AP Physics C Mechanics Momentum MCQ

A system consists of two objects having masses ml and m2 (ml < m2). 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) (m1+m2)v

(B) (m2-m1)v

(C) 0.5(m1+m2)v

(D)0.5(m2-m1)v

(E) m2v

(b) (m2-m1)v

Two particles of equal mass mo, moving with equal speeds vO along paths inclined at 60° to the x-axis as shown above, collide and stick together. Their velocity after the collision has magnitude

(A) v0/4 (B) v0/2 (C) 2v0/2 (D) 3v0/2 (E) v0

(b) v0/2

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

(b) point b

Mass M1 is moving with speed v toward stationary mass M2. The speed of the center of mass of the system is

(e) (m1/m1+m2)v

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

(A) 0m/s

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

(C) 3 m/s

A projectile of mass M1 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 M2. If the kinetic energy of the projectile after firing is K, the gun will recoil with a kinetic energy equal to

(A) K

(B) (m2/m1)K

(C) (m1sqrd/m2sqrd)K

(D) (m1/m2-m1)K

(E) 6 m/s

(D) (m1/m2-m1)K

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)

(A) (15/14, 6/7)

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?

(D) 37 degrees, 8 m/s

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.

(D) Down with a speed less than v

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

(A) change in momentum of the object

An object of mass m is moving with speed v0 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 v0/2 to the left. The speed of the other piece of the object is

(A) vo/2

(B) vo/3

(C) 7vo/5

(D) 3vo/2

(E) 2vo

(E) 2vo

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

(B) B

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

(C) 0 kg m/s

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

(C) 2v/3

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

(A) Zero

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?

E

A 2kg ball collides with the floor at an angle θ and rebounds at the same angle and speed as shown above. Which of the following vectors represents the impulse exerted on the ball by the floor?

E

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

(A) 3kt2

What is the total kinetic energy of the two-puck system before the collision?

(A) 13 J

(B)5.0J

(C) 7.0J

(D)10J

(E)11J

(B)5.0J

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

(C) 5.0 kg•m/s

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.

C

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) 0N

(B)6N

(C)10N

(D)18N

(E)36N

(B)6N

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) L/2

(B) L

(C) d/2

(D) d

(E) 2d

(E) 2d

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

(E) is moving faster

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

(B) 0.8 m/s

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?

D

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.

E