Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - 6.5 Work and Energy - Exercises - Page 318: 35


$G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2})$

Work Step by Step

The work needed to increase the separation from a distance $r_1$ to a distance $r_2$ can be calculated as: $ Work \ done =\int_{r_1}^{r_2} \dfrac{G Mm}{r^2} \ dr \\=[\dfrac{-G Mm}{r^2}]_{r_1}^{r_2} \\=G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2})$
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