Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 7 - Exercises and Problems: 47

Answer

Please see the work below.

Work Step by Step

According to law of conservation of energy $(\frac{1}{2})kx^2=mgh+mgx$ This can be rearranged as: $x^2-(\frac{2mg}{k})x-(\frac{2mgh}{k})=0$ This simplifies to: $x=\frac{(\frac{2mgh}{k})+\sqrt{(\frac{2mg}{k})^2+(4)(\frac{2mgh}{k})}}{2}$ $\implies x=(\frac{mg}{k})(1+\sqrt{1+\frac{2kh}{mg}})$
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