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 15 - Oscillations - Exercises and Problems - Page 416: 22


(a) $m = 0.169~kg$ (b) $v_{max} = 0.565~m/s$

Work Step by Step

(a) We can find the period as: $T = \frac{time}{oscillations}$ $T = \frac{20.0~s}{30~oscillations}$ $T = 0.667~s$ Wethencan find the mass of the ball: $T = 2\pi~\sqrt{\frac{m}{k}}$ $m = \frac{T^2~k}{(2\pi)^2}$ $m = \frac{(0.667~s)^2(15.0~N/m)}{(2\pi)^2}$ $m = 0.169~kg$ (b) We can find the maximum speed as: $v_{max} = A~\omega$ $v_{max} = A~\sqrt{\frac{k}{m}}$ $v_{max} = (0.0600~m)~\sqrt{\frac{15.0~N/m}{0.169~kg}}$ $v_{max} = 0.565~m/s$
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