## Essential University Physics: Volume 1 (4th Edition) Clone

Published by Pearson

# Chapter 8 - Exercises and Problems - Page 148: 66

#### Answer

The proof is below.

#### Work Step by Step

We know equation 8.5: $U=GMm(\frac{1}{r_1}-\frac{1}{r_2})$ We must show that $U=mg\Delta r$, so we find: $GMm(\frac{1}{r_1}-\frac{1}{r_2})=mg\Delta r$ $GM(\frac{1}{r_1}-\frac{1}{r_2})=g\Delta r$ We know from the book the $\Delta r = r_1-r_2$, so we find: $GM(\frac{1}{r_1}-\frac{1}{r_2})=g( r_1-r_2)$ $g( r_1-r_2)=g( r_1-r_2)$

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