1. ©1997 by Eric Mazur
Published by Pearson Prentice Hall
Upper Saddle River, NJ 07458
ISBN
No portion of the file may be distributed, transmitted in any form, or included in other documents without express written permission from the publisher.

2. Interactions

3. 1. A is put in motion but B remains at rest.
Two carts of identical inertial mass are put back-to-back on a track. Cart A has a spring-loaded piston; cart B is entirely passive. When the piston is released, it pushes against cart B, and
1. A is put in motion but B remains at rest.
2. both carts are set into motion, with A gaining more speed
than B.
3. both carts gain equal speed but in opposite directions.
4. both carts are set into motion, with B gaining more speed
than A.
5. B is put in motion but A remains at rest.
Answer: 3.This is the only answer that satisfies conservation of momentum.

4. Two carts are put back-to-back on a track
Two carts are put back-to-back on a track. Cart A has a spring-loaded piston; cart B, which has twice the inertial mass of cart A, is entirely passive. When the piston is released, it pushes against cart B, and the carts move
apart. How do the magnitudes of the final momenta and kinetic energies compare?
1. pA > pB, kA > kB
2. pA > pB, kA = kB
3. pA > pB, kA < kB
4. pA = pB, kA > kB
5. pA = pB, kA = kB
6. pA = pB, kA < kB
7. pA < pB, kA > kB
8. pA < pB, kA = kB
9. pA < pB, kA < kB
Answer: 4. Conservation of momentum requires the momenta of the two
carts to be equal in magnitude (but in opposite directions). This restriction
eliminates all but choices 4–6. Because the inertial mass of B is twice
that of A, the velocity of B must be half that of A. Because kinetic energy
is momentum times one-half the velocity and because the momenta of the
two carts are equal, the cart having the higher speed (A) has the larger kinetic
energy.

5. 1. A has a larger acceleration than B.
Two carts are put back-to-back on a track. Cart A has a spring-loaded piston; cart B, which has twice the inertial mass of cart A, is entirely passive. When the piston is released, it pushes against cart B, and the carts move apart. Ignoring signs, while the piston is pushing,
1. A has a larger acceleration than B.
2. the two have the same acceleration.
3. B has a larger acceleration than A.
Answer: 1. Cart A gains more speed than cart B. Because both carts gain
speed over the same amount of time, the acceleration of A must be larger
than that of B.

6. 1. standing where they were initially.
Two people on roller blades throw a ball back and forth. After a couple of throws, they are (ignore friction)
1. standing where they were initially.
2. standing farther away from each other.
3. standing closer together.
4. moving away from each other.
5. moving toward each other.
Answer: 4. Each throw is an explosive collision. Let’s assume the two people,
A and B, start at rest. As A throws the ball, he recoils and moves backward—
away from B—so that the total momentum of (ball + A) is
conserved. When B catches the ball, she too moves backward, away from
A. When she throws the ball to A, she recoils and moves backward even
faster. A then catches the ball and receives some more momentum from
it. Upon throwing the ball, A gains even more, and on and on. The net effect
is that A and B accelerate away from each other.

7. A. The interaction mediated by the ball is repulsive.
Two people on roller blades throw a ball back and forth. Which statement(s) is/are true?
A. The interaction mediated by the ball is repulsive.
B. If we film the action and play the movie backward, the
interaction appears attractive.
C. The total momentum of the two people is conserved.
D. The total energy of the two people is conserved.
What about the conservation laws? The ball carries both momentum and energy back and forth between the two roller-bladers. Their momentum and energy therefore cannot
be conserved.
Answer: A. Because it causes the two interacting bodies to accelerate
away from each other, this interaction is repulsive. Statement B is false
because if a movie of this event played backward, we would see A and B
moving toward each other. As they get closer, however, they slow down
more and more, which means their accelerations are still pointing away
from each other. So the interaction is still repulsive.
What about the conservation laws? The ball carries both momentum and
energy back and forth between the two roller-bladers. Their momentum
and energy therefore cannot be conserved.

8. In the following figure, a 10-kg weight is suspended
from the ceiling by a spring. The weight-spring system is at equilibrium with the bottom of the weight about 1 m above the floor. The spring is then stretched until the
weight is just above the eggs. When the spring is released, the weight is pulled up by the contracting
spring and then falls back down under the influence of gravity. On the way down, it
1. reverses its direction of travel well
above the eggs.
2. reverses its direction of travel precisely
as it reaches the eggs.
3. makes a mess as it crashes into the eggs.
Answer: 2. In the initial situation, with the spring stretched until the bottom
of the weight is just above the eggs, all of the energy of the system is
potential. Upon release, some of this energy is converted to kinetic energy
in the moving spring and weight. When the weight returns to its position
just above the eggs, however, all of the energy in the system must
again be potential. Having no kinetic energy, the weight stops at the point
from which it was initially released. The eggs are safe.

9. In part (a) of the figure, an air track cart attached to a spring rests on the track at the position xequilibrium and the spring is relaxed. In (b), the cart is pulled to the position xstart and released. It then oscillates about xequilibrium.
Which graph correctly represents the potential energy of the spring as a function of the position of the cart?
Answer: 3.The cart starts at xstart with no kinetic energy, and so the spring’s
potential energy is a maximum. Once released, the cart accelerates to the
right and its kinetic energy increases as the potential energy of the spring
is converted into kinetic energy of the cart. As the cart passes the equilibrium
position, its kinetic energy is a maximum and so the spring’s potential
energy is a minimum. Once to the right of xequilibrium, the cart starts to
compress the spring and it slows down as its kinetic energy is converted
back to potential energy of the recompressed spring. At the rightmost point
it reaches, the cart reverses its direction of travel. At that instant, it has no
kinetic energy and the spring again has maximum potential energy.

10. Two cars, one twice as heavy as the other, are at rest on a horizontal track. A person pushes each car for 5 s. Ignoring friction and assuming equal force exerted on both cars, the momentum of the light car after the push is
1. smaller than
2. equal to
3. larger than
the momentum of the heavy car.

11. Two cars, one twice as heavy as the other, are at rest on a horizontal track. A person pushes each car for 5 s. Ignoring friction and assuming equal force exerted on both cars, the kinetic energy of the light car after the push is
1. smaller than
2. equal to
3. larger than
the kinetic energy of the heavy car.