Question

The diagram alongside shows a single pulley system when a load of 20 kgf is attached to it.

1. What is the velocity ratio of the pulley system?
2. What is the mechanical advantage of the pulley system?
3. What is the magnitude of effort applied?
4. If the pulley is not ideal and is 80% efficient, calculate the effort applied.

Answer 1

(a) Velocity ratio = No. of supporting segments of the string = 2

(b) Assuming pulley system as ideal

MA = Velocity ratio = 2

(c) \[\mathrm{MA} = \frac{l}{E} \]

\[ \therefore\ 2 = \frac{20\ \mathrm{kgf}}{E}\]

E = 10 kgf

(d) When efficiency of pulley is 80%.

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

MA = η × VR

\[\frac{l}{E} = \eta \times \mathrm{VR} \]

\[\frac{20\ \mathrm{kgf}}{\mathrm{E}} = \frac{80}{100} \times 2 \]

\[ \therefore\ E = \frac{20\ \mathrm{kgf} \times 100}{2 \times 80}\]

\[= \frac{50}{4}\ \mathrm{kgf}\]

= 12.5 kgf