Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 12 - Rotation of a Rigid Body - Exercises and Problems - Page 349: 28

Answer

$ 11.8\;\rm N\cdot m$

Work Step by Step

We know that the net torque exerted on the beam at the pin (or at any point) is zero since the beam is in equilibrium. Thus, $$\sum \tau_{\rm around\;pin}=\tau_{pin}-Mgx_{rod}-mgx_{weight}=0$$ where $M$ is the mass of the rod, and $m$ is the mass of the hnging weight. We chose counterclockwise to be the positive direction. Hence, the two masses are exerting a negative torque. $$\tau_{pin}=Mgx_{rod}+mgx_{weight}$$ Plugging the known; $$\tau_{pin}=2\times 9.8\times(0.4) +0.5\times 9.8 (0.8)$$ $$\tau_{pin} =\color{red}{\bf 11.8}\;\rm N\cdot m$$
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