Finding the Center of Gravity with X and Y Components?

Question

Find the x- and y-coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed. The dimensions of the cutout are a = 4.90 ft and b = 2.10 ft.
x =____ ft
y = ____ft

Answer 1

1. Draw a picture and an X-Y coordinate system if it's not given.

2. Look at this problem as two sheets.
A large sheet (4ft x 8ft)assuming the upper quadrant was still there and a small sheet (4.9ft x 2.1ft) of the removed quadrant.

Create a table
segment, x, y, A, xA, yA
1
2
Sum

where
x is the xcg of the individual sheets
y is the ycg of the individual sheets
A is the area of the sheets. For the removed quadrant it's negative.
xA is x times A
yA is y times A

Now sum the A, xA and yA

X = sum(xA)/sum(A)
Y = sum(yA)/sum(A)

Answer 2

Assuming that the sheet is 8ft in length and 4ft in height,

The center of gravity after the cutout is

in X-coordinate : 3.265 ft (reference from left egde)
in Y-coordinate : 1.55 ft (reference from bottom edge