How Do You Calculate the Center of Mass for Multiple Objects?

AI Thread Summary
To calculate the center of mass for three connected objects with masses of 5 g, 1 g, and 7 g located at specific coordinates, the formulas for the x and y coordinates of the center of mass must be applied. The x-coordinate is determined by the weighted average of the x-positions, resulting in 4.54, while the y-coordinate is calculated similarly, yielding 4.6. The total mass of the system is 13 g, which is used as the denominator in both calculations. The process involves breaking down the calculations into x and y components to find the overall center of gravity. This method is applicable to multiple objects connected by massless rods.
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Three balls with masses of 5 g, 1 g, and 7 g,
respectively, are connected by massless rods.
The balls are located (in meter intervals) as
in the figure.

Imagine the first quadrant of a graph.
The 5 gram is at point (3,8)
The 7 gram is at point (5,2)
The 1 gram is at point (9,6)

What do do to find the center of gravity? I've looked online and I only see formulas for 2 objects instead of 3 so I'm stuck. Forgot to say they are all connected by massless rods.
 
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the sum of the equations...
 
Sum of what equations?
 
the sum of the center mass equation... and you got to break it down into y and x... there is an similar example online, i'll look it up for you
 
Thanks so much! Would the answer be:

In the X direction
((5x3) + (7x5) + (1x9))/13=4.54

In the Y direction
((5x8) + (7x2) + (1x6))/13=4.6
 
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