Find Center of Mass: Calculate x,y Coordinates with R = sum(m*r)/sum(m)

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SUMMARY

The discussion focuses on calculating the center of mass coordinates (x,y) for an object with varying densities in two parts: part A with density p (kg/m³) and part B with density p/2 (kg/m³). The formula R = sum(m*r)/sum(m) is confirmed as the correct approach to find the center of mass. Participants suggest breaking the object into three rectangles to simplify the calculation of mass and individual centers of mass, ultimately treating these as point masses for the final computation.

PREREQUISITES
  • Understanding of center of mass calculations
  • Familiarity with density concepts in physics
  • Basic knowledge of 2D geometry and area calculations
  • Ability to perform summation of masses and coordinates
NEXT STEPS
  • Study the derivation and application of the center of mass formula R = sum(m*r)/sum(m)
  • Learn how to calculate mass and center of mass for composite shapes
  • Explore density variations in physical objects and their impact on center of mass
  • Practice problems involving 2D shapes and their centers of mass
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Students in physics or engineering courses, educators teaching mechanics, and anyone involved in calculating the center of mass for irregular shapes.

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1. The density of part A (p)(kg/m^3) and in part B (p/2)(kg/m^3). Find the coordinate (x,y) of the center of mass of this object.

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(consider a piece of the object that is one meter in the z direction)

2. R = sum(m*r) / sum(m)...maybe? I am completely stumped on how to start this problem my teacher has done no sample problems that are anything like this, not even anything in 3D, if anyone could at least provide a hint to get me started on this one? Would be greatly appreciated.
 
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This isn't a 3d problem, it's a 2d problem and he only wants [itex](\overline x,\overline y)[/itex] Break it up into three rectangles, find the mass and center of mass of each. Then find the center of mass of the three masses as if they were point masses at their centers of mass.
 
Awesome, thanks a ton for helping me get started!
 

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