Derivation of equation for mass on pulley and displacement

AI Thread Summary
The discussion focuses on deriving the equation for the vertical displacement of a mass on a pulley system in equilibrium, represented as h = ML / sqrt(16m^2 - 4M^2). The system involves two masses, A and B, each of mass m, with a center mass M. Participants express difficulty in incorporating the lengths L and h into their equations for tension. The equations for forces in both the x and y directions are provided, but there is uncertainty about the relationships between the tensions T5, T2, and T3. Clarifying these relationships and deriving the expressions for tension in terms of the variables is the main goal of the discussion.
TrippingBilly
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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
 
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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?
 
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.
 
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In what relation is T5 with T2 and T3?
 

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