Finding center of gravity with a cut out

[mandy9008]

Homework Statement

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 as shown in the figure below. The dimensions of the cutout are a = 3.50 ft and b = 2.10 ft.

The Attempt at a Solution

I made 2 squares out of this.
The left square: 4.5 x 4 having a center point of (2.25, 2).
The right square: 3.5 x 1.9 having a center point of (1.75, .95)
I then subtracted these coordinates (2.25, 2) - (1.75, .95) = (.5, 1.05)
This is wrong.

 

[hikaru1221]

You forgot to apply the center of mass's position formula when adding the coordinates
What is the formula?

 

[rock.freak667]

Do you know the formulas

$$A \bar{y} = A_1 y_1 + A_2y_2 + A_3y_3+...$$

$$A \bar{x} = A_1 x_1 + A_2x_2 + A_3x_3+...$$

Split the shape into squares or rectangles. The A_n terms are the areas of the different sections and the x_n terms are the distance of the centroid of the sections from the reference axis.

So choose the y-axis as a reference and apply the formula.

Alternatively, you can consider it as one entire big rectangle and the part where the hole is would have negative area.