A pulley system with VR = 4 is used to lift a load of 175 kgf through a vertical height of 15 m. The effort required is 50 kgf in the downward direction, (g = 10 N kg-1). [4] Calculate:
Distance moved by the effort.
Topic: Machines, levers and pulleys
Answer
Given: velocity ratio VR = 4, load distance d_L = 15 m
Velocity ratio = distance moved by the effort ÷ distance moved by the load VR = d_E ÷ d_L
4 = d_E ÷ 15 d_E = 4 × 15 d_E = 60 m
Distance moved by the effort = 60 m
The velocity ratio tells you how much FURTHER the effort must move than the load. VR = 4 means the effort travels four times as far — that is the price paid for needing a smaller force.
So multiply, do not divide: dividing gives 3.75 m, which would mean the effort moved less than the load, and no pulley system does that. In any machine the effort end always moves the greater distance.