Derivation of equation for mass on pulley and displacement

[TrippingBilly]

http://filesaur.us/files/1858/pulley/

Derivation of equation for mass on pulley and displacement


Sorry that the picture stinks, but its all I got. The system is in equilibrium.The counter mass on the left is mass A and the mass on the right is mass B, both of mass m. The center mass of mass M is denoted as B. The length of the system is denoted as L. h stands for the vertical displacement of the center mass. The equation is..

h= ML / sqrt(16m^2 - 4M^2)

I wrote the equations for the sum of the forces and my teacher told me I could derive it from those but I can't get any further than what I have.
Forces in x direction = T(sub c)cos(theta) - T(sub a)cos(theta) =0 and
Forces in y direction = T(sub c)sin(theta) + T(sub a)sin(theta) - T(sub b) = 0

 

[physics girl phd]

You don't have the tensions T described in the drawing.

Also -- can you give us expressions for the tensions in terms of m, M, L, h?

 

[TrippingBilly]

http://filesaur.us/files/1912/pulley/
T1 = T2 = T3 = T4 = mg
T5=Mg

I don't know how to bring L or h into this.

 

[radou]

In what relation is T5 with T2 and T3?