JAMB 2014 Physics · Question 36

A machine whose efficiency is 75% is used to lift a load of 1000N. Calculate the effort put in to the machine if it has a Velocity ratio of 4.

Options

A.343.32N
B.233.33N
C.333.33N
D.334.33N

Answer: C. 333.33N

Explanation written with AI and checked against the answer key

1. Analyze the question

We are given:

Efficiency ( $\eta$ ): 75% (or 0.75)
Load ( $L$ ): 1000 N
Velocity Ratio ( $VR$ ): 4
Goal: Calculate the Effort ( $E$ )

2. Explain the concept

In simple machines, efficiency is defined as the ratio of Mechanical Advantage ( $MA$ ) to Velocity Ratio ( $VR$ ), expressed as a percentage:

\text{Efficiency} (\eta) = \frac{MA}{VR} \times 100\%

We also know that Mechanical Advantage is the ratio of Load to Effort:

MA = \frac{\text{Load}}{\text{Effort}} = \frac{L}{E}

By combining these, we get the formula:

\eta = \frac{L}{E \times VR} \times 100\%

3. Show the solution

Step 1: Write down the formula

\eta = \frac{L}{E \times VR}

(Note: Since we are using 0.75 for efficiency, we do not need to multiply by 100)

Step 2: Rearrange the formula to solve for Effort ( $E$ )

E = \frac{L}{\eta \times VR}

Step 3: Substitute the given values

E = \frac{1000}{0.75 \times 4}

Step 4: Perform the calculation

E = \frac{1000}{3}

E = 333.333... \text{ N}

4. Identify the answer

Comparing our result to the options provided, the correct value is 333.33N. This matches option C.

5. Exam Tip

When dealing with machine problems, always remember that Efficiency is always less than 1 (or 100%) for real-life machines due to friction. If your calculated effort is lower than the load divided by the velocity ratio, you might have inverted your formula. Also, keep your units consistent—since the load is in Newtons, your effort will also be in Newtons.

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