# The z coordinate of the center of mass of the box

1. Feb 21, 2008

### hateAleen

1. The problem statement, all variables and given/known data
A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box.

2. Relevant equations
rcom=(1/M)sum(mi*ri)

3. The attempt at a solution
I could not figure out what to do with a three dimensional object since we are not given a mass.

2. Feb 22, 2008

### Shooting Star

Assume some $\sigma$ as the two dimensional mass density, that is, mass per unit area of the faces. Multiplying $\sigma$ by area, you'll get the mass. I think you know where the CM of a rectangle is. Now, apply the formula you know.

3. Feb 22, 2008

### andrevdh

If you assume that the mass of one side is M then the com of the four upright sides will correspond to a "particle" of mass 4M in the middle of the box. You now need to combine this with a "particle" of mass M in the middle of the bottom to get the overall com.