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

Published by Pearson

# Chapter 10 - Energy - Conceptual Questions - Page 271: 5

#### Answer

We need to increase the height of the track by a factor of 4

#### Work Step by Step

The potential energy at the top of the track is equal to the kinetic energy at the bottom of the track. Let the height be $h_0$ when the speed at the bottom is $v_0$. $PE_0 = KE_0$ $mg~h_0 = \frac{1}{2}mv_0^2$ $h_0 = \frac{v_0^2}{2g}$ Suppose the speed at the bottom is $2v_0$. We can find an expression for the initial height $h_2$. $PE_2 = KE_2$ $mg~h_2 = \frac{1}{2}m(2v_0)^2$ $h_2 = 4\times~\frac{v_0^2}{2g}$ $h_2 = 4\times h_0$ We need to increase the height of the track by a factor of 4.

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