In raising a 5000N piano with a pulley system, the movers note that for every 2m of rope pulled down, the piano rises 0.2m. What is the effort force required to lift the piano?

The effort force required to lift the piano is ##500 N##

There are two ways to arrive at this result.

First Method: The first way to think about this problem is to use the fact that is always conserved. This means the total required is the same whether we pull the piano up with or without the pulley system.

Work is defined as: ##W = F*d## where W is work, F is force and d is distance.

The work done by the pulley system on the piano is: ##W = 5000N * 0.2m = 1000Nm##

So the work required to pull on the pulley system is the same: ##1000Nm = F * 2m##

So the effort force ##F## is: ##F = (1000Nm) / (2m) = 500N##

Second Method: Mechanical Advantage The second is by using mechanical advantage.

##ME = (2m)/(0.2m) = 10##

We can then use the mechanical advantage, to find out how much effort force was used:

##ME = (5000 N)/(?)## ##10 = (5000 N)/(?)##

The effort force is thus: ##(5000 N)/10 = 500N##