Question

suppose a pulley with an IMA of 2 was used with an input force of 50N to lift a box 45 cm that weighs 100N. What distance was the rope pulled?

Answer 1

The mechanical advantage of output force/input force comes from the grater
distance the pulley rope moves.

The work has to be the same, by conservation of energy:

50 x = (100)(45) where x is the distance the rope was pulled.

Answer 2

x = 90 cm