Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 9 - Rotational Dynamics - Check Your Understanding - Page 230: 8

Answer

b) is correct.

Work Step by Step

The net force in the system is composed of the weight of the wine rack $W_r$ and the weight of the bottle $W_b$. If we choose the axis of rotation to be passing through the point $P$ the rack contacts the tabletop and consider the torques produced by $W_r$ and $W_b$, then because the system is in equilibrium, the net torque is zero: $$\sum\tau=\tau_r+\tau_b=0$$ Now the net torque $\sum\tau=\sum Wx_{cg}$. Because $\sum\tau=0$, if we consider $\sum W$ a single force passing through $x_{cg}$, then it has to pass through the point of the rotation axis, which is $P$, too, so that there is no torque produced. This means $x_{cg}$ and $P$ are connected in a straight line perpendicular to the tabletop, or $x_{cg}$is directly above $P$.
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