Center of Mass involving three cubes

AI Thread Summary
To find the center of mass (CM) of three cubes with sides l, 2l, and 3l placed in a line, the masses must be calculated based on their volumes, assuming uniform density. The formula for CM is applied using the masses and their respective positions along the line. The key challenge was determining the masses and the correct positions of the cubes, which are based on their centers. The problem was ultimately resolved with a simpler approach than initially anticipated. The discussion highlights the importance of understanding mass relationships and positioning in calculating the CM of a system.
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Homework Statement


Three cubes, of side l, 2l, and 3lo, are placed next to one another (in contact) with their centers along a straight line and the l = 2lo cube in the center. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material.


Homework Equations


CM = (m1x1 + m2x2 + m3x3)/ (m1 + m2 + m3)


The Attempt at a Solution



The one thing that stumped me the most was how to find the mass of the object. I'm inferring that since the cubes are all made out of the same material, they have the same density, meaning that the masses have an inverse-square relationship with each other.

And I have trouble determining the positions of the boxes; I always go by the center of the objects, correct?

Damion
 
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I figured out the problem on my own! Ahh, it was simpler than I thought it would be.
 

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