Calculate the total chain mass based on the balance and counterweight problem specified.

Question

A chain of 10 links length is hung over a frictionless pulley, such that 4 links hang free of the pulley on the left, and 2 links hang free of the pulley on the right. Counterweights of mass W1 and W2 are hung on the right and left respectively so as to balance the chain exactly. What is the expression for the total mass of the chain?

Answer 1

Wait, I can almost hear you object, how do I know anything about this system? And what units can I possibly state my answer in?

The only units you can use are the variables given, W1 and W2. The chain has 2 links unbalanced in and of itself; the counterweights must compensate for that. So W1 - W2 = 2 chain links mass. Just proportionate that up to 10 links of chain length, and you have 5W1- 5W2.

SAT math tests won't give you more complicated problems with levers and compound pulleys (that's physics), but a simple balance problem like this could appear.