Finding Center of Gravity in a 4-Object Arrangement

[stanton]

Homework Statement

Consider the following mass distribution where the xy coordinates are given in meters: 5 kg at (0.0, 0.0) m, 3 kg at (0.0, 4.0) m, and 4 kg at (3.0, 0.0) m. Where should a fourth object of 8 kg be placed so the center of gravity of the four-object arrangement will be at (0.0, 0.0) m?

Homework Equations

Just guessing,

Xc of m = $$\Sigma mi*xi\Sigma mi<h2>The Attempt at a Solution</h2><br /> <br /> I am guessing that it should be in the bottom left of the xy coordinate. Buy I don't know how to start the problem.$$

 

[ideasrule]

The equation you have is right: the sum of the mi*xi for each individual mass is equal to the x-coordinate of the center of mass. The same applies to the y-coordinate of the mass center: it's equal to sigma mi*yi.