Two students submit different pulley designs A and B to lift a load of 2500 N with maximum effort 500 N and efficiency 80%. Design A has a V.R. of 5 and design B has a V.R. of 7.
Calculate the effort for each design and justify which design is better.

Given,

• Load = 2500 N
• Maximum effort = 500 N
• Efficiency = 80% = 0.8
• V.R. of A = 5
• V.R. of B = 7

As, efficiency of a machine is given by,

$\text {Efficiency} = \dfrac {\text {Mechanical advantage (M.A.)}}{\text {Velocity ratio (V.R.)}} \\[1em] \Rightarrow {\text {M.A.}} = \text {Efficiency} \times \text {V.R.}$

For design A :

${\text {M.A.}} = \text {Efficiency} \times \text {V.R.} \\[1em] = 0.8 \times 5 \\[1em] = 4$

Also, mechanical advantage (M.A.) of the pulley A is given by,

$\text {M.A.} = \dfrac{\text {Load}}{\text {Effort}} \\[1em] \Rightarrow \text {Effort} = \dfrac{\text {Load}}{\text {M.A.}} \\[1em] = \dfrac{2500}{4} \\[1em] = 625\ \text N$

For design B :

${\text {M.A.}} = \text {Efficiency} \times \text {V.R.} \\[1em] = 0.8 \times 7 \\[1em] = 5.6$

Also, mechanical advantage (M.A.) of the pulley B is given by,

$\text {M.A.} = \dfrac{\text {Load}}{\text {Effort}} \\[1em] \Rightarrow \text {Effort} = \dfrac{\text {Load}}{\text {M.A.}} \\[1em] = \dfrac{2500}{5.6} \\[1em] = \dfrac{25000}{56} \\[1em] \approx 446\ \text N$

Design A requires 625 N, which is greater than the allowed effort, so it is not suitable but design B requires about 446 N, which is less than 500 N, so it satisfies the condition.

Therefore, design B is the better design.