Physics: Principles with Applications (7th Edition)

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

Chapter 11 - Oscillations and Waves - General Problems - Page 326: 73

Answer

(a) $k = 37,000~N/m$ (b) The car is in contact with the spring for 0.50 seconds.

Work Step by Step

(a) We find the spring constant as: $\frac{1}{2}kA^2 = \frac{1}{2}mv^2$ $k = \frac{mv^2}{A^2}$ $k = \frac{(950~kg)(25~m/s)^2}{(4.0~m)^2}$ $k = 37,000~N/m$ (b) We find the period of oscillation as: $T = 2\pi~\sqrt{\frac{m}{k}}$ $T = 2\pi~\sqrt{\frac{950~kg}{37,000~N/m}}$ $T = 1.0~s$ Since the car is only in contact with the spring for half an oscillation, the car is in contact with the spring for 0.50 seconds.
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