# Equilibrium in a walkway

• Archived
This problem is trying to find out how much weight can be placed in the middle of a system before the weights on the outside go over the pulleys.

A diagram of the problem can be found here http://www.physics.umn.edu/classes/...ds/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/√(d2+(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.

## Answers and Replies

haruspex
Science Advisor
Homework Helper
Gold Member
The linked page is not public, so the diagram is unknown. Taking the algebra on trust to the final equation, and assuming theta is known, it is just a matter of squaring both sides, multiplying out to remove the fraction, and collecting up like terms, to find a simple expression for d2.