Essential University Physics: Volume 1 (4th Edition)

Published by Pearson
ISBN 10: 0-134-98855-8
ISBN 13: 978-0-13498-855-9

Chapter 5 - Exercises and Problems - Page 91: 41


a) $375.31 \ N$ b) The force of tension is 2.62 times greater.

Work Step by Step

a) We know that the monkey is not moving in either the horizontal or the vertical direction, so we know that all of the forces cancel. We call the force of tension $F_t$, meaning that the force pulling the monkey upward is $2F_tsin\theta$, since there are two sides of the rope that are pulling on the monkey. We set this equal to gravity, since that is the downward force: $mg =2F_t sin\theta\\F_t=\frac{mg}{2sin\theta}=\frac{(14.6)(9.81)}{2sin11}=375.31 \ N$ b) We compare this to the force of gravity: $=\frac{375.31}{mg}=\frac{375.31}{(14.6)(9.81)}=2.62$ The force of tension is 2.62 times greater.
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