(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Center of Mass locations of a thin stick of mass M and length L, whose left ends are at x=0.

The stick has uniform mass density λ_{1}= 2M/3L along the left half, and has uniform mass density λ_{2}= 4M/3L along the right half.

2. Relevant equations

I know that this is a center of mass problem dealing with 1-dimension; the x-direction. Thus the equation to find this that we've covered in this class is, the First Moment of the mass (x) divided by the total Mass:

x_{cm}= FM(x) / M

I'm assuming (but don't know for certain that the formula they derived for mass density was mass / length. But I thought density was mass / volume. I'm just lost.

3. The attempt at a solution

I've drawn the picture of what this looks like with the 0 at the very left end, 1/2L at the middle of the stick, and L at the very right end.

I cut the stick in half, and now am totally lost on where to place the λ_{1}on the left half and the λ_{2}on the right half.

Can someone please help give me some semblance of direction on where to start this problem? All these word problems are starting to depress me with how I'm unable to find the method to solve them.

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# Finding Ctr of Mass of object w/ given uniform mass density

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