1. The problem statement, all variables and given/known data 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: 2. Relevant equations Can't think of any, it seems like this problem just uses some common sense I am clearly lacking. 3. 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!
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.
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)) ?