Question 1

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 
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

Question 2

For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as:

Accepted Answer

A)  the total kinetic energy before the collision 
B)  the difference in the kinetic energies of the objects before the collision 
C)  1/2Mv2com, where M is the total mass and vcom is the velocity of the center of mass 
D)  the kinetic energy of the more massive body before the collision 
E)  the kinetic energy of the less massive body before the collision 
A)  the total kinetic energy before the collision 
B)  the difference in the kinetic energies of the objects before the collision 
C)  1/2Mv2com, where M is the total mass and vcom is the velocity of the center of mass 
D)  the kinetic energy of the more massive body before the collision 
E)  the kinetic energy of the less massive body before the collision

Question 3

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have:

Accepted Answer

A)  the greater speed 
B)  the greater acceleration 
C)  the smaller momentum 
D)  the greater momentum 
E)  the same momentum as the other body 
A)  the greater speed 
B)  the greater acceleration 
C)  the smaller momentum 
D)  the greater momentum 
E)  the same momentum as the other body

Question 4

A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3 m/s as shown. After the sack rests on the flatcar, the speed of the flatcar is:

Accepted Answer

A)  0.6 m/s 
B)  1.2 m/s 
C)  1.8 m/s 
D)  2.4 m/s 
E)  3.6 m/s 
A)  0.6 m/s 
B)  1.2 m/s 
C)  1.8 m/s 
D)  2.4 m/s 
E)  3.6 m/s

Question 5

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:

Accepted Answer

A)  constant and in the forward direction 
B)  constant and in the backward direction 
C)  variable and in the forward direction 
D)  variable and in the backward direction 
E)  zero 
A)  constant and in the forward direction 
B)  constant and in the backward direction 
C)  variable and in the forward direction 
D)  variable and in the backward direction 
E)  zero

Question 6

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 
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 7

What magnitude impulse will give a 2.0-kg object a momentum change of magnitude + 50 kg · m/s.

Accepted Answer

A)  + 25 N · s 
B)  - 25 N · s 
C)  + 50 N · s 
D)  - 50 N · s 
E)  + 100 N · s 
A)  + 25 N · s 
B)  - 25 N · s 
C)  + 50 N · s 
D)  - 50 N · s 
E)  + 100 N · s

Question 8

A 640-N hunter gets a rope around a 320-N polar bear. They are stationary, 20 m apart, on frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move:

Accepted Answer

A)  1.0 m 
B)  3.3 m 
C)  10 m 
D)  12 m 
E)  17 m 
A)  1.0 m 
B)  3.3 m 
C)  10 m 
D)  12 m 
E)  17 m

Question 9

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) $\Delta$px > 0, $\Delta$py > 0 B) $\Delta$px y > 0 C) $\Delta$px = 0, $\Delta$py > 0 D) $\Delta$px = 0, $\Delta$py x > 0, $\Delta$py < 0 A) $\Delta$px > 0, $\Delta$py > 0 B) $\Delta$px y > 0 C) $\Delta$px = 0, $\Delta$py > 0 D) $\Delta$px = 0, $\Delta$py x > 0, $\Delta$py < 0

Question 10

A student's life was saved in an automoblie accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag:

Accepted Answer

A)  causes a much smaller change in momentum 
B)  exerts a much smaller impulse 
C)  causes a much smaller change in kinetic energy 
D)  exerts a much smaller force 
E)  does much more work 
A)  causes a much smaller change in momentum 
B)  exerts a much smaller impulse 
C)  causes a much smaller change in kinetic energy 
D)  exerts a much smaller force 
E)  does much more work

Question 11

When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:

Accepted Answer

A)  the force of your foot on the accelerator 
B)  the force of friction of the road on the tires 
C)  the force of the engine on the drive shaft 
D)  the normal force of the road on the tires 
E)  none of the above 
A)  the force of your foot on the accelerator 
B)  the force of friction of the road on the tires 
C)  the force of the engine on the drive shaft 
D)  the normal force of the road on the tires 
E)  none of the above

Question 12

A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest the heavier object moves downward and the lighter object moves upward with the same magnitude acceleration. Which of the following statements is true for the system consisting of the two objects?

Accepted Answer

A)  The center of mass remains at rest. 
B)  The net external force is zero. 
C)  The velocity of the center of mass is a constant. 
D)  The acceleration of the center of mass is g, downward. 
E)  None of the above statements are true. 
A)  The center of mass remains at rest. 
B)  The net external force is zero. 
C)  The velocity of the center of mass is a constant. 
D)  The acceleration of the center of mass is g, downward. 
E)  None of the above statements are true.

Question 13

A 3.0-kg and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40 J. The speed of their center of mass is:

Accepted Answer

A)  zero 
B)  2.8 m/s 
C)  4.0 m/s 
D)  5.2 m/s 
E)  6.3 m/s 
A)  zero 
B)  2.8 m/s 
C)  4.0 m/s 
D)  5.2 m/s 
E)  6.3 m/s

Question 14

Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinectic energy of 50 J and Y has a kinetic erengy of:

Accepted Answer

A)  20 J 
B)  8 J 
C)  310 J 
D)  125 J 
E)  50 J 
A)  20 J 
B)  8 J 
C)  310 J 
D)  125 J 
E)  50 J

Question 15

Block A, with a mass of 2.0 kg, moves along the x axis with a velocity of 5.0 m/s in the positive x direction. It suffers an elastic collision with block B, initially at rest, and the blocks leave the collision along the x axis. If B is much more massive than A, the velocity of A after the collision is:

Accepted Answer

A)  0 
B)  +5.0 m/s 
C)  -5.0 m/s 
D)  +10 m/s 
E)  -10 m/s 
A)  0 
B)  +5.0 m/s 
C)  -5.0 m/s 
D)  +10 m/s 
E)  -10 m/s

Question 16

A uniform narrow bar, resting on ice, is given a transverse horizontal impulse   at one end as shown. The center of mass of the bar COM will then:

Accepted Answer

A)  remain at rest 
B)  move in a circle 
C)  move in a straight line 
D)  move in a parabola 
E)  move along some other curve 
A)  remain at rest 
B)  move in a circle 
C)  move in a straight line 
D)  move in a parabola 
E)  move along some other curve

Question 17

A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the bullet was:

Accepted Answer

A)  unknown since the heat generated in the collision was not given 
B)  8.0 * 102 m/s 
C)  24.0 m/s 
D)  8.0 m/s 
E)  2.4 * 104 m/s 
A)  unknown since the heat generated in the collision was not given 
B)  8.0 * 102 m/s 
C)  24.0 m/s 
D)  8.0 m/s 
E)  2.4 * 104 m/s

Question 18

Blocks A and B are moving toward each other along the x axis. 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 an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is:

Accepted Answer

A)  0 
B)  2500 J 
C)  5000 J 
D)  7500 J 
E)  10000 J 
A)  0 
B)  2500 J 
C)  5000 J 
D)  7500 J 
E)  10000 J

Question 19

The center of mass of a system of particles obeys an equation similar to Newton's second law   where:

Accepted Answer

A)    is the total internal force and m is the total mass of the system 
B)    is the total internal force and m is the mass acting on the system 
C)    is the total external force and m is the total mass of the system 
D)    is the force of gravity and m is the mass of Earth 
E)    is the force of gravity and m is the total mass of the system 
A)    is the total internal force and m is the total mass of the system 
B)    is the total internal force and m is the mass acting on the system 
C)    is the total external force and m is the total mass of the system 
D)    is the force of gravity and m is the mass of Earth 
E)    is the force of gravity and m is the total mass of the system

Question 20

If the total momentum of a system is changing:

Accepted Answer

A)  particles of the system must be exerting forces on each other 
B)  the system must be under the influence of gravity 
C)  the center of mass must have constant velocity 
D)  a net external force must be acting on the system 
E)  none of the above 
A)  particles of the system must be exerting forces on each other 
B)  the system must be under the influence of gravity 
C)  the center of mass must have constant velocity 
D)  a net external force must be acting on the system 
E)  none of the above

Exam 9: Center of Mass and Linear Momentum

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

For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as:

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have:

A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3 m/s as shown. After the sack rests on the flatcar, the speed of the flatcar is:

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:

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:

What magnitude impulse will give a 2.0-kg object a momentum change of magnitude + 50 kg · m/s.

A 640-N hunter gets a rope around a 320-N polar bear. They are stationary, 20 m apart, on frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move:

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:

A student's life was saved in an automoblie accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag:

When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:

A 3.0-kg and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40 J. The speed of their center of mass is:

Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinectic energy of 50 J and Y has a kinetic erengy of:

A uniform narrow bar, resting on ice, is given a transverse horizontal impulse at one end as shown. The center of mass of the bar COM will then:

A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the bullet was:

Blocks A and B are moving toward each other along the x axis. 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 an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is:

The center of mass of a system of particles obeys an equation similar to Newton's second law where:

If the total momentum of a system is changing:

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