Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 6 - Work and Energy - Problems - Page 167: 71

Answer

The cyclist's required power output is 610 W.

Work Step by Step

If the cyclist coasts down the hill at a steady speed, then the force $F_R$ which opposes the motion must be equal in magnitude to $mg~sin(\theta)$. This means that when the cyclist climbs the hill at a steady speed, the cyclist's force $F_p$ will be equal to the sum of opposing forces.: $F_p = mg~sin(\theta) + F_R = 2mg~sin(\theta)$ We can use this force to find the cyclist's power. $P = F_p\cdot v$ $P = 2mg~sin(\theta) \cdot v$ $P = (2)(75~kg)(9.80~m/s^2)~sin(6.0^{\circ}) \cdot (4.0~m/s)$ $P = 610~W$ Therefore, the cyclist's required power output is 610 W.
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