Question

A pulley system has five pulleys in all and is 90% efficient. Calculate (a) the mechanical advantage (b) the effort required to lift a load of 1000 N (c) the resistance due to the movable parts of the machine and friction.

Answer 1

Velocity ratio = No. of pulleys = 5.

Knowing, \[ \eta = \frac{\mathrm{MA}}{\mathrm{VR}} \]

MA = η × VR

\[= \frac{90}{100} \times 5\]

= 4.5

Also, \[ \frac{l}{E} = \mathrm{MA} \]

\[\text{E} = \frac{l}{\mathrm{MA}}\]

\[= \frac{1000\ \mathrm{N}}{4.5}\]

= 222.2 N

Knowing, \[ \mathrm{MA} = \mathrm{VR} - \frac{x}{E} \]

∴ x = E(VR − MA)

= 222.2(5 − 4.5)

= 111.1 N