Calculating Center of Mass, 1988 Physics C Mechanics MC

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SUMMARY

The discussion focuses on calculating the center of mass for a uniformly cross-sectioned wire bent into a specific shape. The correct coordinates for the center of mass are determined to be (15/14, 6/7). Participants debated whether to integrate the wire along all four sides, highlighting the importance of understanding the center of mass for each segment of the wire and how to combine them effectively to find the overall center of mass.

PREREQUISITES
  • Understanding of center of mass concepts
  • Familiarity with integration techniques in physics
  • Knowledge of geometric shapes and their properties
  • Ability to analyze composite shapes
NEXT STEPS
  • Study the principles of center of mass in two-dimensional shapes
  • Learn about integration methods for calculating mass distributions
  • Explore examples of composite shapes in physics
  • Review the use of coordinate systems in physics problems
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Physics students, educators, and anyone interested in mechanics and the calculation of center of mass in physical systems.

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A piece of wire of uniform cross section is bent in the shape shown above (for picture: http://tinypic.com/r/23tjr45/5). What are the coordinates of the center of mass?
Relevant equations:
Was I supposed to integrate the wire on all 4 sides? I wasn't sure exactly what to do at this point.The attempt at a solution
Basically, I eyeballed the graph and picked a point in the far right corner because I thought that would be where the most mass is concentrated. The correct answer, however, is (A)(15/14, 6/7)
 
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Hint:

You know where the cm of each bar is so how do you combine them?
 

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