University Physics with Modern Physics (14th Edition)

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

Chapter 4 - Newton's Laws of Motion - Problems - Exercises - Page 128: 4.57


The correct answer is (d) 180 N.

Work Step by Step

We can find the rate of deceleration of the head. $a = \frac{v-v_0}{t} = \frac{0-4.0~m/s}{0.20~s}$ $a = -20~m/s^2$ The magnitude of acceleration is $20~m/s^2$, and this acceleration is directed upward. We can find the mass of the dancer's head. $m = (0.094)(65~kg) = 6.11~kg$ We can find the average force $F_N$ exerted on the head by the neck. $\sum F = ma$ $F_N - mg = ma$ $F_N = ma+mg$ $F_N = (6.11~kg)(20~m/s^2)+(6.11~kg)(9.80~m/s^2)$ $F_N = 180~N$ The correct answer is (d) 180 N.
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