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

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SUMMARY

The discussion centers on calculating the center of mass (CM) for three aligned cubes with side lengths L1, L2, and L3. The user initially attempted to use surface area instead of volume in their calculations, leading to an incorrect CM position of 12.25 cm. The correct approach requires using the volumes of the cubes, which are derived from the formula for volume (V = side^3) rather than area. The final correct calculation for the CM position must incorporate the volumes and their respective distances from a reference point.

PREREQUISITES
  • Understanding of center of mass concepts in physics
  • Familiarity with volume calculations for three-dimensional shapes
  • Basic algebra for manipulating equations
  • Knowledge of uniform material properties in physics
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of center of mass in multi-object systems, particularly in three-dimensional contexts.

Bones
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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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