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: 30

Answer

$d = 1.4~m$

Work Step by Step

Let the left end of the 1.0-kg object be the position x = 0. Let $M_1$ be the 1.0-kg object. We can find $r_1$, the distance from the center of mass to the pivot. $r_1 = d - 1.0 ~m$ Let $M_2$ be the 4.0-kg object. We can find $r_2$, the distance from the center of mass to the pivot. $r_2 = 1.5~m - d$ Since the two objects are in equilibrium, the magnitude of their torques about the pivot are equal. We can find $d$. $\tau_1 = \tau_2$ $r_1~ F_1 = r_2~ F_2$ $(d-1.0~m)~ M_1~g = (1.5~m-d)~ M_2~g$ $(d)(M_1+M_2) = (1.5~m)~M_2+(1.0~m)~M_1$ $d = \frac{(1.5~m)~M_2+(1.0~m)~M_1}{M_1+M_2}$ $d = \frac{(1.5~m)(4.0~kg)+(1.0~m)(1.0~kg)}{1.0~kg+4.0~kg}$ $d = 1.4~m$
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