# Finding center of gravity with a cut out

1. Jul 7, 2010

### mandy9008

1. The problem statement, all variables and given/known data
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.

3. 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.

2. Jul 7, 2010

### hikaru1221

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

3. Jul 7, 2010

### 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 An terms are the areas of the different sections and the xn 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.

Last edited: Jul 7, 2010