Center of Mass involving three cubes

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SUMMARY

The discussion centers on calculating the center of mass (CM) of three cubes with side lengths l, 2l, and 3l, arranged in a straight line. The formula used is CM = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3), where the masses are determined by the cubes' volumes and uniform density. The participant initially struggled with finding the mass and determining the positions of the cubes but ultimately solved the problem independently, confirming the simplicity of the calculation.

PREREQUISITES
  • Understanding of center of mass calculations
  • Knowledge of volume and mass relationships in uniform materials
  • Familiarity with basic algebra and equations
  • Concept of linear arrangement of objects
NEXT STEPS
  • Study the derivation of the center of mass formula for composite objects
  • Explore the concept of density and its impact on mass calculations
  • Learn about the properties of uniform materials in physics
  • Investigate examples of center of mass in different geometric configurations
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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.

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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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