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 9 - Work and Kinetic Energy - Exercises and Problems: 30

Answer

The box was moving with a speed of 0.49 m/s

Work Step by Step

The spring brings the box to rest when the spring compresses by 6.5 cm. The work done by the spring on the box is $W = -\frac{1}{2}kx^2$. We can use the work-energy theorem to find the initial speed of the box. $KE_1+W = KE_2$ $\frac{1}{2}mv^2-\frac{1}{2}kx^2 = 0$ $\frac{1}{2}mv^2=\frac{1}{2}kx^2$ $v^2=\frac{kx^2}{m}$ $v=\sqrt{\frac{kx^2}{m}}$ $v=\sqrt{\frac{(85~N/m)(0.065~m)^2}{1.5~kg}}$ $v = 0.49~m/s$ The box was moving with a speed of 0.49 m/s
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