The z coordinate of the center of mass of the box

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SUMMARY

The discussion focuses on calculating the z coordinate of the center of mass of a cubical box with an edge length of 97 cm, constructed from a uniform metal plate. The formula for the center of mass, rcom = (1/M)Σ(miri), is applied, where mass density (σ) is assumed for the two-dimensional faces. The center of mass of the four upright sides, treated as particles of mass 4M, is combined with the mass of the bottom face (M) to determine the overall center of mass.

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hateAleen
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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.
 
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hateAleen said:

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

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