What Is the Center of Mass Position for Three Aligned Cubes?

AI Thread Summary
The discussion focuses on calculating the center of mass (CM) position for three aligned cubes of varying sizes. The initial attempt incorrectly used surface area instead of volume, leading to an incorrect CM calculation. The correct formula involves using the volumes of the cubes, which are derived from their dimensions. After realizing the mistake, the user corrected their approach to find the accurate CM position. The importance of using the right parameters for 3D shapes in physics problems is emphasized.
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Homework Statement



Three cubes, of side L1, L2, and L3, are placed next to one another (in contact) with their centers along a straight line as shown in the figure. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material and L1= 3.5 cm.

http://www.webassign.net/gianpse4/9-44.gif

Homework Equations





The Attempt at a Solution


Xcm=73.5cm^3(d)*1.75cm+294cm^3(d)*7cm+661.5cm^3(d)+15.75cm/73.5(d)+294(d)+661.5(d)
Xcm=12.25
This is not correct and I am not sure what I am doing wrong. I got the area of each cube by multiplying 6*side^2 and then multiplied that by each location of the center of mass and divided by sum of the masses. Please help!
 
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Never mind, I figured it out. I was using area and I needed to use volume for a 3D shape.
 

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