The effort force required to lift the piano is
There are two ways to arrive at this result.
First Method: Conservation of Energy
The first way to think about this problem is to use the fact that energy is always conserved. This means the total work required is the same whether we pull the piano up with or without the pulley system.
Work is defined as:
where W is work, F is force and d is distance.
The work done by the pulley system on the piano is:
So the work required to pull on the pulley system is the same:
So the effort force
Second Method: Mechanical Advantage
The second is by using mechanical advantage.
We can then use the mechanical advantage, to find out how much effort force was used:
The effort force is thus: