Chapter 9, Problem 3Q

You can find the center of gravity of a meter stick by resting it horizontally on your two index fingers, and then slowly drawing your fingers together. First the meter stick will slip on one finger, and then on the other, but eventually the fingers meet at the cg.Why does this work?

To determine

You can find the center of gravity of a meter stick by resting it horizontally on your two index fingers, and then slowly drawing your fingers together. First, the meter stick will slip on one finger, and then on the other, but eventually the fingers meet at the CG. Why does this work?

Answer to Problem 3Q

Solution:

The fingers meet at the CG because at that point the meter stick reaches the equilibrium: net force is zero and net torque is zero.

Explanation of Solution

Given info:

Center of gravity of a meter stick.

At the center of gravity (CG)the meter stick is in equilibrium. That is, the net force on it is zero and the net torque on it is zero.Initially, the index fingers are placed at the ends of the meter stick. Before starting to slide the fingers, the net force on the meter stick is zero. Then, when the fingers begin to slide, one finger does it first while the other finger is at rest; at that instant the net torque is different to zeroand the meter stick tends to rotate; then the finger that was at rest begins to slide to counteract the initial torque. Finally at the point where the meter stick returns to equilibrium is precisely at the center of gravity of the object where the fingers meet.