A machine is used to lift a load of 20 N through a height of 10 m. if the efficiency of the machine is 40%, how much work is done?

Analyze the question

A machine lifts a 20 N load through 10 m. Its efficiency is 40%. We need the work done. In this type of question, "work done" means the work put into the machine (the input energy), since the useful work is the work done on the load.

Concept

• Work output (useful work) = force × distance = load × height
• Efficiency = (work output / work input) × 100%
• So, work input = work output / efficiency

Solution

1. Work output = 20 N × 10 m = 200 J
2. Efficiency = 40% = 0.40
3. Work input = 200 / 0.40 = 500 J

Answer

The work done by the machine (the energy supplied to it) is 500 J.

Check the other options. 200 J is the useful work, which is not listed. 80 J would be 40% of 200, which is the wrong way round (multiplying instead of dividing). That is the trap in option A.

Tip

Efficiency is always less than 100%, so the input must be larger than the output. If your answer for input work is smaller than the useful work, you have used the formula the wrong way round. Remember: Input = Output ÷ Efficiency.