Momentum Chap. 7 Review Questions & Solutions
Review Questions
1. Distinguish between mass and momentum. Which is inertia and which is inertia in motion. (7.1) An objects inertia is basically defined
by its mass. An objects momentum is its mass multiplied by its velocity. This means that Mass is Inertia and Momentum is
inertia in motion.
2. a. Which has the greater mass, a heavy truck at rest or a rolling skateboard? The truck as the greater mass
b. Which has the greater momentum? The rolling skateboard (7.1)
3. Distinguish between impact and impulse. Which designates a force and which is the force multiplied by time. (7.2) Impact is basically
just the force applied to an object and impulse is the force multiplied by the amount it is applied for. This means that the force is
impact and the impulse is force multiplied by time.
4. When the force of impact on an object is extended in time, does the impulse increase or decrease? (7.2) The impulse increases.
5. Distinguish between impulse and momentum. Which is force x time and which is inertia in motion. (7.2) Impulse is how long a force is
applied for and momentum is mass multiplied by velocity. This means that impulse is force multiplied by time and momentum is
inertia in motion.
6. Does impulse equal momentum or a change in momentum? (7.2) Impulse is equal to the change in momentum.
7. For a constant force, suppose the duration of impact on an object is doubled (7.2)
a. How much is the impulse increased? It is doubled
b. How much is the resulting change in momentum increased? It is doubled
8. In a car crash, why is it advantageous for an occupant to extend the time during which the collision takes place? (7.2) Because no
matter how long it takes the impact will be the same because all of the momentum needs to be taken away. Since impact is force
multiplied by time, we know that the longer you make that crash take, the less force needs to be exerted on you and your car to
take away the momentum you had before the crash.
9. If the time of impact in a collision is extended by four times, how much does the force of impact change? (7.2) It is reduced to one
fourth of what it was before the time was reduced.
10. Why is it advantageous for a boxer to ride with the punch? Why should he avoid moving into an oncoming punch? (7.2) Saying that a
boxer rides with a punch implies that he moves away as the punch hits him, this is one way to make the impact of the force take
longer, thus decreasing the amount of force that he feels. He should avoid moving into an oncoming punch because this would do
the opposite and would make the impact of the punch take less time and so it would increase the amount of force that he feels.
11. Visualize yourself on a skateboard. (7.3)
a. When you throw a ball, do you experience an impulse? Yes because when you push on the ball the ball pushes back on you. This
force has an impulse.
b. Do you experience an impulse when you catch a ball of the same speed? Yes because when you catch the ball it exerts a force on you.
This force has an impulse.
c. Do you experience an impulse when you catch it and throw it out again? Yes you experience the impulse that was described in b
when you catch it and the one described in a when you throw it.
d. Which impulse is greatest? Catching it and throwing it out again because you experience the impulse of catching it and the
impulse of throwing it.
12. Why is more impulse delivered during a collision when bouncing occurs than during one when it doesn’t? (7.3) Because there is the
impulse that comes from stopping the balls downward momentum when it hits the ground and the impulse of giving the ball
upward momentum as it goes back up.
13. In terms of momentum conservation, why does a cannon recoil when fired? (7.4) Because the initial system had no momentum. If
the cannonball has momentum after it is fired, then the momentum of the cannon must be equal to and opposite from that
momentum otherwise momentum would not be conserved – and we know that momentum has to be conserved.
14. What does it mean to say that momentum is conserved? (7.4) It means that the momentum before and after the collision is the same.
15. Distinguish between an elastic and an inelastic collision. (7.5) In an elastic collision the objects basically bounce off of each other
(they are not permanently deformed and do not generate heat). In an inelastic collision the objects do not bounce off of each
other, but instead become attached or tangled in some way.
16. Imagine that you are hovering next to the space shuttle in an Earth orbit. Your buddy of equal mass, who is moving at 4 km/h with
respect to the shuttle, bumps into you. If he holds onto you, how fast do you both move with respect to the ship? (7.5) 2 km/h faster
than the ship. This is because the momentum of the system needs to be conserved. Momentum is equal to mass multiplied by
velocity. The velocity for just one mass was 4. In order to have the same momentum once the mass is doubled the velocity will be
cut in half.
17. Is momentum conserved for colliding objects that are moving at angles to each other? (7.6) Yes, this is explained in section 7.6. In
order to see this you need to use vectors and vector addition. However, no matter what the angles are, the total (or net)
momentum before the collision must equal the total (or net) momentum after.
Plug and Chug
18. a. What is the momentum of an 8-kg bowling ball rolling at 2 m/s? Momentum is equal to force multiplied by velocity, so 8 kg x 2
m/s = 16 kg·m/s
b. If the bowling ball rolls into a pillow and stops in 0.5 s, calculate the average force it exerts on the pillow. 16 / 0.5 = 32 W e know
that it initial momentum was 16 and that if it stops then it loses all of that momentum, therefore the change in momentum is 16.
Impulse is equal to the change in momentum. Impulse is also equal to force multiplied by time. Therefore if I divide my change
in momentum by the time it takes to stop I will get the force it took to stop the ball. (change in momentum = impulse = force x
time using this information I know that change in momentum / time = force)
c. What average force does the pillow exert on the ball? We know from Newton’s Third law that the action force equals the reaction
force so the force of the pillow on the ball is the same as the force of the ball on the pillow which is 32.
19. a. What is the momentum of a 50-kg carton that slides at 4 m/s across an icy surface? Momentum is mass multiplied by velocity, so 50
x 4 = 200
b. The sliding carton skids onto a rough surface and stops in 3 s. Calculate the force of friction it encounters. 200/3=66.6N The change
is momentum is equal to the impulse. The impulse is the force multiplied by the time. Therefore the force is equal to the change
in momentum divided by the time.
20. a. What impulse occurs when an average force of 10 N is exerted on a cart for 2.5 seconds? 10 N x 2.5 s = 25 N·s Impulse is force
multiplied by time.
b. What change in momentum does the cart undergo? 25 kg·m/s Change in momentum is equal to impulse.
c. If a the mass of the cart is 2 kg and the cart is initially at rest, calculate its final speed. 25 kg·m/s divided by 2kg = 12.5 m/s
Momentum is equal to mass multiplied by velocity. The change in momentum is 25 kg·m/s and since it started at rest, then this is
equal to its final momentum. To get velocity we divide momentum by mass.
21. A 2-kg blob of putty moving at 3 m/s slams into a 2 kg blob of putty at rest.
a. Calculate the speed of the two stuck-together blobs of putty immediately after colliding. Momentum of the system before the
collision was 6 kg·m/s, and since momentum has to be conserved the momentum after collision has to be 6 kg·m/s. The mass after
the collision is 4 kg, so the velocity after the collision is 1.5 m/s.
b. Calculate the speed of the two blobs is the one at rest was 4 kg. The momentum of the system before the collision was 6 kg·m/s, and
since momentum has to be conserved, the momentum after the collision has to be 6 kg·m/s. The total mass after the collision in
this case would be 6 kg, making the velocity 1 m/s.
Think and Explain (Extra Credit)
23. When you ride a bicycle at full speed and the bike stops suddenly, why do you have to push hard on the handlebars to keep from flying
forward? So that the reaction force of the handlebars on you will produce a backward-acting impulse.
24. In terms of impulse and momentum, why are air bags in automobiles a good idea? In a crash you lose all momentum. Your change in
momentum is equal to impulse. Impulse is force multiplied by time. The air bag makes your collision with the dashboard take
longer so there is less force to hurt you.
25. Why is it difficult for a firefighter to hold a hose that ejects large amounts of water at high speed? The hose tends to recoil from the
ejected water.
26. You can’t throw a raw egg against a wall without breaking it, but you can throw it at the same speed into a sagging sheet without
breaking it. Explain. The sheet makes the collision take longer, and therefore there is a smaller force on the egg. Remember that
the impulse is equal to the change in momentum. The change in momentum is defined by the mass and velocity, neither of which
are changed by how you stop the egg. So this means that the only way to decrease the force on the egg is to increase the time it
takes to change the momentum, the sheet does this nicely.
27. Suppose you roll a bowling ball into a pillow and the ball stops. Now suppose you roll it against a spring and it bounces back with an
equal and opposite momentum.
a. Which object exerts a greater impulse, the pillow or the spring? The spring because the forward momentum is stopped and an equal
and opposite backward momentum is created, making the impulse twice as big because there is twice as much change in
momentum.
b. If the time it takes the pillow to stop the ball is the same as the time of contact of the ball with the spring, how do the average forces on
the ball compare? The force of the spring is twice as big. We know this because we found in part a that the impulse is double.
Impulse is time multiplied by force. If the time is the same and the impulse is double that means that the force has to be double.
28. If you topple from your tree house, you’ll continuously gain momentum as you fall to the ground below. Doesn’t this violate the law of
conservation of momentum? Defend your answer. If the system is you and the Earth, then your momentum toward Earth is equal
and opposite to Earth’s momentum toward you. There is no net change in momentum because while you’re falling down, Earth
is falling (much less noticeably) up.
29. A bug and the windshield of a fast-moving car collide. Indicate whether each of the following statements is true or false.
a. The forces of impact on the bug and on the car are the same size. True
b. The impulses on the bug and on the car are the same size. True
c. The changes in speed of the bug and of the car are the same. False the changes of speed are very different due to the different masses
and resulting accelerations.
d. The changes in momentum of the bug and of the car are the same size. True, since the impulses are of the same size.
30. What difference in recoil would you expect in firing a solid ball versus firing a hollow ball from the same cannon? Explain. There is
more kick from the solid ball because of a greater change in momentum for the solid ball.
31. A group of playful astronauts, each with a bag full of balls, form a circle as they free-fall in space. Describe what happens when they
begin tossing balls simultaneously to one another. The astronauts would recoil and the circle would widen.
32. A proton from an accelerator strikes an atom. An electron is observed flying forward in the same direction the proton was moving and at
a speed much greater than the speed of the proton. What conclusion can you draw about the relative mass of a proton and an electron?
The electron has much less mass than the proton.