# Complex Pulley System (five different pulleys)

by mxyplizk
Tags: pulleys, ropes, weight
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 P: 8 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!
 HW Helper P: 4,433 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.
 P: 8 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)) ?
 HW Helper P: 4,433 Complex Pulley System (five different pulleys) Yes.

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