Physics: Principles with Applications (7th Edition)

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

Chapter 6 - Work and Energy - General Problems - Page 167: 72

Answer

The effective spring constant of the web is 11 N/m.

Work Step by Step

$v = (60 \frac{km}{h})(\frac{1000 ~m}{1 ~km})(\frac{1 ~h}{3600 ~s})$ $v = 16.67 ~m/s$ The potential energy in the web will equal the original kinetic energy of the train. Therefore, $\frac{1}{2}kx^2 = \frac{1}{2}mv^2$ $k = \frac{mv^2}{x^2}$ $k = \frac{(10^4 ~kg)(16.67 ~m/s)^2}{(500 ~m)^2}$ $k = 11.11\approx11 ~N/m$ Therefore, the effective spring constant of the web is 11 N/m.
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