Question

A pulley system has five pulleys in all, 2 in the movable block and three in fixed block, such that effort is applied in the upward direction and a load of 60 kgf is attached to the movable block.

1. What is the velocity ratio of pulley system?
2. Assuming pulley system an ideal one, what is the mechanical advantage?
3. What is the magnitude of effort applied?
4. If the pulley system is not ideal but is 75% efficient, what is the effort required?

Answer 1

(a) Velocity ratio = No. of supporting segments of the string = 6

(b) Assuming pulley system as ideal.

MA = Velocity ratio = 6

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

\[ \therefore\ 6 = \frac{60\ \mathrm{kgf}}{E}\]

E = 10 kgf

(d) When efficiency of pulley is 75%.

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

MA = η × VR

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

\[\frac{60\ \mathrm{kgf}}{\mathrm{E}} = \frac{75}{100} \times 6 \]

\[ \therefore\ E = \frac{60\ \mathrm{kgf} \times 100}{6 \times 75}\]

\[= \frac{6000}{450}\ \mathrm{kgf}\]

= 13.33 kgf