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1) Three objects are moving along a straight line as shown in Figure 8.1. Taking the positive direction to be to the right, what is the total momentum of this system?
A) +106 kg m/s
B) -106 kg m/s
C) +14 kg m/s
D) -14 kg m/s
E) 0 kg m/s
Answer: D
2) A 328 kg car moving at 19.1 m/s hits from behind another car moving at 13.0 m/s in the same direction. If the second car has a mass of 790 kg and a new speed of 15.1 m/s, what is the velocity of the first car after the collision?
A) 14.0 m/s
B) 18.2 m/s
C) 24.2 m/s
D) -14.0 m/s
Answer: A
3) Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.
A) 13.1 m/s at 79°
B) 16.3 m/s at 79°
C) 12.5 m/s at 79°
D) 15.7 m/s at 79°
Answer: A
4) A 0.140 kg baseball is thrown with a velocity of 28.9 m/s. It is struck with an average force of 5000.0 N, which results in a velocity of 37.0 m/s in the opposite direction. How long were the bat and ball in contact?
A) 1.85 × 10-3 s
B) 1.32 × 10-2 s
C) 3.17 × 10-2 s
D) 4.44 × 10-3 s
Answer: A
5) A golf ball of mass 0.050 kg is at rest on the tee and has a velocity of 102 m/s immediately after being struck. If the club and ball were in contact for 0.81 ms, what is the average force exerted on the ball?
A) 6.3 kN
B) 7.1 kN
C) 5.5 kN
D) 4.9 kN
Answer: A
6) A 0.24 kg blob of clay is thrown at a wall with an initial velocity of 16 m/s. If the clay comes to a stop in 91 ms, what is the average force experienced by the clay?
A) 42 N
B) 26 N
C) 35 N
D) 51 N
Answer: A
7) A 1200 kg car moving at 15.6 m/s collides with a stationary car of mass 1500 kg. If the two vehicles lock together, what is their combined velocity immediately after the collision?
A) 6.9 m/s
B) 8.6 m/s
C) 12.1 m/s
D) 5.5 m/s
Answer: A
8) A 1200 kg ore cart is rolling at 10.8 m/s across a flat surface. A crane dumps 858 kg of ore (vertically) into the cart. How fast does the cart move after being loaded with ore? Assume that frictional forces with the flat surface may be neglected.
A) 6.3 m/s
B) 3.8 m/s
C) 4.2 m/s
D) 5.7 m/s
Answer: A
9) A 1200 kg cannon fires a 100.0 kg cannonball at 35 m/s. What is the recoil velocity of the cannon? Assume that frictional forces are negligible and the cannon is fired horizontally.
A) 2.9 m/s
B) 35 m/s
C) 3.5 m/s
D) 3.2 m/s
Answer: A
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10) A car heading north collides at an intersection with a truck heading east. If they lock together and travel at 28 m/s at 15° north of east just after the collision, how fast was the car initially traveling? Assume that the two vehicles have the same mass.
A) 14 m/s
B) 7 m/s
C) 28 m/s
D) 11 m/s
Answer: A
11) Three cars, car X, car Y, and car Z, begin accelerating from rest, at the same time. Car X is more massive than car Y, which is more massive than car Z. The net force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum?
A) They all have the same amount of momentum
B) Car X
C) Car Y
D) Car Z
Answer: A
12) A 5 kg ball collides head-on with a 10 kg ball, which is initially stationary. The collision is inelastic. Which statement is true?
A) The magnitude of the change of velocity the 5 kg ball experiences is greater than that of the 10 kg ball.
B) The magnitude of the change of velocity the 5 kg ball experiences is less than that of the 10 kg ball.
C) The magnitude of the change of velocity the 5 kg ball experiences is equal to that of the 10 kg ball.
D) The magnitude of the change of the momentum of the 5 kg ball is equal to the magnitude of the change of momentum of the 10 kg ball.
E) Two of the above statements are true.
Answer: A
13) Two friends are standing on opposite ends of a canoe. The canoe is initially at rest with respect to the lake. The person on the right throws a very massive ball to the left, and the person on the left catches it. After the ball is caught, the canoe is (ignore friction between the canoe and the water)
A) stationary
B) moving to the right.
C) moving to the left.
Answer: A
14) You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to maximize your speed on the skateboard?
A) catch the ball
B) deflect the ball back
C) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.
Answer: B
15) A steady horizontal force lasting for 2.10 s gives a 1.25 kg object an acceleration of 3.20 m/s2 on a frictionless table. What impulse does this force give to the object?
A) 25.7 kg m/s
B) 10.9 kg m/s
C) 8.40 kg m/s
D) 4.00 kg m/s
E) 2.63 kg m/s
Answer: C
16) An egg falls from a bird’s nest in a tree and feels no effects due to the air. As it falls,
A) only its kinetic energy is conserved.
B) only its momentum is conserved.
C) both its kinetic energy and its momentum are conserved.
D) only its mechanical energy is conserved.
E) both its mechanical energy and its momentum are conserved.
Answer: D
17) A block of mass m = 4.4 kg, moving on frictionless surface with a speed vi = 9.2 m/s, makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 4.4 kg block recoils with a speed of vf = 2.5 m/s. In Figure 8.2, the mass M is closest to:
A) 7.7 kg
B) 12 kg
C) 5.6 kg
D) 21 kg
E) 4.4 kg
Answer: A
18) A block of mass m = 3.6 kg, moving on a frictionless surface with a speed vi = 9.3 m/s, makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.6 kg block recoils with a speed of vf = 2.7 m/s. In Figure 8.2, the speed of the block of mass M after the collision is closest to:
A) 6.6 m/s
B) 8.0 m/s
C) 9.3 m/s
D) 10.7 m/s
E) 12.0 m/s
Answer: A
19) A block of mass m = 5.6 kg, moving on a frictionless surface with a speed vi = 6.5 m/s, makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 5.6 kg block recoils with a speed of vf = 0.7 m/s. In Figure 8.2, the blocks are in contact for 0.20 s. The average force on the 5.6 kg block, while the two blocks are in contact, is closest to:
A) 202 N
B) 192 N
C) 182 N
D) 34 N
E) 162 N
Answer: A
20) A block of mass m = 9 kg has a speed V and is behind a block of mass M = 27 kg that has a speed of 0.5 m/s. The surface is frictionless. The blocks collide and couple. After the collision, the blocks have a common speed of 0.9 m/s. In Figure 8.3, the loss of kinetic energy of the blocks due to the collision is closest to:
A) 8.6 J
B) 2.0 J
C) 4.6 J
D) 11 J
E) 31 J
Answer: A
21) A block of mass m = 34 kg has a speed V and is behind a block of mass M = 81 kg that has a speed of 0.5 m/s. The surface is frictionless. The blocks collide and couple. After the collision, the blocks have a common speed of 0.9 m/s. In Figure 8.3, the impulse on the 12 kg block due to the collision is closest to:
A) 32 N ∙ s
B) 14 N ∙ s
C) 41 N ∙ s
D) 57 N ∙ s
E) 73 N ∙ s
Answer: A
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22) A 51 g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for 0.5 ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 3.00 s. In this situation, the average force exerted on the ball during contact with the plate is closest to:
A) 3000 N
B) 1500 N
C) 2490 N
D) 2000 N
E) 3500 N
Answer: A
23) A 83 g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for 0.5 ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 4.00 s. In this situation, assume the plate does not deform during contact. The maximum elastic energy stored by the ball is closest to:
A) 16 J
B) 24 J
C) 32 J
D) 48 J
E) 64 J
Answer: A
24) In Figure 8.4, a bullet of mass 0.01 kg moving horizontally strikes a block of wood of mass 1.5 kg which is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a distance of 0.40 m. What was the velocity of the bullet just before it struck the wooden block? The length of the string is 2 meters.
A) 66.7 m/s
B) 250 m/s
C) 366 m/s
D) 423 m/s
E) 646 m/s
Answer: A
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25) Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?
A) Hitting the other car.
B) Hitting the brick wall.
C) The force would be the same in both cases.
D) We cannot answer this question without more information.
E) None of these is true.
Answer: C
26) An 8 g bullet is shot into a 4.0 kg block, at rest on a frictionless horizontal surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 3.7 cm. The force constant of the spring is 2500 N/m. In Figure 8.5, the initial velocity of the bullet is closest to:
A) 460 m/s
B) 440 m/s
C) 480 m/s
D) 500 m/s
E) 520 m/s
Answer: A
27) An 8 g bullet is shot into a 4.0 kg block, at rest on a frictionless horizontal surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 8.9 cm. The force constant of the spring is 1400 N/m. In Figure 8.5, the impulse of the block (including the bullet), due to the spring, during the entire time interval in which block and spring are in contact is closest to:
A) 13 N ∙ s
B) 12 N ∙ s
C) 10 N ∙ s
D) 8.3 N ∙ s
E) 6.7 N ∙ s
Answer: A
28) A girl of mass 55 kg throws a ball of mass 0.8 kg against a wall. The ball strikes the wall horizontally with a speed of 25 m/s, and it bounces back with this same speed. The ball is in contact with the wall 0.05 s. What is the average force exerted on the wall by the ball?
A) 800 N
B) 400 N
C) 55,000 N
D) 27,500 N
E) 13,750 N
Answer: A
29) During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a long barrel. What is the reason for using a long barrel in these guns?
A) To provide a larger ratio of kinetic energy to potential energy.
B) To reduce frictional losses.
C) To allow the force of the expanding gases from the gunpowder to act for a longer time.
D) To increase the force exerted on the bullet due to the expanding gases from the gunpowder.
E) To reduce the force exerted on the bullet due to the expanding gases from the gunpowder.
Answer: C
30) Ball A, of mass 3.0 kg, is attached to a 0.4 m light rod, freely pivoted at P. Ball B is suspended from Q by a 0.6 m rope and is at rest. Ball A is raised to a certain level and is released. Ball A descends, and has a speed V1 = 3.6 m/s at the bottom, prior to striking ball B. The speed of balls A and B after the collision are V2 = 1.6 m/s and V3 = 2.0 m/s, as shown. In Figure 8.6, the mass of ball B is closest to:
A) 7.8 kg
B) 6.8 kg
C) 5.8 kg
D) 4.9 kg
E) 3.9 kg
Answer: A
31) Ball A, of mass 3.0 kg, is attached to a 0.4 m light rod, freely pivoted at P. Ball B is suspended from Q by a 0.6 m rope and is at rest. Ball A is raised to a certain level and is released. Ball A descends, and has a speed V1 = 3.6 m/s at the bottom, prior to striking ball B. The speed of balls A and B after the collision are V2 = 1.1 m/s and V3 = 1.9 m/s, as shown. In Figure 8.6, the magnitude of the impulse on ball A is closest to:
A) 14.1 N ∙ s
B) 7.5 N ∙ s
C) 9.7 N ∙ s
D) 8.6 N ∙ s
E) 15.2 N ∙ s
Answer: A
Figure 8.7
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32) In Figure 8.7, four point masses are placed as shown. The x- and y-coordinates of the center of mass are closest to:
A) (2.2, 2.6)
B) (2.2, 2.7)
C) (2.3, 2.6)
D) (2.3, 2.7)
E) (2.3, 2.8)
Answer: E
33) In Figure 8.8, a 60 cm length of uniform wire, of 60 g mass, is bent into a right triangle. The x- and y-coordinates of the center of mass, in cm, are closest to:
A) (8, 3)
B) (8, 5)
C) (9, 4)
D) (10, 3)
E) (10, 5)
Answer: D
34) In Figure 8.9, an L-shaped piece is cut from a uniform sheet of metal. Which of the points indicated is closest to the center of mass of the object?
A) A
B) B
C) C
D) D
E) E
Answer: C
35) In Figure 8.10, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is:
A) perfectly elastic.
B) partially inelastic.
C) completely inelastic.
D) characterized by an increase in kinetic energy.
E) not possible because momentum is not conserved.
Answer: A
36) In Figure 8.11, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is:
A) perfectly elastic.
B) partially inelastic.
C) completely inelastic.
D) characterized by an increase in kinetic energy.
E) not possible because momentum is not conserved.
Answer: E
37) In Figure 8.12, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is:
A) perfectly elastic.
B) partially inelastic.
C) completely inelastic.
D) characterized by an increase in kinetic energy.
E) not possible because momentum is not conserved.
Answer: C
38) An object initially at rest explodes in two fragments of masses 2.6 kg and 3.3 kg that move in diametrically opposite directions. If the speed of the first fragment is 3.6 m/s, find the internal energy of the explosion.
A) 30J
B) 30kJ
C) 38J
D) 38kJ
Answer: A
39) Two pendulums of equal length l = 0.45 m are suspended from the same point. The pendulum bobs are steel spheres. The first bob is drawn back to make a 35° angle with the vertical. If the first bob has mass 0.25 kg and the second has mass 0.54 kg, how high will the second bob rise above its initial position when struck elastically by the first bob after it is released?
A) 3.3 cm
B) 2.7 cm
C) 3.9 cm
D) 4.4 cm
Answer: A
40) A car of mass 1411 kg collides head-on with a parked truck of mass 2000 kg. Spring mounted bumpers ensure that the collision is essentially elastic. If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity) after the collision, what is the initial speed of the car?
A) 21 km/h
B) 42 km/h
C) 32 km/h
D) 11 km/h
Answer: A
1) Find the magnitude and direction of the net momentum of the system shown in Figure 8.13. Express the direction by giving the angle the net momentum makes with the +x-axis.
Figure 8.13
Answer: 123 kg m/s, 212°
2) A 475 gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in ms) was it in contact with the ball?
Answer: 7.64 ms
3) On a frictionless horizontal surface, a 1.50 kg mass traveling at 3.50 m/s collides with and sticks to a 3.00 kg mass that is initially at rest, as shown in Figure 8.14. This system then runs into an ideal spring of force constant 50.0 N/cm. (a) What will be the maximum compression of the spring? (b) How much mechanical energy is lost during this process? During which parts of the process (the collision and compression of the spring) is this energy lost?
Answer: (a) 3.50 cm, (b) 6.13 J during the inelastic collision
4) Three balls are moving along a straight line having the instantaneous positions shown in Figure 8.15. At that instant, find the location and velocity of the center of mass of this system.
Answer: 7.00 m to the right of the 2.00 kg ball, 1.11 m/s to the right
5) A pitcher is employing a ballistic pendulum to determine the speed of his fastball. A 3.3 kg lump of clay is suspended from a cord 2.0 m long. When the pitcher throws his fastball aimed at the clay, the ball becomes embedded in the clay and the two swing up to a maximum height of 0.08 m. If the mass of the baseball is 0.21 kg, find the speed of the pitch.
Answer: 21 m/s
6) A force of 5.3 N is needed to hold on to an umbrella in a strong wind. If the air molecules each have a mass of 4.7 × 10-26 kg, and each strikes the umbrella (without rebounding) with a speed of 2.0 m/s in the same direction, how many atoms strike the umbrella each second? Assume that the wind blows horizontally so that the gravity can be neglected.
Answer: 5.6 × 1025 per second
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