The efficiency is a system is defined as:

• • the ratio of the useful energy output to the total energy input of the system,
    OR
  • the ratio of the useful power output to the total power input of the system,

Efficiency is usually expressed as a percentage.

 

Efficiency = ((useful energy output) /(total energy input) ) × 100%

OR

Efficiency = ((useful power output) /(total power input) ) × 100%

 

Since useful energy output (or power output) cannot be greater than the total energy input (or power input), the efficiency of a system cannot be greater than 100%.

Example
A lift is able to carry a load of 1000 kg at a constant velocity of 1.5 m/s. Given that the motor driving the lift has an input power of 20 kW, calculate the efficiency of the lift. Output power =Work / time = F v = mgv = 1000 × 10 × 1.5 = 15 kW Efficiency = (output power / input power) × 100% = (15 / 20) × 100% = 75% Show Answer

Example
Calculate the efficiency of a machine if 4500 J of work has to be applied on it to lift a weight of 2400 N through a vertical distance of 1.6 m. useful work done = gain in GPE = mgh =2400 × 1.6 =3840 J Efficiency = 3840 /4500 × 100% = 85% (2 s.f.) Show Answer

Example
The efficiency of a electric motor is 70 % when it is used to raise a load of 55 kg at a constant speed of 20 cm s-1. What is the input power of the motor? Efficiency = 70% = (output power /input power) × 100% Input power = (550 × 0.20)/70 × 100 = 157 W = 160 W (2 s.f.) Show Answer

 

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