Question

A block and tackle system has 5 pulleys and is 90% efficient. If the effort required to lift a load is 1000 N, the effort required by the system is .

• A. 122.2 N
• B. 222.2 N
• C. 322.2 N
• D. 422.2 N

Answer 1

The correct option is B 222.2 N

Given, Load = 1000 N and $\eta$ = 90%

We know that, if load moves through a distance 'd', the effort moves through a distance 'nd', where n is the number of pulley in the system.
$\therefore$ Velocity Ration (VR) = $\frac{d_E}{d_L}=\frac{nd}{d}=n=5$ [n = 5 (given)]

Also, efficiency is equal to the ratio of mechanical advantage to the velocity ratio i.e.,

$\eta$ = $\frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}}$
$\Rightarrow$ MA = $\eta \times$ VR

MA = $\frac{90}{100}$ $\times$ 5 = $\frac{9}{2}$

MA = $\frac{\text{Load}}{\text{Effort}}$

$\frac{9}{2}$ = $\frac{1000}{\text{E}}$

$\therefore$ Effort (E) = $\frac{2000}{9}$ = 222.2 N