## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson

# Chapter 10 - Interactions and Potential Energy - Exercises and Problems - Page 256: 22

#### Answer

When there are two springs, the block's speed is $1.4~v_0$.

#### Work Step by Step

When there is one spring, the kinetic energy of the block when it leaves the spring is equal to the initial energy stored in the spring. When there are two springs, the kinetic energy of the block when it leaves the springs is equal to the sum of the initial energy stored in each spring. The block's kinetic energy in this case will be double the block's kinetic energy when there was just one spring. We can find the speed of the block when there are two springs. $KE_2 = 2KE_1$ $\frac{1}{2}mv_2^2 = 2~(\frac{1}{2}mv_0^2)$ $v_2^2 = 2~v_0^2$ $v_2 = \sqrt{2~v_0^2}$ $v_2 = 1.4~v_0$ When there are two springs, the block's speed is $1.4~v_0$

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