Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 7 - Think and Explain: 72


4 times as much. 9 times as much.

Work Step by Step

The amount of work done on the hammer head, and the amount it does on the nail, is the change in kinetic energy. Kinetic energy scales as the square of the speed, so if the speed is doubled, KE is multiplied by $2^{2} = 4$. The amount of stopping force multiplied by the distance is the KE, so for the same friction force on the nail, with 4 times the initial KE for the hammer, the stopping distance goes up by a factor of 4. An identical argument shows that for a tripled hammer speed, the nail is driven 9 times farther. This is discussed on pages 114-115.
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