Question

Find the x and y coordinates of the center of gravity of a 4ft by 8ft uniform sheet of plywood with the upper right quadrant removed?
with out mass of the plywood how do go about calculating the center gravity for x/y coordinates?

Answer 1

The CG location can be quickly calculated by treating the board as three rectangles with mass concentrated in the center of each. The CG of the 3/4 complete board is the mass-weighted mean location of those 3 CGs. Let x=0, y=0 be the center of the complete 4x8 board.

If x is the long (8') axis and y the short (4') axis of the board, the CG for the x direction is (2 + 2 - 2)/3 = 2/3 feet (+8 inches) and the CG for the y direction is (-1-1+1)/3 = -1/3 feet (-4 inches)