AP Physics C Multiple Choice Practice – CofM and Momentum
1. A system consists of two objects having masses m l and m 2 (m l < m 2 ). The objects are connected by a massless
string, hung over a pulley as shown above, and then released. When the speed of each object is v, the
magnitude of the total linear momentum of the system is
(A) (m 1 + m 2 ) v (B) (m 2 - m 1 ) v (C) ½(m l + m 2 )v (D) ½(m 2 - m 1 )v (E) m 2 v
2. Two particles of equal mass m o , moving with equal speeds v O along paths inclined at 60° to the x-axis as
shown above, collide and stick together. Their velocity after the collision has magnitude
v0 v0 2v 0 3v 0
(A) 4 (B) 2 (C) 2 (D) 2 (E) v o
3. The center of mass of a uniform wire, bent in the shape shown above, is located closest to point
(A) A (B) B (C) C (D) D (E) E
4. Mass M 1 is moving with speed v toward stationary mass M 2 . The speed of the center of mass of the system is
M1 M1 M2 M1 M1
(A) v ( B) 1 + v (C) 1 + v (D) 1 − v (E) v
M2 M2 M1 M2 M1 + M 2
101
Questions 5-6
A 4-kilogram mass has a speed of 6 meters per second on a horizontal frictionless surface, as shown above. The
mass collides head-on and elastically with an identical 4-kilogram mass initially at rest. The second 4-kilogram
mass then collides head-on and sticks to a third 4-kilogram mass initially at rest.
5. The final speed of the first 4-kilogram mass is
(A) 0 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s (E) 6 m/s
6. The final speed of the two 4-kilogram masses that stick together is
(A) 0 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s (E) 6 m/s
7. A projectile of mass M 1 is fired horizontally from a spring gun that is initially at rest on a frictionless surface.
The combined mass of the gun and projectile is M 2 . If the kinetic energy of the projectile after firing is K, the
gun will recoil with a kinetic energy equal to
2
M2 M1 M1
(A) K (B) K (C) M 1 K D) K (E) K
M1 M 22 M 2 − M1 M 2 − M1
8. A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates
( x , y) of the center of mass?
(A) (15/14, 6/7) (B) (6/7, 6/7) (C) (15/14, 8/7) (D) (1,1) (E) (1,6/7)
9. Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 meters per second, as shown in
Figure I above. It then collides elastically with identical ball Y. which is initially at rest. After the collision, ball
X moves at 6 meters per second along a path at 530 to its original direction, as shown in Figure II above. Which
of the following diagrams best represents the motion of ball Y after the collision?
102
10. A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder
hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground.
How does the balloon move relative to the ground?
(A) Up with speed v
(B) Up with a speed less than v
(C) Down with speed v
(D) Down with a speed less than v
(E) The balloon does not move.
11. If one knows only the constant resultant force acting on an object and the time during which this force acts, one
can determine the
(A) change in momentum of the object
(B) change in velocity of the object
(C) change in kinetic energy of the object
(D) mass of the object
(E) acceleration of the object
12. An object of mass m is moving with speed v 0 to the right on a horizontal frictionless surface, as shown above,
when it explodes into two pieces. Subsequently, one piece of mass 2/5 m moves with a speed v 0 /2 to the left.
The speed of the other piece of the object is
(A) v o /2 (B) v o /3 (C) 7v o /5 (D) 3v o /2 (E) 2v o
13. A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above.
Which of the five lettered points represents the center of mass of the sphere-rod combination?
(A) A (B) B (C) C (D) D (E) E
14. The graph above shows the force on an object of mass M as a function of time. For the time interval 0 to 4 s,
the total change in the momentum of the object is
(A) 40 kg m/s (B) 20 kg m/s (C) 0 kg m/s (D) -20 kg m/s
(E) indeterminable unless the mass M of the object is known
103
15. As shown in the top view above, a disc of mass m is moving horizontally to the right with speed v on a table
with negligible friction when it collides with a second disc of mass 2m The second disc is moving horizontally
to the right with speed v/2 at the moment of impact The two discs stick together upon impact The speed of the
composite body immediately after the collision is
(A) v/3 (B) v/2 (C) 2v/3 (D) 3v/2 (E) 2v
16. Two people are initially standing still on frictionless ice. They push on each other so that one person, of mass
120 kg, moves to the left at 2 m/s, while the other person, of mass 80 kg, moves to the right at 3 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
17. An object having an initial momentum that may be represented by the vector above strikes an object that is
initially at rest. Which of the following sets of vectors may represent the momenta of the two objects after the
collision?
(A)
(B)
(C)
(D) (E)
18. A θ own above.
Which of the following vectors represents the impulse exerted on the ball by the floor?
19. The momentum p of a moving object as a function of time t is given by the expression p = kt3, where k is a
constant. The force causing this motion is given by the expression
(A) 3kt2 (B) 3kt2/2 (C) kt2/3 (D) kt4 (E) kt4/4
104
Questions 20-21
Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving
directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s.
20. What is the total kinetic energy of the two-puck system before the collision?
(A) 13 J (B) 5.0 J (C) 7.0 J (D) 10 J (E) 11 J
21. What is the magnitude of the total momentum of the two-puck system after the collision?
(A) 1.0 kg•m/s (B) 3.5 kg•m/s (C) 5.0 kg•m/s (D) 7.0 kg•m/s (E) 5.5 5 kg•m/s
22. As shown above, two students sit at opposite ends of a boat that is initially at rest. The student in the front
throws a heavy ball to the student in the back. What is the motion of the boat at the time immediately after the
ball is thrown and, later, after the ball is caught? (Assume that air and water friction are negligible.)
Immediately
After the Throw After the Catch
(A) Boat moves forward Boat moves forward
(B) Boat moves forward Boat moves backward
(C) Boat moves forward Boat does not move
(D) Boat moves backward Boat does not move
(E) Boat moves backward Boat moves forward
23. A person holds a portable fire extinguisher that ejects 1.0 kg of water per second horizontally at a speed of 6.0
m/s. What horizontal force in newtons must the person exert on the extinguisher in order to prevent it from
accelerating?
(A) 0 N (B) 6 (C) 10 N (D) 18 (E)
105
24. A person is standing at one end of a uniform raft of length L that is floating motionless on water, as shown
above. The center of mass of the person-raft system is a distance d from the center of the raft. The person then
walks to the other end of the raft. If friction between the raft and the water is negligible, how far does the raft
move relative to the water?
(A) (B) L (C) (D) d (E) 2d
25. Objects 1 and 2 have the same momentum. Object 1 can have more kinetic energy than object 2 if, compared
with object 2, it
(A) has more mass
(B) has the same mass
(C) is moving at the same speed
(D) is moving slower
(E) is moving faster
26. A 5 kg object is propelled from rest at time t =0 by a net force F that always acts in the same direction. The
magnitude of F in newtons is given as a function of t in seconds by F = 0.5t. What is the speed of the object at
t = 4 s?
(A) 0.5 m/s (B) 0.8 m/s (C) 2.0 m/s (D) 4.0 m/s (E) 8.0 m/s
106
27. Two balls with masses m and 2m approach each other with equal speeds υ on a horizontal frictionless table, as
shown in the top view above. Which of the following shows possible velocities of the balls for a time soon after
the balls collide?
(A) (B) (C)
(D) (E)
107
28. Three identical disks are initially at rest on a frictionless, horizontal table with their edges touching to form a
triangle, as shown in the top view above. An explosion occurs within the triangle, propelling the disks
horizontally along the surface. Which of the following diagrams shows a possible position of the disks at a later
time? (In these diagrams, the triangle is shown in its original position.)
(A) (B)
(C) (D)
(E)
108
