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 kilograms is
accelerated from rest. The graph shows the
magnitude of the net force as a function of time.
At t=4 seconds the object’s velocity would have
been closest to which of the following?
(A) 2 m/s
(B) 4 m/s
(D) 13 m/s
(E) 20 m/s
(C) 10 m/s
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
(E) 70 kg m/s
(B) 15 kg m/s
(C) 30 kg m/s
(D) 50 kg m/s
Questions 6 - 8
6. 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 9-10
9. A hockey stick hitting a 0.5 kg puck is in contact with the ball for a time of .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 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 ball for a time of .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
Questions 11-12
11. 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 +x direction. The
force time relations presented by the graph.
What is the net impulse delivered by this
force?
(A) 6 N·s
(B) 8 N·s
(D) 30 N·s
(E) 36 N·s
(C) 24 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 +x direction. The force time relations presented by the
graph. 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
(D) 2mvsinθ
(E) zero
(C) 2mvcosθ
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 diagram. What is the approximate direction of the
velocity of the second ball after the collision?
(A)
(B)
(D)
(E)
(C)
Questions 15-16
15. A stationary cannon ball explodes in three pieces of masses m, m, and 2m. The two
momenta of equal masses presented by the diagram. What is the direction of the
momentum of 2m mass?
(A)
(B)
(C)
(D)
16. What is the magnitude of the velocity of 2m cannon ball piece?
(A)
√2
𝑣
2
(B)
√3
𝑣
2
(C)
√5
𝑣
2
1
2
(D) 𝑣
3
2
(E) 𝑣
(E)
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 18-19
A 6 kg block moves with a constant speed 5 m/s on a horizontal frictionless surface and
collides elastically with an identical block initially at rest. The second block 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
Questions 20-21
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
(D) 20 m/s
(E) 25.5 m/s
(C) 12.7 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?
𝑣
(A) √2 v
(B) 2
√2𝑣
2
(C)
(D)
√3𝑣
2
(E) v
23. Block m1 is moving with speed vo toward stationary block m2 collides and sticks with
it. The speed of the center of mass of the system is
𝑚
(A) 𝑚1 𝑣𝑜
(B)
2
(E)
𝑚2 +𝑚1
𝑣𝑜
𝑚2
(C)
𝑚2 +𝑚1
𝑣𝑜
𝑚1
(D) (1 + 𝑚1 )𝑣𝑜
𝑚1
𝑣
𝑚1 +𝑚2 𝑜
24. A cannonball of mass 2m is moving towards the right with initial velocity vo and
explodes into two equal pieces each with mass m. What is the speed of the center of
mass after the explosion?
(A) vo
(B) 0.5 vo
(C) 2 vo
(D) 4 vo
(E) 0
25. A bullet of mass M1 is fired from a gun that is initially at rest. The combined mass of
the gun and bullet is M2. 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)
𝑀2
𝐾𝐸
𝑀1
(C)
𝑀12
𝐾𝐸
𝑀22
𝑀1
𝐾𝐸
𝑀2 −𝑀1
𝑀1
𝐾𝐸
𝑀2 −𝑀1
(D)
(E) √
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
(D) 2.4 m/s to the left
(C) 1 m/s to the right
(E) 2.5 m/s to the right
28. What is the rebound speed of a 4 kg ball falling straight down that hits the platform at
4 m/s, if the average normal force exerted by the platform on the ball was 40 N for
0.5s?
(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 mass 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
𝑀
(A) 𝑚 𝑣
𝑀
(B) − 𝑚 𝑣
𝑚
(C) 𝑀 𝑣
𝑚
(D) − 𝑀 𝑣
𝑚
(E) 𝑚+𝑀 𝑣
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 32-33
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
𝑣
(C) 2 √3𝑀/𝐾
(D) v√2𝑀/𝐾
(E) v√𝑀/2𝐾
33. What is the speed of the spring after the collision?
(B) 𝑣⁄2
(A) v
(C) 𝑣⁄4
(E) 𝑣⁄3
(D) 2v
Questions 34-35
A 6 kg mass is 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 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
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 vo 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 vo/2 to the left while the other piece of the object moves with velocity
(A) vo/2
(B) 2vo/3
(C) 11vo/2
(D) 7vo/5
(E) 2vo
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 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) mv2
(C) 2mv2
(D) 3mv2
(E) mv
39. A railway artillery gun of mass 1400 tonnes is initially at rest on a horizontal surface
when fires a 7 tonnes 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
40. Two equal forces are exerted for the same length of time on two blocks with different
masses m1 and m2 (m2 >m1). Which of the following will describe the change is
kinetic energy of the blocks?
(A) Blocks have the same change in kinetic energy
(B) The change in kinetic energy of each block is zero
(C) Block m2 has greater change in kinetic energy
(D) Block m1 has greater change in kinetic energy
(E) Non from the above is correct
41. A boy launches a 20 g dart in horizontal 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) 1.0 N
(B) 2.0 N
(C) 2.5 N
(D) 5.0 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√2𝑔(ℎ − ℎ𝑜 )
(E) 𝑚√2𝑔(ℎ + ℎ𝑜 )
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 + 2t2. What is the magnitude of
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 = 10 + 6t2 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
45. Block of mass m moves to the right at a constant velocity v and collides elastically
with another block of mass 3m. Which of the following is the velocity of each block
after the collision?
Block m
Block 3m
(A) Zero
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 of a
stationary skateboard with a mass of 8 kg. What is the velocity of the
skateboard 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
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 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
3
(B) − 2v
1
(C) − 3v
(D) 2v
(E) -2v
Answer Key
1.A
6.B
11.D
16.A
21.B
26.D
31.C
36.A
41.C
46.E
2.A
7.A
12.D
17.E
22.D
27.A
32.E
37.C
42.E
47.B
3.B
8.D
13.C
18.E
23.E
28.E
33.A
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.E