Question

Draw a diagram of combination of three movable pulleys with a fixed pulley showing the directions of load, effort and tension in each strand. Find: (i) mechanical advantage, (ii) Velocity ration and (iii) efficiency of the combination in ideal situation.

Answer 1

Tension T₁ in the string passing over the pulley A is given as

2T₁ = L or T₁ = L/2

Tension T₂ in the string passing over the pulley B is given as

2T₂ = T₁ or T₂ = T₁/2 = L/2²

Tension T3 in the string passing over the pulley C is given as

2T³ = T² or T3 = T₂/2 = L/2³

In equilibrium, T₃ = E

E = L/2³ 

Mechanical advantage = MA = L/E = 2³

As one end of each string passing over a movable pulley is fixed, so the free end of string moves twice the distance moved by the movable pulley.

If load L moves up by a distance x, d_L = x, effort moves by a distance 2³x, dE = 2³x

Velocity Ration VR = Distance moved by the effort d_E/Distance moved by the load d_L = 2³ x/X = 2³ 

Efficiency = MA/VR = 2³/2³ = 1 OR 100%