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A diagram of the problem can be found here http://www.physics.umn.edu/classes/2013/fall/Phys 1201W.100/downloads/208321-1201Lab3_P4_Equilibrium_Walkway.pdf

We are trying to find d (the distance of the sag) in terms of known quantities. We will know m (the mass of each counterweight), L (the length), and M the mass of the center weight.

So far I have...

∑F=Fc+Fa-Fb=0

ƩFx=Fc cosθ+Fa cosθ=0

∑Fy=Fc sinθ+Fa sinθ-Fb=0

All from the middle point P, where Fb is the force down, Fa is the force up to the left, and Fc is the force up to the right.

sinθ=d/L1 =d/√(d

^{2}+(L/2)

^{2})

That check mark is supposed to be a squareroot if that wasn't clear.

I am not sure where to go from here to solve for d.