College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 10 - Problems - Page 400: 49


(a) The maximum displacement is $0.172~mm$ (b) The maximum speed is $0.13~m/s$ (c) The maximum net force is $514~N$

Work Step by Step

(a) We can find the angular frequency: $\omega = 2\pi~f = (2\pi)(120~Hz) = 754~rad/s$ We can find the maximum displacement $A$: $a_m = A~\omega^2$ $A = \frac{a_m}{\omega^2}$ $A = \frac{98~m/s^2}{(754~rad/s)^2}$ $A = 0.172\times 10^{-3}~m$ $A = 0.172~mm$ The maximum displacement is $0.172~mm$ (b) We can find the maximum speed $v_m$: $v_m = A~\omega$ $v_m = (0.172\times 10^{-3}~m)(754~rad/s)$ $v_m = 0.13~m/s$ The maximum speed is $0.13~m/s$ (c) We can find the maximum net force: $F_m = m~a_m$ $F_m = (5.24~kg)(98~m/s^2)$ $F_m = 514~N$ The maximum net force is $514~N$
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