront sources (in the case of Young's experiments, it was two slits), is the angular separation between the central fringe and the th order fringe, where the central maximum is . This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a diffraction grating that contains a large number of slits at equal spacing. More complicated models of diffraction require working with the mathematics of Fresnel or Fraunhofer diffraction. X-ray diffraction makes use of the fact that atoms in a crystal have regular spacing at distances that are on the order of one angstrom. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to Bragg reflection, with the associated bright spots occurring in unique patterns and being twice the spacing between atoms. Diffraction effects limit the ability for an optical detector to optically resolve separate light sources. In general, light that is passing through an aperture will experience diffraction and the best images that can be created (as described in diffraction-limited optics) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and the central bright lobe as an Airy disk. The size of such a disk is given by
where θ is the angular resolution, Ν is the wavelength of the light, and D is the diameter of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved .Rayleigh defined the somewhat arbitrary "Rayleigh criterion" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution. Interferometry, with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.
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For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric scattering and dispersion which cause stars to twinkle. Astronomers refer to this effect as the quality of astronomical seeing. Techniques known as adaptive optics have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit. Dispersion and scattering
Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least. Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is Thomson scattering which occurs when electromagnetic waves are deflected by single particles. In the limit of Thompson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to Compton scattering which is frequency-dependent and strictly a quantum mechanical process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as Rayleigh scattering while the similar process for scattering by particles that are similar or larger in wavelength is known as Mie scattering with the Tyndall effect being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo Raman scattering, wherein the frequency changes due to excitation of the atoms and molecules. Brillouin scattering occurs when the frequency of light changes due to local changes with time and movements of a dense material. Dispersion occurs when different frequencies of light have different phase velocities, due either to material properties (material dispersion) or to the geometry of an optical waveguide (waveguide dispersion). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all dielectric materials, in wavelength ranges where the material does not absorb light.[61] In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion". Young Ji International School / College
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The separation of colours by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n). Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow pattern.
Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity). Material dispersion is often characterized by the Abbe number, which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the propagation constant. Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:
where is the group velocity.[62] For a uniform medium, the group velocity is
where n is the index of refraction and c is the speed of light in a vacuum.[63] This gives a simpler form for the dispersion delay parameter:
If D is less than zero, the medium is said to have positive dispersion or normal dispersion. If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more Young Ji International School / College
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than the lower frequency components. The pulse therefore becomes positively chirped, or upchirped, increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time. The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fibres, since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal. Polarization Polarization is a general property of waves that describes the orientation of their oscillations. For transverse waves such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction (linear polarization), or the oscillation direction may rotate as the wave travels (circular or elliptical polarization). Circularly polarized waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's chirality. The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a Lissajous figurethat describes the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.
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Linear
Circular
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Elliptical polarization
In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarization. The direction of this line depends on the relative amplitudes of the two components. In the middle figure, the two orthogonal components have the same amplitudes and are 90째 out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the x component can be 90째 ahead of the y component or it can be 90째 behind the y component. In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization. The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization. In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90째, the polarization is called elliptical polarizationbecause the electric vector traces out an ellipse in the plane (the polarization ellipse). This is shown in the above figure on the right. Detailed mathematics of polarization is done using Jones calculusand is characterized by the Stokes parameters. Changing polarization Young Ji International School / College
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Media that have different indexes of refraction for different polarization modes are called birefringent. Well known manifestations of this effect appear in optical wave plates/retarders (linear modes) and in Faraday rotation/optical rotation (circular modes). If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. For example, this is the case with macroscopic crystals of calcite, which present the viewer with two offset, orthogonally polarized images of whatever is viewed through them. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism, often gives rise to bright colours and rainbow-like effects. In mineralogy, such properties, known as pleochroism, are frequently exploited for the purpose of identifying minerals using polarization microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress, a phenomenon which is the basis of photoelasticity. Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic polarization rotators which use total internal reflection in a prism set designed for efficient collinear transmission.
A polarizer changing the orientation of linearly polarized light. In this picture, θ1 – θ0 = θi. Media that reduce the amplitude of certain polarization modes are called dichroic. with devices that block nearly all of the radiation in one mode known as polarizing filters or simply "polarisers". Malus' law, which is named after Étienne-Louis Malus, says that when a perfect polarizer is placed in a linear polarized beam of light, the intensity, I, of the light that passes through is given by where Young Ji International School / College
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I0 is the initial intensity, and θi is the angle between the light's initial polarization direction and the axis of the polariser. A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of is 1/2, the transmission coefficient becomes
In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarizers but considerably higher (>49.9%) for some birefringent prism types. In addition to birefringence and dichroism in extended media, polarization effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle. When light reflects from a thin film on a surface, interference between the reflections from the film's surfaces can produce polarization in the reflected and transmitted light. Natural light
The effects of a polarizing filter on the sky in a photograph. Left picture is taken without polarizer. For the right picture, filter was adjusted to eliminate certain polarizations of the scattered blue light from the sky. Most sources of electromagnetic radiation contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be correlated, in which case the light is said to be unpolarized. If there is partial correlation between the emitters, the light is partially polarized. If the polarization is consistent across the spectrum of Young Ji International School / College
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the source, partially polarized light can be described as a superposition of a completely unpolarized component, and a completely polarized one. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.[43] Light reflected by shiny transparent materials is partly or fully polarized, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Ă&#x2030;tienneLouis Malus to make the measurements that allowed for his development of the first mathematical models for polarized light. Polarization occurs when light is scattered in the atmosphere. The scattered light produces the brightness and color in clear skies. This partial polarization of scattered light can be taken advantage of using polarizing filters to darken the sky in photographs. Optical polarization is principally of importance in chemistry due to circular dichroism and optical rotation ("circular birefringence") exhibited by optically active (chiral) molecules. Optical physics and Optical engineering Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics, quantum optics, deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as photomultipliers and channeltrons, respond to individual photons. Electronic image sensors, such as CCDs, exhibit shot noise corresponding to the statistics of individual photon events. Light-emitting diodes and photovoltaic cells, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics. Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics and metal materials. Other research focuses on the phenomenology of electromagnetic waves as in singular optics, non-imaging optics, non-linear optics, statistical optics, and radiometry. Additionally, computer engineers have taken an interest in optics, machine, and photonic computing as possible components of the "next generation" of computers. Today, the pure science of optics is called optical science or optical physics to distinguish it from applied optical sciences, which are referred to as optical engineering. Prominent subfields of optical engineering include illumination engineering, photonics, and optoelectronics with practical applications like lens design, fabrication and testing of optical components, and image processing. Some of these fields overlap, with nebulous boundaries between the subjects terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology. Young Ji International School / College
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Lasers
Experiments such as this one with high-power lasers are part of the modern optics research. A laser is a device that emits light (electromagnetic radiation) through a process called stimulated emission. The term laser is an acronym for Light Amplification by Stimulated Emission of Radiation. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow,low-divergence beam, or can be converted into one with the help of optical components such as lenses. Because the microwave equivalent of the laser, themaser, was developed first, devices that emit microwave and radio frequencies are usually called masers.
VLTâ&#x20AC;&#x2DC;s laser guided star. The first working laser was demonstrated on 16 May 1960 by Theodore Maiman at Hughes Research Laboratories. When first invented, they were called "a solution looking for a problem". Since then, lasers have become a multi-billion dollar industry, finding utility in thousands of highly varied applications. The first application of lasers visible in the daily lives of the general population was the supermarket barcodescanner, introduced in 1974. The laserdisc player, introduced in 1978, was the first successful consumer product to include a laser, but the compact disc player was the first laser-equipped device to become truly common in consumers' homes, beginning in 1982. These optical storage devices use a semiconductor laserless than a millimetre Young Ji International School / College
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wide to scan the surface of the disc for data retrieval. Fibre-optic communication relies on lasers to transmit large amounts of information at the speed of light. Other common applications of lasers include laser printers and laser pointers. Lasers are used in medicine in areas such as bloodless surgery, laser eye surgery, and laser capture microdissection and in military applications such as missile defense systems, electro-optical countermeasures (EOCM), and lidar. Lasers are also used in holograms, bubble grams, laser light shows, and laser hair removal.
Kapitsaâ&#x20AC;&#x201C;Dirac effect The Kapitsaâ&#x20AC;&#x201C;Dirac effect causes beams of particles to diffract as the result of meeting a standing wave of light. Light can be used to position matter using various phenomena.
Applications Optics is part of everyday life. The ubiquity of visual systems in biology indicates the central role optics plays as the science of one of the five senses. Many people benefit from eyeglasses or contact lenses, and optics are integral to the functioning of many consumer goods including cameras. Rainbows and mirages are examples of optical phenomena. Optical communication provides the backbone for both the Internet and modern telephony. Human eye
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Model of a human eye. Features mentioned in this article are 3. ciliary muscle, 6. pupil, 8. cornea, 10. lens cortex, 22. optic nerve, 26. fovea, 30. retina
Human eye and Photometry (optics) The human eye functions by focusing light onto a layer of photoreceptor cells called the retina, which forms the inner lining of the back of the eye. The focusing is accomplished by a series of transparent media. Light entering the eye passes first through the cornea, which provides much of the eye's optical power. The light then continues through the fluid just behind the corneaâ&#x20AC;&#x201D; the anterior chamber, then passes through the pupil. The light then passes through the lens, which focuses the light further and allows adjustment of focus. The light then passes through the main body of fluid in the eyeâ&#x20AC;&#x201D;the vitreous humor, and reaches the retina. The cells in the retina line the back of the eye, except for where the optic nerve exits; this results in a blind spot. There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light. Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for black-and-white vision. Rod cells are not present on the fovea, the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for peripheral vision. In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of color and photonic. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most night vision is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells. Ciliary muscles around the lens allow the eye's focus to be adjusted. This process is known as accommodation. The near point and far point define the nearest and farthest distances from the eye at which an object can be brought into sharp focus. For a person with normal vision, the far point is located at infinity. The near point's location depends on how much the muscles can increase the curvature of the lens, and how inflexible the lens has become with age. Optometrists, ophthalmologists, and opticians usually consider an appropriate near point to be closer than normal reading distanceâ&#x20AC;&#x201D;approximately 25 cm. Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as presbyopia. Similarly, Young Ji International School / College
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people suffering from hyperopia cannot decrease the focal length of their lens enough to allow for nearby objects to be imaged on their retina. Conversely, people who cannot increase the focal length of their lens enough to allow for distant objects to be imaged on the retina suffer from myopia and have a far point that is considerably closer than infinity. A condition known as astigmatism results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images. All of these conditions can be corrected using corrective lenses. For presbyopia and hyperopia, a converging lens provides the extra curvature necessary to bring the near point closer to the eye while for myopia a diverging lens provides the curvature necessary to send the far point to infinity. Astigmatism is corrected with a cylindrical surface lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea. The optical power of corrective lenses is measured in diopters, a value equal to the reciprocal of the focal length measured in meters; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism. Visual effects
For the visual effects used in film, video, and computer graphics, see visual effects.
The Ponzo Illusion relies on the fact that parallel lines appear to converge as they approach infinity. Optical illusions (also called visual illusions) are characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a percept that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. Young Ji International School / College
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brightness, tilt, color, movement), and cognitive illusions where the eye and brain make unconscious inferences. Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the Ames room, Hering,Müller-Lyer, Orbison, Ponzo, Sander, and Wundt illusions all rely on the suggestion of the appearance of distance by using converging and diverging lines, in the same way that parallel light rays (or indeed any set of parallel lines) appear to converge at a vanishing point at infinity in two-dimensionally rendered images with artistic perspective. This suggestion is also responsible for the famous moon illusion where the moon, despite having essentially the same angular size, appears much larger near the horizon than it does at zenith. This illusion so confounded Ptolemy that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, Optics. Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the café wall, Ehrenstein, Fraser spiral, Poggendorff, and Zöllner illusions. Related, but not strictly illusions, are patterns that occur due to the superimposition of periodic structures. For exampletransparent tissues with a grid structure produce shapes known as moiré patterns, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré patterns. Optical instruments
Illustrations of various optical instruments from the 1728 Cyclopedia
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Optical instruments Single lenses have a variety of applications including photographic lenses, corrective lenses, and magnifying glasses while single mirrors are used in parabolic reflectors and rear-view mirrors. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a periscope is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the microscope and the telescope which were both invented by the Dutch in the late 16th century. Microscopes were first developed with just two lenses: an objective lens and an eyepiece. The objective lens is essentially a magnifying glass and was designed with a very small focal length while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the conservation of energy and the spreading of light rays over a larger surface area. Modern microscopes, known as compound microscopes have many lenses in them (typically four) to optimize the functionality and enhance image stability. A slightly different variety of microscope, the comparison microscope, looks at side-by-side images to produce a stereoscopic binocular view that appears three dimensional when used by humans. The first telescopes, called refracting telescopes were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification. Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are reflecting telescopes, that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.
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Photography Science of photography
Photograph taken with aperture f/32
Photograph taken with aperture f/5 The optics of photography involves both lenses and the medium in which the electromagnetic radiation is recorded, whether it be a plate,film, or charge-coupled device. Photographers must consider the reciprocity of the camera and the shot which is summarized by the relation Exposure â&#x2C6;? ApertureArea Ă&#x2014; ExposureTime Ă&#x2014; SceneLuminance In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the Sunny 16 rule which gives a rough estimate for the settings needed to estimate the proper exposure in daylight. A camera's aperture is measured by a unitless number called the f-number or f-stop, f/#, often notated as , and given by
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where is the focal length, and is the diameter of the entrance pupil. By convention, "f/#" is treated as a single symbol, and specific values of f/# are written by replacing the number sign with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a zoom lens, this can be done by simply adjusting the lens). Higher f-numbers also have a larger depth of field due to the lens approaching the limit of a pinhole camera which is able to focus all images perfectly, regardless of distance, but requires very long exposure times. The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:
Normal lens: angle of view of about 50° (called normal because this angle considered roughly equivalent to human vision) and a focal length approximately equal to the diagonal of the film or sensor. Wide-angle lens: angle of view wider than 60° and focal length shorter than a normal lens. Long focus lens: angle of view narrower than a normal lens. This is any lens with a focal length longer than the diagonal measure of the film or sensor. The most common type of long focus lens is the telephoto lens, a design that uses a special telephoto group to be physically shorter than its focal length. Modern zoom lenses may have some or all of these attributes. The absolute value for the exposure time required depends on how sensitive to light the medium being used is (measured by the film speed, or, for digital media, by the quantum efficiency). Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras. Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the diffraction limitassociated with the pupil size and given, roughly, by the Rayleigh criterion. Atmospheric optics
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A colorful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the October 2007 California wildfires. The unique optical properties of the atmosphere cause a wide range of spectacular optical phenomena. The blue color of the sky is a direct result of Rayleigh scattering which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a sunrise or sunset. Additional particulate matter in the sky can scatter different colors at different angles creating colorful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for halos, afterglows, coronas, rays of sunlight, and sun dogs. The variation in these kinds of phenomena is due to different particle sizes and geometries. Mirages are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the Novaya Zemlya effect where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a temperature inversioncalled the Fata Morgana where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles". Rainbows are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the
OPTICS WORKSHEET 1. Which of the following best describes the image of a concave mirror when the object is at a distance greater than twice the focal point from the mirror? (A) virtual, erect; and magnification greater than one (B) virtual, inverted; and magnification greater than one (C) real, inverted; and magnification less than one (D) virtual, erect; and magnification less than one (E) real, inverted; and magnification greater than one 2. If a man‘s face is 25.0 cm in front of a concave shaving mirror creating an erect image 2.25 times as large as the object, what is the object‘s focal length? M = - si / s o
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3. An object is placed at a distance of 35.0 cm from a thin lens along an axis. If a virtual image forms at a distance of 70.0 cm from the lens, on the same side of the object, what is the focal length of the lens? 1/ so – 1/ si = 1/ f 4. Two thin lenses of focal lengths 15.0 and 20.0 cm, respectively, are placed in contact so that their optic axes coincide. What is the focal length of the two in combination? 1/ f1 +1/ f2 = 1/ fS Questions 5 - 7. A concave spherical mirror has a radius of curvature of 24 cm. An object is placed 32 cm from the mirror‘s vertex. 5. What is the focal length of this mirror? f = R/2 6. Sketch a ray diagram. 7. Calculate the image distance and describe the image. 1/ f = 1/ so + 1 /si 8. A concave spherical mirror has a radius of curvature of 30 cm. An object is placed 12 cm from the mirror‘s vertex.Sketch a ray diagram. 9. A double-convex lens has a 20 cm radius of curvature for both sides. An object is placed 7 cm from the mirror‘s vertex on the left-hand side. Sketch a ray diagram. 10. A Young‘s double slit apparatus has a slit separation of 4.75 x 10-5 m on which a monochromatic light beam is directed. The resultant bright fringes on a screen 1.30 m away are separated by 1.75 x 10-2 m. What is the wavelength of the beam? xm 11. Constructive interference occurs when light of wavelength 565 nm shines on soap bubble film (n = 1.46). What is the minimum thickness of the film? 12. A beam of unpolarized light strikes a flat piece of glass at an incidence angle of 49.5o. If the reflected beam is completely polarized, what is the glass‘ index of refraction? p
13. In a Young‘s double-slit experiment, by what factor is the distance between adjacent light and dark fringes changed when the wavelength of the source is tripled? xm 14. A possible means for making an airplane radar-invisible is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 2.25 cm and the index of refraction of the polymer is n = 1.62, how thick would the coating be?
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Questions 15 - 16. Light in the form of plane waves of a single wavelength are incident on two parallel slits. A viewing screen is a distance D from the slits. A point P on the screen is a distance r1 from one slit and r2 from the other. Questions 15 - 16. Diagram
15. If the difference in the distances (r2 – r1 at P? 16. If the difference in the distances (r2 – r1 P?
ld be observed at
REFLECTION, REFRACTION, and OPTICS Worksheet
1. A ray of light in air is incident on an air-to-glass boundary at a 77.2o angle to the surface. If the index of refraction of the glass is 1.87, what is the angle of refraction within the glass with respect to the normal? n1 1 = n2 2 2. A beam of light in air is incident on an air-to-glass boundary at a 52.7o angle to the normal. It is refracted in the glass at a 27.5o angle to the normal. What is the glass‘ index of refraction? n1 1 = n2 2 Questions 3 - 4. A laser beam, incident at 75o to the surface of a glass block, is partially reflected and partially transmitted at the block‘s upper surface. The index of refraction of the glass is 2.1. 3. What is the speed of light in this glass expressed as a fraction of c? n = c/v 4. Calculate the angle of refraction in degrees. n1 1 = n2 2 Young Ji International School / College
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Questions 5 - 6. A beam of light in water strikes a boundary with air. The index of refraction of water is 1.33. 5. If the angle of incidence is 29.4 degrees to the normal, what is the angle of refraction relative to the normal? n1 1 = n2 2 6. Calculate the critical angle for these rays. n1 1 = n2 2 7. A man‘s face is 25.0 cm in front of a concave shaving mirror. It creates an erect image 3 times as large as the object. What is the object‘s focal length? M = - si / s o 8. Two thin lenses of focal lengths 10 and 20 cm, respectively, are placed in contact so that their optic axes coincide. What is the focal length of the two in combination? 1/ f1 + 1/ f2 = 1/ fS 9. A Young‘s double slit apparatus has a slit separation of 4.12 x 10-5 m on which a monochromatic light beam is directed. The resultant bright fringes on a screen 1.49 m away are separated by 2.41 x 10-2 m. What is the wavelength of the beam? xm 10. Constructive interference occurs when light of wavelength 605 nm shines on soap bubble film (n = 1.91). What is the minimum thickness of the film? 11. A beam of unpolarized light strikes a flat piece of glass at a 57.2o angle to the normal. If the reflected beam is completely polarized, what is the glass‘ index of refraction. p
12. Light in the form of plane waves of a single wavelength are incident on two parallel slits. A viewing screen is a distance D from the slits. A point P on the screen is a distance r1 from one slit and r2 from the other. If the difference in the distances (r2 – r1 what would be observed at P? 13. A concave spherical mirror has a radius of curvature of 25 cm. An object is placed 10 cm from the mirror‘s vertex.Sketch a ray diagram. 14. Light in air enters a material (n = 1.71) at an angle of incidence 52.5o relative to the surface. What is the angle of refraction inside the material relative to the normal? n1 1 = n2 2 15. If the velocity of light through an unknown liquid is 2.42 x 108 m/s, what is the liquid‘s index of refraction? n = c/v
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16. The critical angle for internal reflection inside a transparent material is 35.1o What is the material‘s index of refraction? (Air is outside the material). c = n2 / n1 17. A double-convex lens has a 25 cm radius of curvature for both sides. An object is placed 5 cm from the mirror‘s vertex on the left-hand side. Sketch a ray diagram. Questions 18 - 19. A concave spherical mirror has a radius of curvature of 40 cm. An object is placed 80 cm from the mirror‘s vertex. 18. Sketch a ray diagram. 19. Calculate the image distance. 1/ f = 1/ so + 1/ si
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