A block and tackle system consisting of 5 pulleys is used to raise a load of 200\text{ N} … — JAMB UTME

A block and tackle system consisting of $5$ pulleys is used to raise a load of $200\text{ N}$ through a vertical height of $4\text{ m}$ . If the efficiency of the system is $80\%$ , what is the work done against friction, in joules, during the lifting process?

Answer: 200 J

Answer

The work done against friction during the lifting process is

200\text{ J}

The useful work output is achieved by lifting the

200\text{ N}

load through a vertical height of

4\text{ m}

, yielding

W_{\text{out}} = 200 \times 4 = 800\text{ J}

. Given an efficiency of

80\%

(

0.80

), the total work input required from the effort force is

W_{\text{in}} = \frac{800}{0.80} = 1000\text{ J}

. The energy lost to overcome frictional resistance in the pulleys equals the total work input minus useful work output:

1000\text{ J} - 800\text{ J} = 200\text{ J}

Step-by-Step Solution

Calculate useful work output

W_{\text{out}} = 800\text{ J}

Useful work output is the energy required to raise the load through the specified height (

W_{\text{out}} = \text{Load} \times \text{height}

Determine total work input

W_{\text{in}} = 1000\text{ J}

The total work input is calculated from the efficiency formula:

\text{Efficiency} = \frac{W_{\text{out}}}{W_{\text{in}}}

Compute work done against friction

W_{\text{friction}} = 200\text{ J}

The work lost overcoming friction is the difference between total work input and useful work output (

W_{\text{in}} - W_{\text{out}}

Key Concept

Work and Efficiency in Pulley Systems

Estimated Time:1m 30s

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