Question

A pulley system has five pulleys in all and is 90% efficient such that it lifts a load of 1000 N. Answer the following question:

The resistance of movable parts of pulley system is:

Options

• 112.2 N

• 111.1 N

• 110.0 N

• 113.3 N

Answer 1

111.1 N

Explanation:

Given:

Total number of pulleys (n) = 5

Therefore, Velocity Ratio (VR) = 5

Efficiency (η) = 90% = 0.90

Load (L) = 1000 N

Formula:

\[ \text{Efficiency } (\eta) = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \]

MA = η × VR

= 0.90 × 5

= 4.50

\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load (L)}}{\text{Effort (E)}} \]

\[ \text{Effort (E)} = \frac{\text{Load (L)}}{\text{MA}} \]

\[= \frac{1000}{4.50}\]

\[= \frac{10000}{45}\]

= 222.2 N

In a real pulley system, the relation between Load, Effort, number of pulleys, and resistance of movable parts (ω) is:

Load (L) = (n × E) − ω

ω = (n × E) − L

ω = (5 × 222.2) − 1000

ω = 1111.1 − 1000

ω = 111.1 N