Conservation Laws
Lead Author(s): University of Colorado Boulder
Source: UC Boulder PhET
Student Price: FREE
Learn about the use of conservation laws of momentum and energy, as well as the workenergy theorem, for solving problems involving elastic and inelastic collisions.
This content is licensed under the Creative Commons Attribution 4.0 International License.
[UColorado] A ball bounces off the floor as shown. The direction of the impulse on the ball, $\Delta$$\bf{p}$, is ...
straight up $\uparrow$
straight down $\downarrow$
to the right $\rightarrow$
to the left $\leftarrow$
[UColorado] A car moves in the +x direction at 55 mph. It makes a uturn, and is then returning (x direction) at 55 mph. Is $\Delta$$\bf{p}$ ....
zero
to the right (+x direction)
to the left (x direction)
not enough information to decide.
[Mazur] Suppose a pingpong 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$$\bf{p}$/$\Delta$t
It takes less time to stop the pingpong ball.
Both take the same time.
It takes more time to stop the pingpong ball.
[Mazur] Suppose a pingpong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the $\it{distances}$ needed to stop them compare?
Hint: The workenergy theorem says Work = $\bf{F}$. $\Delta$$\bf{x}$ = $\Delta$$\bf{KE}$
It takes a shorter distance to stop the pingpong ball.
Both take the same distance.
It takes a longer distance to stop the pingpong ball.
[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.
four times
twice
equal to
onehalf
onequarter
[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 xcomponent of $\bf{p}_{1f}$?
0
1
2
3
None of these
[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 xcomponent of $\bf{p}_{1f }$?
0
1
2
3
None of these
[Mazur] A compact car and a large truck collide head on and stick together. Which undergoes the larger momentum change?
car
truck
The momentum change is the same for both vehicles.
Can’t tell without knowing the initial velocities.
[Mazur] A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision?
car
truck
Both experience the same acceleration.
Can’t tell without knowing the initial velocities.
[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?
Cart A is hollow.
The two carts are identical.
Cart B is hollow.
[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?
Yes.
No.
[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
increases.
does not change.
decreases.
[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)
standing still, where they were initially.
standing still, farther away from each other.
standing still, closer together than initially.
moving away from each other.
moving toward each other.
[Mazur] Think fast! You’ve just driven around a curve in a narrow, oneway 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
hit the other car.
hit the wall.
hit either one—it makes no difference.
consult your lecture notes.
[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?
I
II
III
II,III only
All three.
[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?
Yes, it moves to the right.
Yes, it moves to the left.
No, it remains in place.
[Mazur] A block slides without friction down a ramp as shown.
As the block slides down the speed and the magnitude of the acceleration .
increases, increases
increases, decreases
decreases, increases
decreases, decreases
[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...
+

0
[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...
+

0
[UColorado] Albert Einstein lowers a book of mass m downward a distance h at constant speed v. The net force on the book is...
+

0
[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)
+5 J
5 J
+10 J
10 J
0 J
[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)
+5 J
5 J
+10 J
10 J
0 J
[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...
same
different.
[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?
Yes
No
Impossible to determine without knowing the mass of the puck.
[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..
 (positive)
 (negative)
0
[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
four times smaller.
half as big.
twice as big.
the same.
undetermined—depends on time taken.
[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?
12 J
10 J
6 J
2 J
0 J
[Mazur] At the bowling alley, the ballfeeder mechanism must exert a force to push the bowling balls up a 1.0m 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 5.0kg bowling ball?
200 N
50 N
25 N
5.0 N
impossible to determine
[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?
Same, 1 m.
2 m.
4 m.
1/2 m.
(not enough information)
[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..
as much kinetic energy as the lighter one.
twice as much kinetic energy as the lighter one.
half as much kinetic energy as the lighter one.
four times as much kinetic energy as the lighter one.
impossible to determine.
[Mazur] Suppose you drop a 1kg rock from a height of 5 m above the ground.When it hits, how much force does the rock exert on the ground?
0.2 N
5 N
50 N
100 N
(need more information)
[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?
100 N/m
50 N/m
5000 N/m
2 N/m
.02 N/m
[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
twice as high
4 times as high
half as high
16 times as high
(need more information)
[Mazur] A springloaded 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?
48 m
24 m
12 m
6 m
3 m
[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=$
mgR
mg$\ast$(2R)
mg$\ast$(3R)
0
None of these
[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")
mgR
2 mgR
3 mgR
 mgR
something entirely different
[UColorado] A small mass, starting at rest, slides without friction down a rail to a loopdeloop 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?
Yes, the ball makes it to the top of the loop.
No, the ball will not make it to the top.
Not enough info to say, or don&amp;#39;t know.
[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?
h
Less than h
More than h
Not enough information to decide.
[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 $\it{minimum}$.
KE Max at 100; PE Min at 100
KE Max at 50; PE Min at 50
KE Max at 100; PE Min at 50
KE Max at 50; PE Min at 100
KE Max at 30; PE Min at 30