The z coordinate of the center of mass of the box

[hateAleen]

Homework Statement

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.

Homework Equations

rcom=(1/M)sum(mi*ri)

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.

 

[Shooting Star]

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.

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.

 

[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.