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: 63

Answer

The boy can walk to the point that is 1.0 meter from the end of the beam without the beam tipping.

Work Step by Step

Let $m_b$ be the mass of the beam and let $m_y$ be the mass of the boy. When the boy reaches the limit just before the beam starts to tip, the upward force exerted by the left post will be zero. We can consider the net torque about an axis of rotation located at the position of the right post. We can find $r_y$, the boy's distance from the right post. Note that the beam's center of mass is 0.5 meters from the right post. $\sum \tau = 0$ $r_b~m_b~g - r_y~m_y~g = 0$ $r_b~m_b~g = r_y~m_y~g$ $r_y = \frac{r_b~m_b}{m_y}$ $r_y = \frac{(0.5~m)(40~kg)}{20~kg}$ $r_y = 1.0~m$ The boy can go up to 1.0 meter past the right post. The boy can walk to the point that is 1.0 meter from the end of the beam without the beam tipping.
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