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:
Efficiency of the pulley system.
Topic: Machines, levers and pulleys
Answer
Given: MA = 3.5 (from part (iii)), VR = 4
Efficiency, η = (MA ÷ VR) × 100 % = (3.5 ÷ 4) × 100 = 0.875 × 100 = 87.5 %
Efficiency of the pulley system = 87.5 %
MA on top, VR underneath. The other way up gives 114 %, and no machine can be more than 100 % efficient — that impossible answer is your signal the fraction is inverted.
You can also get the same figure from the energies: useful work out ÷ total work in = (175 × 10 × 15) ÷ 30 000 = 26 250 ÷ 30 000 = 87.5 %. Both routes are worth knowing, because some questions give you forces and some give you energies.