Page 155 - Schaum's Outline of Theory and Problems of Applied Physics

140 EQUILIBRIUM [CHAP. 11

m 2
m 1 m 3

0 x 1 x 2 x 3
m g m g m g
1
2
3
0 X

Mg

Fig. 11-15

such that the torque exerted by a single particle of mass M = m 1 + m 2 + m 3 at X equals the sum of the torques
exerted by the particles at their locations x 1 , x 2 , and x 3 . Thus

m 1 gx 1 + m 2 gx 2 + m 3 gx 3 = MgX = (m 1 + m 2 + m 3 )gX

m 1 x 1 + m 2 x 2 + m 3 x 3
X =
m 1 + m 2 + m 3
This formula can be extended to any number of particles. If the complex object involves two or three dimensions
rather than just one, the same procedure is applied along two or three coordinate axes to find X and Y or X, Y,
and Z, which are the coordinates of the center of gravity.

SOLVED PROBLEM 11.14
Find the location of the center of gravity of the L-shaped piece of plywood shown in Fig. 11-16.

Fig. 11-16