Linear Momentum Test

Multiple Choice Questions

1 The law of conservation of momentum applies to a system of colliding objects only if:

(A) there is no change in kinetic energy of the system

(B) the coefficient of restitution is one

(C) the coefficient of restitution is zero

(D) the net external impulse is zero

(E) the collisions are all elastic

2 A ball on a rope swings around a pole.

In which direction will the ball fly if released at the location shown?

(A) A (B) B (C) C (D) D (E) E

3 Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 13 m/s. To design a similar ramp for 26 m/s one should:

(A) increase radius by factor of 2

(B) decrease radius by factor of 2

(C) increase radius by factor of 4

(D) decrease radius by factor of 4

(E) increase radius by factor of √

4 The momentum of an object at a given instant is independent of its:

(A) inertia (B) mass (C) speed (D) velocity (E) acceleration

5 A particle moves along the axis. Its momentum is graphed below as a function of time. Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest.

(A) 1, 2, 3, 4 (B) 2, 3, 4, 1 (C) 1, 4, 3, 2 (D) 1, 3, 4, 2 (E) 2, 4, 3, 1

6 A force acting on an object varies as a function of time according to the equation , where is a constant. If the object had an initial momentum of 0 at time , what is the momentum of the object at time ?

7 In collisions between two objects, kinetic energy is conserved only

(A) if one of the objects was initially at rest.

(B) if the two objects have the same mass.

(C) if potential energy converts to work energy.

(D) in inelastic collisions.

(E) in elastic collisions.

(A)

(B)

(C)

(D)

(E)

Name: _________________________

( )

∫

Impulse is the integral of

force as a function of time.

From Newton’s 2nd Law,

the force acting on the

particle is the slope of the

momentum vs. time graph.

Mr. Kepple

At a given instant, the velocity

would be effectively constant,

therefore momentum does not

depend on acceleration.

When released the object will

follow a straight line path in the

direction is was initially moving

(tangent to the circle).

Momentum is

conserved only

when there are

no external

forces acting on

the system.

This is just the

definition of an

elastic collision.

8

A large cannon is mounted on a cart with frictionless wheels that is initially at rest on a horizontal surface. The cannon fires a large cannonball to the right with a speed , which is then caught by a trap firmly attached to the cart. What is the final speed of the cannon-cart-cannonball system?

(A) , to the left

(B) , to the right

(C) 0

(D) , to the left

(E) , to the right

9 One end of a 1 m long string is fixed; the other end is attached to a 2 kg stone. The stone swings in a vertical circle, passing the top point at 4 m/s. The tension force of the string at this point is about:

(A) 0

(B) 12 N

(C) 30 N

(D) 32 N

(E) 52 N

10 If the total momentum of a system is changing:

(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

11

A disk travels along the essentially frictionless surface of an air hockey table and strikes a second disk of identical mass that was initially at rest. Which of the following diagrams shows the motion of the two disks immediately after the glancing elastic collision occurs?

(A)

(B)

(C)

(D)

(E)

For a glancing elastic collision of

two objects of equal mass they

must rebound at 90 degrees.

Since the cannonball is

caught by the trap, it never

leaves the system. As a

result the momentum, and

therefore the speed, will

remain zero.

( )( )( )

( )( )

The momentum of an object is constant unless a net

force is exerted on it. Since forces internal to the system

cancel out, the only way to change the momentum of a

system is by exerting a net external force.

12 The difference between a conservative system and a nonconservative system is

(A) Momentum is not conserved in nonconservative systems.

(B) Energy is not conserved in nonconservative systems.

(C) Mechanical energy is not conserved in nonconservative systems.

(D) In a conservative system mechanical energy is transformed into thermal energy.

(E) In a nonconservative system there is no change in mechanical energy.

13 A 5-kg object can move along the axis. It is

subjected to a force in the positive

direction; a graph of as a function of time is shown below. Over the time the force is applied what is the object’s change in speed?

(A) 0.8m/s

(B) 1.1m/s

(C) 1.6m/s

(D) 2.3m/s

(E) 4.0m/s

14 An object moving on a circular path of radius meters at a constant speed of 4 m/s. The time required for one revolution is:

(A) s

(B) s

(C) s

(D) s

(E) 2/ s

15

A cannon is mounted on a cart, and carrying a cannonball. The total mass of the cart, cannon, and ball is , and the car is rolling with no friction at a velocity in the positive -direction as shown above. The ball, of mass , is fired with a velocity of in the positive -direction. What is the velocity of the cart and cannon after the ball is fired?

16 A car travels north at constant velocity. It goes over a piece of mud, which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is…

(A) vertically upward.

(B) horizontally to the north.

(C) horizontally to the south.

(D) zero.

(E) upward and forward at 45° to the horizontal.

17 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 the…

(A) greater speed

(B) greater acceleration

(C) smaller momentum

(D) greater momentum

(E) same momentum as the other body

(A)

(B)

(C)

(D)

(E)

This is just the

definition of a

conservative

system.

∫

( )( )

( )

( )

( )

Conservation of momentum

Equation:

Now solve for

Mud moves

in a circle,

acceleration

must be

centripetal.

From , we

see the change in

momentum will be

the same for both.

18 Force:

(A) equals the negative integral (with respect to distance) of the potential energy function

(B) is the ability to do work

(C) is the rate of change of doing work

(D) equals the time rate of change of momentum

(E) has dimensions of momentum multiplied by time

19

Two ice skaters, of mass 30 kg and 80 kg, are skating across the surface of a frozen lake on a collision course, with respective velocities of 2.0 m/s in a general north direction, and 1.0 m/s generally west, as shown above. After they collide, the pair of skaters move off in a direction north of west with a momentum of approximately 100 kgm/s. How much kinetic energy was lost in the collision?

(A) 0 J

(B) 110 J

(C) 55 J

(D) 70 J

(E) 120 J

20

A billiard ball hits the side of a pool table at an angle as shown in the top view above, and bounces away at the same angle, and with the same speed. Which vector indicates the direction of the net change in momentum of the billiard ball?

(A) (B)

(C) (D)

(E)

Definition of

momentum

from

Newton’s 2nd

Law:

(

)

( )

( )( )

( )( )

From this we see that is a

little less than 50 J.

Since the initial kinetic energy was 100 J

and less than 50 J remains after the

collision, by process of elimination we

choose the answer that 55 J were lost.

Vector subtraction, we are looking

for the direction of .

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��𝑓

��𝑓 ��𝑖

Directions: Answer both questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in the spaces provided after each part. Mech. 1. Two pendulums A and B are aligned side-by-side such that the bobs of each pendulum just barely touch. The mass of each string is negligible and has identical length . Pendulum A has mass while pendulum B has mass . Pendulum A is pulled back away from the equilibrium position to a height 0.10 meters and then released.

(a) Assuming the system is conservative; calculate the speed of the pendulum A just before it collides with pendulum B. (b) The collision between the two pendulums is a perfectly elastic head-on collision. Use conservation principles to write the following equations in terms of , , and .

i. Conservation of momentum ii. Conservation of kinetic energy. (Use the easy

one if you can remember it!)

Name: ___________________________ Linear Momentum Test Free Response Questions

m

𝑙

𝑚

𝑚 A B

A

B

√

Mr. Kepple

√ ( )( )

(c) Using the equations you wrote down in part (b), calculate the speed of each pendulum immediately after the collision.

i. speed of pendulum A ii. speed of pendulum B (d) Assuming a conservative system, calculate the maximum height reached by pendulum B. (e) If the two pendulum had the same mass, indicate whether the height reached by pendulum B would be greater than, less than, or equal to the height you calculated in part (d).

___ Greater Than ___ Less Than ___ Equal to

Justify your answer.

(

)

( )

(

)

( )

( )

( )

X

If the two pendulums had the same mass then the speed of pendulum B after the

collision would be equal to the speed of pendulum A before the collision. As a result

pendulum B would have more kinetic energy after the collision and would therefore

reach a greater final height.

Mech. 2. A 2-kilogram block and an 8-kilogram block are both attached to an ideal spring (for which N/m) and both are initially at rest on a horizontal frictionless surface, as shown in the diagram above. In an experiment, a 100-gram (0.1 kg) ball of clay is thrown at the 2-kilogram block. The clay is moving horizontally with speed when it hits and sticks to the block. The 8-kilogram block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4 meters.

(a) Calculate the energy stored in the spring at maximum compression. (b) Calculate the speed of the clay ball and 2-kilogram block immediately after the clay sticks to the block but before the spring compresses significantly.

( )( )

√

√ ( )

( )

(c) Calculate the initial speed of the clay. In a second experiment, an identical ball of clay is thrown at another identical 2-kilogram block, but this time the stop is removed so that the 8-kilogram block is free to move.

(d) Indicate whether the maximum compression of the spring will be greater than, equal to, or less than 0.4 meter.

___ Greater Than ___ Less Than ___ Equal to

Justify your answer. (e) State the principle or principles that can be used to calculate the velocity of the 8-kilogram block at the instant that the spring regains its original length. Write the appropriate equation(s) and show the numerical substitutions, but do not solve for the velocity.

( )

(

)

(

) ( )

X

With the stopper in place the block and clay came to rest. As a result all of the kinetic

energy of the block and clay was transformed into the elastic potential energy of the

spring. With the stopper removed the blocks are not brought to rest. As a result, a

smaller amount of kinetic energy is transferred to the spring. Therefore the spring

does not compress as great a distance as before.

( )( )

Conservation of Momentum

( )( )

Conservation of Energy