Momentum Practice Problems

Transcription

1 Momentum Practice Problems PSI AP Physics C Name Multiple Choice 1. A steel ball and a piece of clay have equal mass. They are dropped from the same height on a horizontal steel platform. The ball bounces back with nearly the same speed with which it hit. The clay sticks to the platform. Which object experiences the greater momentum change? (A) the ball (B) the clay (C) Both experience the same momentum change (D) there is no momentum change for either (E) more information is required 2. A car of mass m is moving with a momentum p. How would you represent its kinetic energy in terms of these two quantities? (A) p2/(2m) (B) 1/2 mp2 (C) mp (D) mp/2 (E) zero 3. A bowling ball moving with speed v collides head-on with a stationary tennis ball. The collision is elastic, and there is no friction. The bowling ball barely slows down. What is the speed of the tennis ball after the collision? (A) nearly v (B) nearly 2v (C) nearly 3v (D) nearly infinite (E) Zero 4. An object with a mass of 2 kg is accelerated from rest. The graph shows the magnitude of the net force as a function of time. At t = 4 s, the object s velocity would have been closest to which of the following? (A) 2 m/s (B) 4 m/s (C) 10 m/s (D) 13 m/s (E) cannot be determined 5. A 3 kg ball is dropped onto a concrete floor. What is the magnitude of the ball s change in momentum if its speed just before striking the floor is 7 m/s and its rebound speed is 3 m/s? (A) 10 kg m/s (B) 15 kg m/s (C) 30 kg m/s (D) 50 kg m/s (E) 70 kg m/s

2 Questions Two blocks are on a frictionless surface and have the same mass m. Block 2 is initially at rest. Block 1 moves to the left with speed 4v. Block 1 collides inelastically with block 2. Which of the following choices is closest to the final speed of the system of two blocks? (A) v (B) 2v (C) 3v (D) 4v (E) 5v 7. Two blocks are on a frictionless surface and have the same mass m. Block 2 is initially at rest. Block 1 moves to the left with speed 4v. Block 1 collides elastically with block 2. What is the final speed of block 1? (A) zero (B) v (C) 2v (D) 3v (E) 4v 8. Two blocks are on a frictionless surface and have the same mass m. Block 2 is initially at rest. Block 1 moves to the left with speed 4v. Block 1 collides elastically with block 2. What is the final speed of block 2? (A) v (B) 2v (C) 3v (D) 4v (E) 6v Questions A hockey stick hitting a 0.5 kg puck is in contact with the puck for a time of 0.05 s. The puck travels in a straight line as it approaches and then leaves the hockey stick. If the puck arrives at the stick with a velocity of 6.4 m/s and leaves with a velocity of -3.6 m/s, what is the magnitude of the change in momentum of the puck? (A) 2 kg m/s (B) 3 kg m/s (C) 5 kg m/s (D) 6 kg m/s (E) 10 kg m/s 10. A hockey stick hitting a 0.5 kg puck is in contact with the puck for a time of 0.05 seconds. The puck travels in a straight line as it approaches and then leaves the hockey stick. If the puck arrives at the stick with a velocity of 6.4 m/s and leaves with a velocity of -3.6 m/s, what is the magnitude of the average force acting on the puck? (A) 100 N (B) 150 N (C) 200 N (D) 300 N (E) 500N

3 Questions An object of mass 3 kg starts from rest and moves along the x-axis. A net horizontal force is applied to the object in the +x direction. Refer to the Force time graph on the right. What is the net impulse delivered by this force? (A) 6 N s (B) 8 N s (C) 24 N s (D) 30 N s (E) 36 N s 12. An object of mass 3 kg starts from rest and moves along the x-axis. A net horizontal force is applied to the object in the +x direction. Refer to the Force time graph above. What is the net work done on the object? (A) 30 J (B) 50 J (C) 90 J (D) 150 J (E) 120 J 13. A tennis ball of mass m rebounds from a vertical wall with the same speed v as it had initially. What is the change in momentum of the ball? (A) mv (B) 2mv (C) 2mvcosθ (D) 2mvsinθ (E) zero

4 14. A steel ball moving at a constant speed v on a horizontal frictionless surface collides obliquely with an identical ball initially at rest. The velocity of the first ball before and after the collision is presented on the above diagram. What is the approximate direction of the velocity of the second ball after the collision? (A) (B) (C) (D) (E) Questions A stationary cannon ball explodes in three pieces of masses m, m, and 2m. The two momenta of the equal masses is presented by the diagram below. What is the direction of the momentum of the 2m mass? (A) (B) (C) (D) (E) 16. What is the magnitude of the velocity of the 2m cannon ball piece? (A) v (B) v (C) v (D) 1 v (E) 3 v

5 17. An object with an initial momentum shown on the diagram collides with another object at rest. Which of the following combinations of two vectors may represent the momenta of the two objects after the collision? (A) (B) (C) (D) (E) Questions A 6 kg block moves with a constant speed of 5 m/s on a horizontal frictionless surface and collides elastically with an identical block initially at rest. The second block then collides and sticks to the last 6 kg block initially at rest. 18. What is the speed of the second 6 kg block after the first collision? (A) zero (B) 2 m/s (C) 2.5 m/s (D) 3 m/s (E) 5 m/s 19. What is the speed of the third 6 kg block after the second collision? (A) zero (B) 2 m/s (C) 2.5 m/s (D) 3 m/s (C) 5 m/s

6 Questions Object A with mass 8 kg travels to the east at 10 m/s and object B with mass 3 kg travels south at 20 m/s. The two objects collide and stick together. 20. What is the magnitude of the velocity they have after the collision? (A) 1.8 m/s (B) 9.1 m/s (C) 12.7 m/s (D) 20 m/s (E) 25.5 m/s 21. What is the direction of the velocity they have after the collision? (A) 30º south of east (B) 37º south of east (C) 45º south of east (D) 53º south of east (E) 60º south of east 22. Two balls of equal mass m move with equal speeds v along paths inclined at 30 from the horizontal as shown. After the collision they stick together. What is the magnitude of their velocity after the collision? (A) 2 v (B) v 2 (C) 2v 2 (D) 3v 2 (E) v 23. Block m 1 is moving with speed v o towards a stationary block m 2, then collides and sticks to it. After the collision, the speed of the center of mass of the system is: (A) m 1 m 2 v o (B) m 2+m 1 m 2 v o (C) m 2+m 1 m 1 v o (D) (1 + m 1 )v o (E) m 1 m 1 +m 2 v o 24. A cannonball of mass 2m is moving towards the right with initial velocity v o, and explodes into two equal pieces each with mass m. What is the speed of the center of mass after the explosion? (A) v o (B) 0.5 v o (C) 2 v o (D) 4 v o (E) 0

7 25. A bullet of mass M 1 is fired from a gun that is initially at rest. The combined mass of the gun and bullet is M 2. If after the bullet is fired its kinetic energy is KE, what is the kinetic energy of the gun when it recoils? (A) KE (B) M 2 KE (C) M 2 1 M 1 M2 KE 2 M 1 (D) KE (E) M 1 M 2 M 1 M 2 M 1 KE 26. A ball of mass m is moving to the right with speed 3v on a frictionless tabletop when it collides with a second ball of mass 3m that is moving to the right with speed v. If the two balls stick together upon impact the speed of the balls immediately after the collision is: (A) v/3 (B) v/2 (C) 2v/3 (D) 3v/2 (E) 2v 27. Person A and Person B are standing on a sheet of frictionless ice. Person A pushes Person B so that Person B who is 60 kg, moves to the right at 3 m/s, while Person A, who is 90 kg, moves to the left at 2 m/s. What is the velocity of their center of mass? (A) Zero (B) 0.5 m/s to the left (C) 1 m/s to the right (D) 2.4 m/s to the left (E) 2.5 m/s to the right 28. What is the rebound speed of a 4 kg ball falling straight down that hits a platform at 4 m/s, if the average normal force exerted by the platform on the ball is 40 N for 0.5 s? (A) 2 m/s (B) 7 m/s (C) 6 m/s (D) 9 m/s (E) 1 m/s 29. A 2 kg mass moving at 12 m/s collides with an identical mass moving at -8 m/s and the masses stick together. What is the final velocity of the two masses? (A) 4/3 m/s (B) 2 m/s (C) 6 m/s (D) 10 m/s (E) 12 m/s 30. A compressed spring is placed between two masses M and m resting on a smooth horizontal surface. When the spring is released, the two fly apart with M moving at velocity v. The velocity of m is (A) M m v (B) M m v (C) m M v (D) m M v (E) m m+m v

8 31. Consider these two cases: First, a car moving at 40 mph hits another car of equal mass moving at 40 mph in the opposite direction. Second, a car moving at 40 mph hits a stationary steel wall. The collision time is the same for the two cases and the collisions are both inelastic. In which of these cases would result in the greatest impact force? (A) Hitting the wall (B) Hitting the other car (C) The force would be the same in both cases (D) More information is needed (E)None of the above are true. Questions A mass M moving with speed v collides with an uncompressed stationary spring of mass M with a spring constant K. The surface is frictionless. 32. What will be the maximum compression of the spring? (A) v M/K (B) v M/4K (C) v M/K (D) v 2M/K (E) v M/2K What is the speed of the spring after the collision? Questions (A) v (B) v 2 (C) v 4 (D) 2v (E) v 3 A 6 kg mass moving at 12 m/s in the +x direction is acted upon by a force with magnitude given as a function of time by the below graph. 34. Find the magnitude of the change in momentum from time t = 0 to time t = 8 s. (A) 12 kg m/s (B) 24 kg m/s (C) 36 kg m/s (D) 40 kg m/s (E) 52 kg m/s 35. What is the velocity of the mass after the force has stopped acting? (A) 6 m/s (B) 10 m/s (C) 18 m/s (D) 24 m/s (E) 40 m/s

9 36. A wire is bent into the shape as shown above. Which of the following best represents the coordinates of the center of mass? (A) (13/14, 6/7) (B) (8/7, 6/7) (C) (13/14, 8/7) (D) (1,1) (E) (1,6/7) 37. A block of mass m is moving with speed v o to the right on a frictionless surface when it explodes into two pieces of unequal mass. One piece of the mass, 3m/4 moves with a speed v o/2 to the left while the other piece of the object moves with velocity: (A) v o/2 (B) 2v o/3 (C) 11v o/2 (D) 7v o/5 (E) 2v o 38. Two blocks with masses m and 2m are placed on a horizontal frictionless surface. There is a compressed spring between the block and after the spring is released, the 2m block moves to the right with a speed of v. What is the total work done by the spring on the system of two blocks? (A) Zero (B) mv 2 (C) 2mv 2 (D) 3mv 2 (E) mv 39. A railway artillery gun of mass 1400 tons is initially at rest on a horizontal surface. It fires a 7 ton shell with a velocity of 800 m/s at an angle of 60. What is the speed of the gun immediately after the shell is fired? (A) Zero (B) 2 m/s (C) 4 m/s (D) 5 m/s (E) 7 m/s

10 40. Two equal forces are exerted for the same length of time on two blocks with different masses m 1 and m 2 (m 2 >m 1). Which of the following will describe the change is kinetic energy of the blocks? (A) The blocks have the same change in kinetic energy. (B) The change in kinetic energy of each block is zero. (C) Block m 2 has a greater change in kinetic energy. (D) Block m 1 has a greater change in kinetic energy. (E) None of the above are correct. 41. A boy launches a 20 g dart horizontally by a spring gun from a balcony 45 m above the ground. The dart lands 15 m away from the balcony. If the length of the gun s barrel is 10 cm, what is the average horizontal force applied by the spring? (A) 1.0N (B) 2.0 N (C) 2.5 N (D) 5. N (E) 7.5 N 42. A mall of mass m is dropped from a height of ho. The ball hits the floor and bounces to a height of h. What is the magnitude of impulse exerted on the ball by the floor? (A) mgh (B) 2mgh (C) 2mgh (D) m( 2gh + 2gh 0 ) (E) m( 2gh 2gh 0 ) 43. A 5 kg object starts from rest on a flat horizontal surface and moves in a straight line. The velocity as a function of time is given by v = 3t + 2t 2. What is the magnitude of the instantaneous force that acts on the object at 2 s? (A) 105 N (B) 75 N (C) 55 N (D) 45 N (E) 35 N 44. A net force F = t 2 is applied to a 30 kg cart that can move on a flat horizontal surface. If the cart starts from rest, what is its speed at 5 s? (A) 10 m/s (B) 8 m/s (C) 5 m/s (D) 3 m/s (E) 1 m/s

11 45. A block of mass m moves to the right at a constant velocity v and collides elastically with another block of mass 3m, which is initially at rest. Which of the following is the velocity of each block after the collision? Block m (A) Zero Block 3m v (B) v/2 v/2 (C) v/2 v/2 (D) 3v/2 v/2 (E) v/2 3v/2 46. A 40 kg skateboarder runs at a constant velocity of 12 m/s and jumps on a stationary skateboard with a mass of 8 kg. What is the velocity of the skateboarder skateboard system after the jump? (A) 12 m/s (B) 90 m/s (C) 60 m/s (D) 20 m/s (E) 10 m/s 47. An 80 kg diver jumps off a moving boat. The boat has a mass of 400 kg and moves at a constant velocity of 2 m/s. What is the velocity of the boat after the jump if the diver jumps with a velocity of 3 m/s in opposite direction to the initial velocity of the boat? (A) 2 m/s (B) 3 m/s (C) 4 m/s (D) 5 m/s (E) 6 m/s

12 48. A tennis ball approaches a racket with a momentum of 5 kg m/s and bounces back with a momentum of 6 kg m/s after the collision with the racket. What is the change in momentum of the tennis ball? (A) 1 kg m/s (B) 5 kg m/s (C) 6 kg m/s (D) 11 kg m/s 0 kg m/s 49. A light beach ball moving with a velocity 2 m/s to the right collides elastically with a stationary bowling ball. After the collision the bowling ball remains stationary. What is the velocity of the beach ball after the collision? (A) 0 m/s (B) 2 m/s to the left (C) 4 m/s to the left (D) 3 m/s to the left (E) 1 m/s to the left 50. A ball of mass m moving at a constant speed v to the right collides elastically with another ball of mass 3m moving to the left at a constant speed v. What is the velocity of ball m after the collision? (A) v (B) 3 v (C) 1 v (D) -2v (E) 3v 2 3

13 Answer Key 1.A 6.B 11.D 16.A 21.B 26.D 31.B 36.A 41.C 46.E 2.A 7.A 12.D 17.E 22.D 27.A 32.E 37.C 42.D 47.B 3.B 8.D 13.C 18.E 23.E 28.E 33.B 38.D 43.C 48.D 4.A 9.C 14.C 19.C 24.A 29.B 34.C 39.B 44.A 49.B 5.C 10.A 15.B 20.B 25.D 30.B 35.C 40.D 45.C 50.D