Den Hartog’s Mechanics

A web-based solutions manual for statics and dynamics

Problem 56

Because the plate is uniform, the center of gravity is at the centroid of the composite plane shape. The centroid of the square is at (a/2, a/2) and its area is a^2. The centroid of the triangle is at (4a/3, a/3) and its area is a^2/2. (Recall that the centroid of a right triangle is one-third of the leg length from the right angle.)

Combining, we get

\bar x = \frac{a^2 (a/2) + a^2/2 (4a/3)}{a^2 + a^2/2} = \frac{7}{9} a

and

\bar y = \frac{a^2 (a/2) + a^2/2 (a/3)}{a^2 + a^2/2} = \frac{4}{9} a

Problem 57Problem 55

Last modified: January 22, 2009 at 8:32 PM.