Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 10 - Interactions and Potential Energy - Exercises and Problems: 12

Answer

(a) A person could jump from a maximum height of 0.34 meters without breaking the leg bones. (b) Of course people can jump from a height that is higher than 0.34 meters without breaking the leg bones. This is possible because people bend the knees during the impact in order to absorb the energy of the impact over a greater distance. If the energy of the impact is spread over a larger distance, then the average force exerted on the bones is decreased. (Remember that Work = Force X Distance)

Work Step by Step

(a) The kinetic energy when a person lands on the ground will be equal to the potential energy at the height $h$. We can find the height $h$ when the potential energy is 200 J. $PE = 200~J$ $mgh = 200~J$ $h = \frac{200~J}{mg}$ $h = \frac{200~J}{(60~kg)(9.80~m/s^2)}$ $h = 0.34~m$ A person could jump from a maximum height of 0.34 meters without breaking the leg bones. (b) Of course people can jump from a height that is higher than 0.34 meters without breaking the leg bones. This is possible because people bend the knees during the impact in order to absorb the energy of the impact over a greater distance. If the energy of the impact is spread over a larger distance, then the average force exerted on the bones is decreased. (Remember that Work = Force X Distance)
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