Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 6 - Work and Energy - Problems: 11

Answer

2m of rope.

Work Step by Step

If the load rises by one meter, the rope on the right side of the pulley becomes shorter by a meter, and so does the rope on the left side. For every meter the load rises, you pull up 2 m of rope. Assume that friction has a negligible effect. We expect that the work you do is equal to the work done on the load, and that checks out. The work done on the load while it moves up a height h is mgh. The force you exert is $\frac{1}{2}mg$ and you exert it over a distance 2d, so the work you do is also mgh.
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