Complex Pulley System (five different pulleys)

[mxyplizk]

Homework Statement

We are asked to find the force (F) needed to maintain equilibrium. I've drawn a picture; the red, blue, and green ropes are three separate ropes. Block W has a weight of 500 lbs, pulley A has a weight of 10 lbs, and pulley B has a weight of 20 lbs.

the picture: http://img60.imageshack.us/img60/2065/pulleysystem.jpg

Homework Equations

Can't think of any, it seems like this problem just uses some common sense I am clearly lacking.

The Attempt at a Solution

I think I figured out what the answer would be if you ignore the weights of the two pulleys. The tension would be 1/2 W on either side of pulley B, and therefore the tension pulling down on pulley A would be 1/2 W. Therefore, the tension on either side of pulley A would be 1/4 W, and since that rope is the rope to which the force F is applied, F=1/4 W=125 lbs. But I just don't know how to take into account the weights of the pulleys. Thanks for any and all help!

 

[rl.bhat]

There are three segments in the red rope. Total hanging weight is W+B. Find the tension in each segment. Apply the same thing to green rope.

 

[mxyplizk]

So tension in the red rope would equal 1/3(W+B), and then tension in the green rope would equal 1/3(A+1/3(W+B)) ?

 

[rl.bhat]

Yes.