©1997 by Eric Mazur Published by Pearson Prentice Hall Upper Saddle River, NJ 07458 ISBN 0-13-565441-6 No portion of the file may be distributed, transmitted in any form, or included in other documents without express written permission from the publisher.

Reference Frames

When a small ball collides elastically with a more massive ball initially at rest, the massive ball tends to remain at rest, whereas the small ball bounces back at almost its original speed. Now consider a massive ball of inertial mass M moving at speed v and striking a small ball of inertial mass m initially at rest. The change in the small ball’s momentum is 1. Mv 2. 2Mv 3. mv 4. 2mv 5. none of the above Answer: 4. Consider the second collision from a reference frame moving along with the massive ball. In this moving frame, the massive ball is at rest and the small ball moves toward the massive one at velocity –v. This, however, is precisely the first collision. After the collision, the small ball bounces back at velocity v. In the frame of Earth, this corresponds to a speed of v + v = 2v. So the change in momentum is 2mv, exactly as in the first collision.

A small rubber ball is put on top of a volleyball, and the combination is dropped from a certain height. Compared to the speed it has just before the volleyball hits the ground, the speed with which the rubber ball rebounds is 1. the same. 2. twice as large. 3. three times as large. 4. four times as large. 5. none of the above Answer: 3.When the volleyball hits the ground, it reverses its velocity and v becomes –v. In a reference frame moving upward along with the volleyball at velocity –v, the volleyball is at rest and the rubber ball comes in at speed 2v.When it hits the volleyball, the rubber ball reverses its speed, and so 2v becomes –2v.This value for the rubber ball’s velocity is valid in the frame moving at velocity –v; in Earth’s frame, the velocity of the small ball is –2v + (–v) = –3mv.

2. deviation from the horizontal orientation Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room? 1. rotation 2. deviation from the horizontal orientation 3. motion at a steady speed 4. acceleration 5. state of rest with respect to ground Answer: 1, 2, and 4. There are no experiments that can detect uniform motion (or rest); we can sense any motion that causes acceleration.

in the following quantities can have any value: An air track cart initially at rest is put in motion when a compressed spring is released and pushes the cart. In the frame of reference of Earth, the velocity-versus-time graph of the cart is shown here. In a frame moving at constant speed relative to Earth, the cart’s change in the following quantities can have any value: 1. velocity 2. momentum 3. kinetic energy 4. none of the above Answer: 3. Changes in velocity and momentum are the same in any two inertial frames moving at constant speed relative to one another. The change in kinetic energy, however, can take on any value.

at constant speed relative to Earth because in the moving frame: An air track cart initially at rest is put in motion when a compressed spring is released and pushes the cart. Earth and the cart constitute an isolated system. The change in the cart’s kinetic energy is different in the frame of reference of Earth and in a frame moving at constant speed relative to Earth because in the moving frame: 1. conservation of energy does not apply. 2. the amount of energy released by the spring is different. 3. the change in the kinetic energy of Earth is different. 4. a combination of 2 and 3. 5. none of the above Answer: 3. Because the system is isolated, conservation of momentum holds in any inertial frame. The amount of energy released by the spring is a measure for the change in its physical state, which must be independent of the reference frame. Option 3 is the only option that satisfies conservation of energy.

1. Yes, but only for certain special initial speeds. Two objects collide inelastically. Can all the initial kinetic energy in the collision be converted to other forms of energy? 1. Yes, but only for certain special initial speeds. 2. Yes, provided the objects are soft enough. 3. No, this violates a fundamental law of physics. 4. none of the above Answer: 1. If all the kinetic energy is converted, then both objects must come to rest.This means the total momentum of the objects after collision is zero.This can happen only if the total momentum was zero to begin with.