How Does a Pulley Find Its Equilibrium Position in a Static System?

[benf.stokes]

Homework Statement

Consider the situation of the figure, where a string of negligible mass and length L is fixed at two points A and B, with B dislocated of A by a distance w(<L) and vertically dislocated by a distance h < sqrt(L^2-w^2) A mass is hung on the rope using a moving pulley of negligible mass. The pulley has no friction and can move freely along the rope until it "finds" the position of equilibrium in which the pulley is at a horizontal distance x of point A, and a vertical distance y of that point.

What are the equilibrium angles Theta(1) and Theta(2)?
What are the values of x, y , L1 and L2 at equilibrium?

Homework Equations

There aren't any besides the fact that the potential energy must be a minimum

The Attempt at a Solution

I can't even get started.

 

[PhanthomJay]

I haven't looked at this problem in any detail, but it seems that there are enough equilibrium equations, and given geometry, to solve it. You should probably start by drawing a free body diagram of the hanging mass, and writing the 2 equilibrium equations using Newton's 1st law. Note that ideal pulleys change the direction of the tension in the cable, but not its magnitude. Then you've got to do some trig work.

 

[benf.stokes]

Thanks for the reply, but my problems is in the trig work. I don't know how to get started