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## Homework Statement

A person with mass m1 = 69 kg stands at the left end of a uniform beam with mass m2 = 108 kg and a length L = 2.5 m. Another person with mass m3 = 67 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 9 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate system be the left end of the original position of the beam as shown in the drawing. Assume there is no friction between the beam and floor.

3)What is the new x-position of the person at the left end of the beam? (How far did the beam move when the ball was throw from person to person?

4)To return the medicine ball to the other person, both people walk to the center of the beam. At what x-position do they end up?

## Homework Equations

[tex]\frac{1}{M_{total}} \sum_{i=1}^{n} m_{i}r_{i} [/tex]

## The Attempt at a Solution

I answered the first 2 parts of the question that have to do with finding the center of mass and I am fine with any sort of easy "find the center of mass of this situation", but I cannot figure out these sort of relative motion questions to do with the distance something is moving from the center of mass.

I understand that since there are no external forces, the center of mass remains at the same place, I just don't know how to quantify what the motion of ball being thrown from one side to the other would do and I have trouble with relative motion questions.

The question is just for practice and I want to figure it out. Any help would be greatly appreciated.