Momentum Concepts

14. Which of the following is a true statement about the conservation of linear momentum? a) It is conserved only when no net external force acts on the system under consideration. b) It is conserved only when the center of mass of a system is at rest. c) It is conserved only in collisions between macroscopic objects. d) It is conserved only in two-body collisions. e) It is conserved only in one-dimensional and two-dimensional motion.

A

17. A railroad flatcar of mass 2,000 kg rolls to the right at 10 m/s and collides with a flatcar of mass 3,000 kg that is rolling to the left at 5 m/s. The flat cars couple together. Their speed after the collision is a) 1 m/s b) 2.5 m/s c) 5 m/s d) 7 m/s e) 7.5 m/s

A

20. A rock is dropped from a high tower and falls freely under the influence of gravity. Which one of the following statements concerning the rock as it falls is true? Neglect the effect of air resistance. a) The rock will gain an equal amount of momentum during each second. b) The rock will gain an equal amount of kinetic energy during each second. c) The rock will gain an equal amount of speed for each meter through which it falls. d) The rock will gain an equal amount of momentum for each meter through which it falls. e) The amount of momentum the rock gains will be proportional to the amount of potential energy that it loses.

A

10. Two objects having the same mass travel towards each other on a flat surface; each with a speed of 1.0 m/s relative to the surface. The objects collide head-on and are reported to rebound after the collision; each with a speed of 2.0 m/s relative to the surface. Which of the following assessments of this report is most accurate? a) Momentum is not conserved, therefore the report is false. b) If potential energy was released to the objects during the collision, the report could be true. c) If the objects had different masses, the report could be true. d) If the surface was inclined, the report could be true. e) If there was no friction between the objects and the surface, the report could be true.

B

15. A sled of mass m is coasting on the icy surface of a frozen river. While it passes under a bridge, a package of equal mass m is dropped straight down and lands on the sled without causing any damage). The sled plus the added load then continues along the original line of motion. How does the kinetic energy of the sled + load compare with the original kinetic energy of the sled? a) It is 1⁄4 the original kinetic energy of the sled. b) It is 1⁄2 the original kinetic energy of the sled. c) It is 3⁄4 the original kinetic energy of the sled. d) It is the same as the original kinetic energy of the sled. e) It is twice the original kinetic energy of the sled.

B

18. A person of mass 60 kg sliding along level ice at a speed of 3.0 m/s collides with a second person who is initially at rest. Assume that friction is negligible. If the two people hold onto each other and their common final speed, after colliding, is 2.0 m/s, the mass of the second person is a) 10 kg b) 30 kg c) 40 kg d) 80 kg e) 90 kg

B

Questions 7 and 8 A ball is dropped and bounces off the floor. Its speed is the same immediately before and immediately after the collision. 7. Which of the following is true about the collision between the ball and the floor? a) The ball's momentum is conserved. b) The ball's momentum changes direction but not magnitude. c) The ball's momentum changes magnitude but not direction. d) The impulse delivered to the ball by the floor is zero. e) The impulse delivered to the floor by the ball is zero.

B

Questions 7 and 8 A ball is dropped and bounces off the floor. Its speed is the same immediately before and immediately after the collision. 8. How does the height to which the ball bounces compare to the height from which it was dropped? a) It is less. b) It is the same. c) It is greater. d) It cannot be determined without knowing the value of the height from which the ball was dropped. e) It cannot be determined without knowing the value of the ball's speed as it hits the floor.

B

11. Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true? a) The kinetic energies of the two people are equal. b) The speeds of the two people are equal. c) The momenta of the two people are equal. d) The center mass of the two-person system moves in the direction of the less massive person. e) The less massive person has a smaller initial acceleration than the more massive person.

C

23. An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively. Which one of the following statements concerning the fragments after the explosion is true? a) They will fly off at right angles. b) They will fly off in the same direction. c) The smaller fragment will have twice the speed of the larger fragment. d) The larger fragment will have twice the speed of the smaller fragment. e) The smaller fragment will have four times the speed of the larger fragment.

C

6. An empty sled of mass M moves without friction across a frozen pond at speed v0. Two objects are dropped vertically into the sled one at a time: first an object of mass m and then an object of mass 2m. Afterward the sled moves with speed vf. What would be the final speed of the sled if the objects were dropped into it in reverse order? a) vf/3 b) vf/2 c) vf d) 2vf e) 3vf

C

16. The two blocks of masses M and 2M shown above initially travel at the same speed v but in opposite directions. They collide and stick together. How much mechanical energy is lost to other forms of energy during the collision? a) 0 b) .5Mv^2 c) .75Mv^2 d) 1.333 Mv^2 e) 1.5 Mv^2

D

30. A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true? a) Kinetic energy is conserved in this process. b) The fragments must have equal kinetic energies. c) The sum of the kinetic energies of the fragments must be zero. d) The vector sum of the linear momenta of the fragments must be zero. e) The velocity of any one fragment must be equal to the velocity of any other fragment.

D

4. Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M>m, which is initially at rest on the surface? a) The collision is elastic. b) All of the initial kinetic energy of the less-massive object is lost. c) The momentum of the objects that are stuck together has a smaller magnitude than the initial momentum of the less-massive object. d) The speed of the objects that are stuck together will be less than the initial speed of the less-massive object. e) The direction of the motion of the objects that are stuck together depends on whether the hit is a head-on collision.

D

5. Which one of the following is characteristic of an inelastic collision? a) Total mass is not conserved b) Total energy is not conserved c) Linear momentum is not conserved d) Kinetic energy is not conserved e) The change in momentum is less than the total impulse

D

13. A railroad car of mass m is moving at speed v when it collides with a second railroad car of mass M, which is at rest. The two cars lock together instantaneously and move along the track. What is the speed of the cars immediately after the collision? a) v/2 b) (mv)/M c) (Mv)/m d) ( (m+M) v )/m e) (mv)/(M+m)

E

26. A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs? a) The bag provides the necessary force to stop the person. b) The bag reduces the impulse on the person. c) The bag increases the amount of time the force acts on the person and reduces the change in momentum. d) The bag decreases the amount of time during which the momentum is changing and reduces the average force on the person. e)The bag increases the amount of time during which the momentum is changing and reduces the average force acting on the person.

E

9. Two objects of equal mass traveling towards each other with equal speeds undergo a head on collision. Which one of the following statements concerning their velocities after the collision is necessarily true? a) They will exchange velocities. b) Their velocities will be reduced. c) Their velocities will be unchanged. d) Their velocities will be zero. e) Their velocities may be zero.

E

12. A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leaves the kicker's foot with a speed of 5.0 m/s in a direction 600 above the horizontal. The magnitude of the impulse imparted by the ball to the foot is most nearly a) 1 Ns b) square root of 3 Ns c) 2 Ns d) 2/square root 3 Ns e) 4 Ns

c

24. A tennis ball of mass m rebounds from a racquet with the same speed v as it had initially, as shown above. The magnitude of the momentum change of the ball is a) 0 b) mv c) 2mv d) 2mvsin@ e)2mvcos@

c

29. An open cart on a level surface is rolling without frictional loss through a vertical downpour of rain, as shown above. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. The speed of the cart will a) increase because of the conservation of momentum b) increase because of the conservation of mechanical energy c) decrease because of the conservation of momentum d) decrease because of the conservation of mechanical energy e) remain the same because the raindrops are falling perpendicular to the direction of the cart's motion

c

Complete the following statement: Momentum will be conserved in a two-body collision only if a) both bodies come to rest b) the collision is perfectly elastic c) the kinetic energy of the system is conserved. d) the net external force acting on the two-body system is zero. e) the internal forces of the two body system cancel in action-reaction pairs.

d