Calculating Center of Mass, 1988 Physics C Mechanics MC

In summary, the conversation discusses finding the coordinates of the center of mass for a piece of wire bent into a specific shape. The individual suggests eyeballing the graph and choosing a specific point, but the correct answer involves combining the center of mass of each bar.
  • #1
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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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  • #2
Hint:

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

1. What is the center of mass?

The center of mass is a point in a system or object where the mass is evenly distributed, meaning the weight of the object can be thought of as acting at a single point.

2. How is the center of mass calculated?

The center of mass can be calculated by finding the weighted average of the positions of all the individual masses in the system, taking into account their respective masses.

3. Why is calculating the center of mass important?

Calculating the center of mass is important because it allows us to understand the overall motion and stability of a system or object. It is also a crucial concept in understanding rotational motion and conservation of momentum.

4. What is the difference between center of mass and center of gravity?

The center of mass is a point where the mass is evenly distributed, while the center of gravity is a point where the weight of an object is evenly distributed. In most cases, the center of mass and center of gravity are the same, but they can differ in systems involving non-uniform gravitational fields.

5. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This can occur in objects with irregular shapes or non-uniform density distributions, where the center of mass may not coincide with the geometrical center of the object.

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