University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 6 - Work and Kinetic Energy - Problems - Exercises - Page 197: 6.58

Answer

The maximum number of passengers is 28.

Work Step by Step

Since the speed is constant, the upward force exerted on the elevator is equal in magnitude to the weight. Note that the speed $v = \frac{20.0~m}{16.0~s} = 1.25~m/s$ Let N be the maximum number of passengers. $P = F~v = 40~hp$ $(600~kg)(9.80~m/s^2)(1.25~m/s)+ N~mg~v = (40~hp)(746~W/hp)$ $N~mg~v = 29840~W - 7350~W$ $N = \frac{22490~W}{(65.0~kg)(9.80~m/s^2)(1.25~m/s)}$ $N = 28$ The maximum number of passengers is 28.
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