# How to find center of gravity?

## 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 = 4.30 ft and b = 1.70 ft.

I found:

xA= 3.7/2 cm
xB=3.7+(4.3/2) cm
Ya=2 cm
Yb=2.3/2 cm
Ycm (Y-coordinates)= 1.689 cm

## Homework Equations

xcm=maxa+mbxb/ma+mb
ycm=maya+mbyb/ma+mb
ma=(mu)A
mb=(mu)B
m=ma+mb
mass of a= area of A/total area
mass of b= area of B/total area

## The Attempt at a Solution

I know the basic steps:
I first 'split' the plywood into two:
A (area: 4 * 3.7 cm^2)
and
B (area: 3.7 * 2.3 cm^2)

I find the centers of gravity of both A and B, and want to find what is the intermediate center of gravity of the whole piece. As I've said before, I've found the y-coordinate of the center of gravity, but somehow miscalculated the x-coordinate.

I've got the y-coordinates (which is 1.689), but somehow I think I made an error in the calculation of the x-coordinates which I calculated as somewhere around 3.3117-3.3118 or 3.312.

## Answers and Replies

PhanthomJay
Science Advisor
Homework Helper
Gold Member
Please get rid of that 'cm' unit..the problem is in feet... that's the way I order my plywood, in 4' X 8' sheets . I haven't checked your numbers, but I note that in calculating ther area of B, you used 3.7 (ft) as one of the dimensions when it should be 4.3 ft... and that of course is feet not centimeters ... That didn't help either It calculated as 3.612, but that was wrong as well.

I guess the usual language in which you solve this is - Consider the full plywood 'minus' the cutout. Choose an origin, find center of gravity of the whole plywood, center of gravity of cutout with a negative mass and find the center of gravity of the two using the equations you wrote in OP.

If you are not comfortable with this language, a more detailed/clear answer can be formed, I'm sleepy >.>