# Center of Mass of a Cubical Box (part c help)

1. Oct 27, 2008

### 97Sport

1. A cubical box has been constructed from a uniform metal plate of neglible thickness. The box is open at the top and has an edge length L=40cm. Find (a)the x coordinate (b) the y coordinate and (c) z coordinate of the center of mass of the box. (part a and b I have solved. I need help with part c. Attached is a diagram associated with the problem)

2. Relevant equations
My professor guided me to use the following equation:
$$\vec{r}$$=$$\sum$$(m(subscript i)$$\vec{r}$$)/M

Im needing the z component of the r therefore $$\vec{}z$$=m$$_{}front$$z$$_{}front$$+m$$_{}back$$z$$_{}back$$+m$$_{}left$$z$$_{}left$$+m$$_{}right$$z$$_{}right$$+m$$_{}bottom$$z$$_{}bottom$$)/5m

Where m is the mass of each side. Since this is uniform, this cancels out in the above equation giving me just the z(top, bottom, left, right, and front).

The superscripts were supposed to be subscripts. m(top)ztop=0 because there is nothing there.

This is where I have gotten stuck. I found parts (a) and (b) by dividing L/2. My professor states that the answer to (c) is 16 cm but I am not seeing where to go. Can anyone help?

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Last edited: Oct 27, 2008