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

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 7 - Newton's Third Law - Exercises and Problems: 28

Answer

$T = \frac{y~m~g}{L}$

Work Step by Step

At any position $y$, the tension $T$ in the rope holds up the weight of the section of rope that is below the position $y$. At any position $y$, the mass of the rope that is below the position $y$ is equal to ($\frac{y}{L}~m$). The tension $T$ at position $y$ is equal to the weight of this mass. Therefore; $T = \frac{y}{L}~m~g$ $T = \frac{y~m~g}{L}$
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