  # Conservation Laws

Source: UC Boulder PhET

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Learn about the use of conservation laws of momentum and energy, as well as the work-energy theorem, for solving problems involving elastic and inelastic collisions.

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[Conservation Laws] 1 [UColorado] A ball bounces off the floor as shown. The direction of the impulse on the ball, $\Delta$$\bf{p}$, is ...

A

straight up $\uparrow$

B

straight down $\downarrow$

C

to the right $\rightarrow$

D

to the left $\leftarrow$

[Conservation Laws] 2

[UColorado] A car moves in the +x direction at 55 mph. It makes a u-turn, and is then returning (-x direction) at 55 mph. Is $\Delta$$\bf{p}$ ....

A

zero

B

to the right (+x direction)

C

to the left (-x direction)

D

not enough information to decide.

[Conservation Laws] 3

[Mazur] Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?

Hint: Fnet = ma = $\Delta$$\bf{p}$/$\Delta$t

A

It takes less time to stop the ping-pong ball.

B

Both take the same time.

C

It takes more time to stop the ping-pong ball.

[Conservation Laws] 4

[Mazur] Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the $\it{distances}$ needed to stop them compare?

Hint: The work-energy theorem says Work = $\bf{F}$. $\Delta$$\bf{x}$ = $\Delta$$\bf{KE}$

A

It takes a shorter distance to stop the ping-pong ball.

B

Both take the same distance.

C

It takes a longer distance to stop the ping-pong ball.

[Conservation Laws] 5

[Mazur] Consider two carts, of masses m and 2m, at rest on an air track. If you push each car for 3 s, exerting equal force on each, the momentum of the light cart after the push is __ the momentum of the heavy cart.

A

four times

B

twice

C

equal to

D

one-half

E

one-quarter

[Conservation Laws] 6

[UColorado] Ball 1 strikes $\it{stationary}$ Ball 2 in a 1D elastic collision. The initial momentum of Ball 1, $\bf{p}_{1i}$, and the final momentum of Ball 2, $\bf{p}_{2f}$, are shown on the graph. (4 units and 5 units, respectively)

What is the magnitude of the x-component of $\bf{p}_{1f}$? A

0

B

1

C

2

D

3

E

None of these

[Conservation Laws] 7

[UColorado] Ball 1 strikes stationary Ball 2 in 2D elastic collision. The initial momentum of Ball 1, $\bf{p}_{1i}$, (4,0) and the final momentum of Ball 2, $\bf{p}_{2f}$ (3,2) are shown on the graph.

What is the x-component of $\bf{p}_{1f }$? A

0

B

1

C

2

D

3

E

None of these

[Conservation Laws] 8

[Mazur] A compact car and a large truck collide head on and stick together. Which undergoes the larger momentum change?

A

car

B

truck

C

The momentum change is the same for both vehicles.

D

Can’t tell without knowing the initial velocities.

[Conservation Laws] 9

[Mazur] A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision?

A

car

B

truck

C

Both experience the same acceleration.

D

Can’t tell without knowing the initial velocities.

[Conservation Laws] 10

[Mazur] You are given two carts, A and B. They look identical, and you've been told they are made of the same material.

You place A at rest on an air track and give B a constant velocity to the right so that it collides elastically with A.

After the collision, both carts move to the right, the velocity of B being smaller than what it was before the collision. What do you conclude?

A

Cart A is hollow.

B

The two carts are identical.

C

Cart B is hollow.

[Conservation Laws] 11

[Mazur] Is it possible for a stationary object that is struck by a moving object to have a larger final momentum than the initial momentum of the incoming object?

A

Yes.

B

No.

[Conservation Laws] 12

[Mazur] Suppose rain falls vertically into an open cart rolling along a straight horizontal track with negligible friction. As a result of the accumulating water, the speed of the cart

A

increases.

B

does not change.

C

decreases.

[Conservation Laws] 13

[Mazur] Two people on roller blades throw a ball back and forth. After a couple of throws, when the first thrower once again is holding the ball, they are (ignore friction)

A

standing still, where they were initially.

B

standing still, farther away from each other.

C

standing still, closer together than initially.

D

moving away from each other.

E

moving toward each other.

[Conservation Laws] 14

[Mazur] Think fast! You’ve just driven around a curve in a narrow, one-way street at 25 mph when you notice a car identical to yours coming straight toward you at 25 mph. You have only two options: hitting the other car head on or swerving into a massive concrete wall, also head on. In the split second before the impact, you decide to

A

hit the other car.

B

hit the wall.

C

hit either one—it makes no difference.

D

[Conservation Laws] 15

[Mazur] If all three collisions in the figure shown here are $\it{totally}$ $\it{inelastic}$, which bring(s) the car on the left to a halt? A

I

B

II

C

III

D

II,III only

E

All three.

[Conservation Laws] 16 [Mazur] Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion?

A

Yes, it moves to the right.

B

Yes, it moves to the left.

C

No, it remains in place.

[Conservation Laws] 17

[Mazur] A block slides without friction down a ramp as shown.

As the block slides down the speed and the magnitude of the acceleration . A

increases, increases

B

increases, decreases

C

decreases, increases

D

decreases, decreases

[Conservation Laws] 18

[UColorado] Albert Einstein lowers a book of mass m downward a distance h at constant speed v. The work done by the force of gravity is...

A

+

B

-

C

0

[Conservation Laws] 19

[UColorado] Albert Einstein lowers a book of mass m downward a distance h at constant speed v. The work done by the force of Albert's hand is...

A

+

B

-

C

0

[Conservation Laws] 20

[UColorado] Albert Einstein lowers a book of mass m downward a distance h at constant speed v. The net force on the book is...

A

+

B

-

C

0

[Conservation Laws] 21

[UColorado] A 1 kg object is moved part way around a square loop as shown. The square is 1m on a side. The final position is 0.5 m lower than where it started. How much work has $\it{gravity}$ done on the object during its journey? (Use g=10 m/s^2) A

+5 J

B

-5 J

C

+10 J

D

-10 J

E

0 J

[Conservation Laws] 22

[UColorado] A 1 kg object is moved part way around a square loop as shown. The square is 1m on a side. The final position is 0.5 m lower than where it started.

How much work have YOU done on the object during its journey? (Use g=10 m/s^2) A

+5 J

B

-5 J

C

+10 J

D

-10 J

E

0 J

[Conservation Laws] 23

[UColorado] A 1 kg object is moved part way around a square loop as shown. The square is 1m on a side. The final position is 0.5 m lower than where it started.

If instead of moving part way around a square, the mass where taken on a long and tortuous journey to the Moon, Tibet, and Lithuania and then returned to the same finish point as before, would the work done by gravity be the... A

same

B

different.

[Conservation Laws] 24

[UColorado] A hockey puck slides without friction along a frozen lake toward an ice ramp and plateau as shown. The speed of the puck is 4m/s and the height of the plateau is 1m. Will the puck make it all the way up the ramp? A

Yes

B

No

C

Impossible to determine without knowing the mass of the puck.

[Conservation Laws] 25 [UColorado] A rock of mass m is twirled on a string in a horizontal plane. The work done by the tension in the string on the rock is..

A
• (positive)
B
• (negative)
C

0

[Conservation Laws] 26

[UColorado] Suppose you want to ride your mountain bike up a steep hill. Two paths lead from the base to the top, one twice as long as the other. (Neglect friction i.e. consider only your "fight against gravity") Compared to the average force you would exert if you took the short path, the average force you exert along the longer path is

A

four times smaller.

B

half as big.

C

twice as big.

D

the same.

E

undetermined—depends on time taken.

[Conservation Laws] 27

[UColorado] An object is pushed by a variable force, plotted below as a function of position, x.

How much work has the force done on the object when it has moved from x=0 to x=+6 m? A

12 J

B

10 J

C

6 J

D

2 J

E

0 J

[Conservation Laws] 28

[Mazur] At the bowling alley, the ball-feeder mechanism must exert a force to push the bowling balls up a 1.0-m long ramp. The ramp leads the balls to a chute 0.5 m above the base of the ramp.

Approximately how much force must be exerted on a 5.0-kg bowling ball? A

200 N

B

50 N

C

25 N

D

5.0 N

E

impossible to determine

[Conservation Laws] 29

[Mazur] A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel before coming to rest?

A

Same, 1 m.

B

2 m.

C

4 m.

D

1/2 m.

E

(not enough information)

[Conservation Laws] 30

[Mazur] Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. (Assume no air resistance.) Just before hitting the ground, the heavier marble has..

A

as much kinetic energy as the lighter one.

B

twice as much kinetic energy as the lighter one.

C

half as much kinetic energy as the lighter one.

D

four times as much kinetic energy as the lighter one.

E

impossible to determine.

[Conservation Laws] 31

[Mazur] Suppose you drop a 1-kg rock from a height of 5 m above the ground.When it hits, how much force does the rock exert on the ground?

A

0.2 N

B

5 N

C

50 N

D

100 N

E

[Conservation Laws] 32

[UColorado] A 20 cm long spring is attached to a wall. The string stretches to a length of 22 cm when you pull on it with a force of 100 N. What is the spring constant, "k" of the spring?

A

100 N/m

B

50 N/m

C

5000 N/m

D

2 N/m

E

.02 N/m

[Conservation Laws] 33 [UColorado] A marble rolls down a frictionless track, and reaches speed v at the bottom.

If you want it to reach a speed of 4v at the bottom, you need the start of the new track to be

A

twice as high

B

4 times as high

C

half as high

D

16 times as high

E

[Conservation Laws] 34

[Mazur] A spring-loaded dart gun shoots straight up, and the dart reaches a maximum height of 24 m.
The same dart is shot straight up again, but this time the spring is compressed only half as far before firing.
How far up does the dart go this time, neglecting friction and assuming an ideal spring?

A

48 m

B

24 m

C

12 m

D

6 m

E

3 m

[Conservation Laws] 35 [UColorado] A mass m is at the end of light (massless) rod of length R, the other end of which has a frictionless pivot so the rod can swing in a vertical plane.
The rod is initially horizontal and the mass is pushed down with an initial speed v$_o$ .

What initial kinetic energy is required for the mass to pivot 270$^\circ$ (to the vertical, or "12 o'clock" position?)

$\frac{1} {2}$$\it{mv}$$^2 _o=$

A

mgR

B

mg$\ast$(2R)

C

mg$\ast$(3R)

D

0

E

None of these

[Conservation Laws] 36 [UColorado] A mass m is at the end of a light (massless) rod of length R, the other end of which has a frictionless pivot. The rod is initially horizontal and the mass is pushed down with an initial speed v$_o$.

What is the change in potential energy of the mass, when it goes from this starting position to the top of the circle ("12 o'clock")

A

mgR

B

2 mgR

C

3 mgR

D
• mgR
E

something entirely different

[Conservation Laws] 37 [UColorado] A small mass, starting at rest, slides without friction down a rail to a loop-de-loop as shown. The maximum height of the loop is the same as the initial height of the mass.

Will the ball make it to the top of the loop?

A

Yes, the ball makes it to the top of the loop.

B

No, the ball will not make it to the top.

C

Not enough info to say, or don&amp;amp;#39;t know.

[Conservation Laws] 38

[UColorado] A mass slides down a frictionless ramp of height h and hits a carpet with kinetic friction coefficient $\mu _K$ = 0.9 Its initial speed is zero. How far does the mass slide along the carpet? A

h

B

Less than h

C

More than h

D

Not enough information to decide.

[Conservation Laws] 39

[UColorado] A roller coaster rolls without friction along a track shown below. Its initial speed at the beginning of the track (which is somewhere off to the left, not shown) is great enough to allow it coast along the whole track. Neglect friction.

At what position, x, is the kinetic energy a $\it{maximum}$, and at what position, x, is the potential energy $\it{minimum}$. A

KE Max at 100; PE Min at 100

B

KE Max at 50; PE Min at 50

C

KE Max at 100; PE Min at 50

D

KE Max at 50; PE Min at 100

E

KE Max at 30; PE Min at 30