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# Center of Mass

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## Richard Datwyler

on 3 June 2014

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#### Transcript of Center of Mass

Center of Mass

This picture isn't perfect but do your best to see 3D.

Three cubes, of sides L,2L, and 3L are placed next to one another (in contact) with their centers along a straight line. What is the position along this line of the CM of this system, Assume the cubes are made of the same uniform material.
3L
2L
L
Recall Density is Mass/volume
and volume of a cube is s .
3
Solving for each of these volumes we get
27L
8L
L
3
3
3
Because the densities are the same, then this will also be the ratio of their masses, and their total mass

1 : 8 : 27 = total = 36
to find the center of mass we need to take both the mass and the location of the mass, let us set zero at the leading edge of the first box.

This will give its center of mass position to be L/2

The center of 2L is just L, but we need to add it to the first box giving 2L

The center of 3L is 1.5 L but we need to add that to the other two boxes distance giving 4.5 L

Now we collect the masses and the distances
1 8 27
.5 L 2 L 4.5 L
And put them in the following equation.
No need for y direction, all on same axis
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