Question 1

A ball hits a wall and rebounds with the same speed, as diagrammed below. The changes in the components of the momentum of the ball are:

Accepted Answer

A)    Δ\DeltaΔ px > 0,  Δ\DeltaΔ py > 0
B)   Δ\DeltaΔ px Δ\DeltaΔ py > 0
C)    Δ\DeltaΔ px = 0,  Δ\DeltaΔ py > 0
D)    Δ\DeltaΔ px = 0,  Δ\DeltaΔ py 
E)    Δ\DeltaΔ px > 0,  Δ\DeltaΔ py < 0  C

Question 2

If a projectile hits a stationary target, and the projectile rebounds and travels back the way it came,

Accepted Answer

A)   the mass of the projectile is much less than the mass of the target.
B)   the mass of the projectile is equal to the mass of the target.
C)   the mass of the projectile is much greater than the mass of the target.
D)   nothing can be said about the masses of the projectile and target without further information.
E)   this is an unphysical situation and will not actually happen. A

Question 3

The center of mass of a system of particles has a constant velocity if:

Accepted Answer

A)   the forces exerted by the particles on each other sum to zero
B)   the external forces acting on particles of the system sum to zero
C)   the velocity of the center of mass is initially zero
D)   the particles are distributed symmetrically around the center of mass
E)   the center of mass is at the geometric center of the system B

Question 4

Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (vA, vB) are:

Accepted Answer

A)   0, v/2
B)   -v/3, 2v/3
C)   -v, v
D)   -2v/3, v/3
E)   none of these

Question 5

Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35 m/s, 45$\degree$ above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground?

Accepted Answer

A)   1.2 m
B)   20 m
C)   31 m
D)   Can't tell because the velocities of the fragments are not given.
E)   Can't tell because the coordinates of the highest point are not given.

Question 6

Momentum may be expressed in:

Accepted Answer

A)   kg/m
B)   gram.s
C)   N.s
D)   kg/(m.s) 
E)   N/s

Question 7

A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg mass is attached to the other end. The masses are placed on a horizontal surface and the spring is compressed 10 cm. The spring is then released with the masses at rest and the masses oscillate. When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s. The mechanical energy that has been lost to this instant is:

Accepted Answer

A)   0 J
B)   0.31 J
C)   0.61 J
D)   0.81 J
E)   1.2 J

Question 8

Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The momentum of the center of mass of the two-block system is:

Accepted Answer

A)   16 m/s in the same direction as A
B)   16 m/s in the same direction as B
C)   32 m/s in the same direction as A
D)   12 m/s in the same direction as B
E)   60 m/s in the same direction as A

Question 9

Sphere X, of mass 2 kg, is moving to the right at 10 m/s. Sphere Y, of mass 4 kg, is moving to the left at 10 m/s. The two spheres collide head-on. The magnitude of the impulse of X on Y is:

Accepted Answer

A)   twice the magnitude of the impulse of Y on X
B)   half the magnitude of the impulse of Y on X
C)   one-fourth the magnitude of the impulse of Y on X
D)   four times the magnitude of the impulse of Y on X
E)   the same as the magnitude of the impulse of Y on X

Question 10

For a two-body collision, involving objects with different masses, a frame of reference which has the same velocity relative to the laboratory as does the center of mass of the two objects is:

Accepted Answer

A)   a frame for which the momentum of the incident object is zero
B)   a frame for which the momentum of the target object is zero
C)   a frame for which the average momentum of the two objects is zero
D)   a frame for which the total momentum of the two objects is zero
E)   none of the above

Question 11

Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The center of mass of the two-block system is moving with the velocity of:

Accepted Answer

A)   1.3 m/s in the same direction as A
B)   1.3 m/s in the same direction as B
C)   2.7 m/s in the same direction as A
D)   1.0 m/s in the same direction as B
E)   5.0 m/s in the same direction as A

Question 12

Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?

Accepted Answer

A)   4 m
B)   5 m
C)   6 m
D)   10 m
E)   need to know the forces they exert

Question 13

The momentum of an object at a given instant is in the same direction as its:

Accepted Answer

A)   displacement
B)   velocity
C)   acceleration
D)   force
E)   Momentum is a scalar and does not have a direction.

Question 14

The x and y coordinates in meters of the center of mass of the three-particle system shown below are:

Accepted Answer

A)   0 m, 0 m
B)   1.3 m, 1.7 m
C)   1.4 m, 1.9 m
D)   1.9 m, 2.5 m
E)   1.4 m, 2.5 m

Question 15

A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:

Accepted Answer

A)   3.0 m/s left
B)   3.0 m/s, right
C)   6.0 m/s, right
D)   6.0 m/s, left
E)   17 m/s, right

Question 16

Two identical carts travel at 1 m/s on a common surface. They collide head-on and are reported to rebound, each with a speed of 2 m/s. Then:

Accepted Answer

A)   momentum was not conserved, therefore the report must be false
B)   if some other form of energy were changed to kinetic during the collision, the report could be true
C)   if the collision were elastic, the report could be true
D)   if the surface were inclined, the report could be true
E)   kinetic energy increased, therefore the report must be false

Question 17

At one instant of time a rocket is traveling in outer space at 2500 m/s and is exhausting fuel at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500 m/s, relative to the rocket, the thrust is:

Accepted Answer

A)   0 N
B)   1.0 * 105 N
C)   1.5 * 105 N
D)   2.9 *105 N
E)   2.5 * 105 N

Question 18

Blocks A and B are moving toward each other. A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of -25 m/s. They suffer a completely inelastic collision. The kinetic energy lost during the collision is:

Accepted Answer

A)   0 J
B)   1250 J
C)   3750 J
D)   5000 J
E)   5600 J

Question 19

A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits there. Afterwards the canoe:

Accepted Answer

A)   is forward of its original position and moving forward
B)   is forward of its original position and moving backward
C)   is rearward of its original position and moving forward
D)   is rearward of its original position and moving backward
E)   is rearward of its original position and not moving

Question 20

A 75-kg man is riding in a 30-kg cart at 2.0 m/s. He jumps off in such a way as to land on the ground with no horizontal velocity. The resulting change in speed of the cart is:

Accepted Answer

A)   0 m/s
B)   2.0 m/s
C)   3.0 m/s
D)   5.0 m/s
E)   7.0 m/s

Exam 9: Center of Mass and Linear Momentum