Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 10 - Energy - Conceptual Questions: 12

Answer

The speed increases by a factor of 2

Work Step by Step

The energy stored in the spring when it is compressed is equal to the kinetic energy of the ball when the ball is released. We can find an expression for the speed $v_0$ as: $KE_0 = U_0$ $\frac{1}{2}mv_0^2 = \frac{1}{2}kx_0^2$ $v_0^2 = \frac{kx_0^2}{m}$ $v_0 = \sqrt{\frac{kx_0^2}{m}}$ We can find an expression for the speed $v_2$ after the spring is compressed $2x_0$ as: $KE_2 = U_2$ $\frac{1}{2}mv_2^2 = \frac{1}{2}k(2x_0)^2$ $v_2^2 = 4\times ~\frac{kx_0^2}{m}$ $v_2 = 2\times ~\sqrt{\frac{kx_0^2}{m}}$ $v_2 = 2~v_0$ The speed increases by a factor of 2.
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