COM of 4D pyramid
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Find the center of mass of a 4D pyramid (cube base) using calculus (25 credits if you can solve it with only algebra).
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Solution Summary
This gives a solution with a partial explanation of how to find the center of mass of a 4D pyramid (cube base, constant density, apex centered over the base). Only algebra (no calculus) is used.
Solution Preview
Note: all of the following is based on the assumptions that the pyramid has constant density and that the apex is centered above the base.
If you were going to find the center of mass of a 2D triangle or a 3D pyramid, you could be able to draw a picture and see that the COM is centered above the base. So, in the case of the triangle, the x-coordinate of the COM is halfway along the base. And in the case of the pyramid, the x- and y-coordinates are ...
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