Efficiency Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Efficiency.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.

What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Efficiency asks what energy enters, leaves, stays stored, or changes form in the chosen system.

Common stuck point: Students often know a formula related to efficiency but skip the recognition step: Can I define the system and track energy before and after the interaction or process? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I define the system and track energy before and after the interaction or process?

Worked Examples

Example 1

easy
A machine uses 500 J500 \text{ J} of input energy and produces 350 J350 \text{ J} of useful output. What is its efficiency?

Answer

η=70%\eta = 70\%

First step

1
Use the efficiency formula: η=useful outputtotal input×100%\eta = \frac{\text{useful output}}{\text{total input}} \times 100\%.

Full solution

  1. 2
    Substitute the given values: η=350500×100%\eta = \frac{350}{500} \times 100\%.
  2. 3
    η=70%\eta = 70\%
Efficiency measures how well a machine converts input energy into useful output. No real machine is 100% efficient because some energy is always lost to heat, sound, or friction.

Example 2

medium
An electric motor with 85%85\% efficiency lifts a 200 kg200 \text{ kg} load by 10 m10 \text{ m}. How much electrical energy is consumed? Use g=10 m/s2g = 10 \text{ m/s}^2.

Example 3

medium
An electric motor is 70%70\% efficient. It must do 14001400 J of useful work. How much input energy is required?

Example 4

medium
A two-stage process: stage 1 is 60%60\% efficient, stage 2 is 70%70\% efficient. Find overall efficiency.

Example 5

hard
A pump lifts 300300 kg of water 2020 m in 4040 s, drawing 20002000 W from the grid. Use g=10g = 10 m/s2^2. Find efficiency.

Example 6

hard
A power plant outputs 700700 MW and operates at 35%35\% efficiency. How many tonnes of coal per hour does it burn if coal yields 3030 MJ/kg?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A coal power plant burns fuel releasing 1,000,000 J1{,}000{,}000 \text{ J} and generates 350,000 J350{,}000 \text{ J} of electrical energy. What is the efficiency?

Example 2

hard
A car engine has an efficiency of 25%25\% and a petrol pump has an efficiency of 90%90\%. The pump delivers 40 litres40 \text{ litres} of fuel containing 1.4×109 J1.4 \times 10^9 \text{ J} of chemical energy. How much useful kinetic energy does the car ultimately produce from this fuel?

Example 3

easy
A machine takes in 200 J and delivers 150 J of useful output. Find its efficiency.

Example 4

easy
A lamp uses 100 J of electrical energy and produces 20 J of light. Find its efficiency.

Example 5

easy
Can a machine have an efficiency of 120%? Why or why not?

Example 6

easy
A motor receives 500 J and wastes 100 J as heat. How much useful output does it produce?

Example 7

easy
Express an efficiency of 0.4 as a percentage.

Example 8

easy
A device is 90% efficient and receives 300 J. How much useful energy comes out?

Example 9

easy
Two engines: A is 30% efficient, B is 45% efficient. Which wastes a larger fraction of input energy?

Example 10

easy
A power plant outputs 400 MW of useful power from 1000 MW of input. Find its efficiency.

Example 11

medium
A crane lifts a 50 kg load 4 m (use g=10g = 10) using 2500 J of input energy. Find its efficiency.

Example 12

medium
A 60% efficient motor must deliver 1200 J of useful work. How much input energy is required?

Example 13

medium
An engine takes in 800 J and wastes 480 J as heat. Find its efficiency.

Example 14

medium
A pump is 75% efficient and uses 4000 J. How much energy is wasted?

Example 15

medium
Two machines do the same 600 J of useful work. Machine X uses 800 J input, machine Y uses 1000 J. Which is more efficient?

Example 16

medium
A car engine is 25% efficient. To deliver 50000 J of useful work, how much fuel energy is needed?

Example 17

medium
A 1000 W motor lifts a 20 kg mass at a steady 2 m/s (use g=10g = 10). Find its efficiency.

Example 18

challenge
A two-stage system: stage 1 is 80% efficient, stage 2 is 50% efficient. Find the overall efficiency.

Example 19

challenge
A power station burns fuel releasing 5000 MJ per second and outputs 1750 MW. It then needs to power 5000 homes each using 350 W. What efficiency, and can it supply the homes?

Example 20

challenge
A 40% efficient engine produces 600 J of useful work each cycle. How much heat does it dump to the surroundings per cycle?

Example 21

medium
A machine is 65% efficient and produces 2600 J of useful work. Find the input energy.

Example 22

medium
A light bulb takes 60 J and produces 9 J of light. Find its efficiency and the energy wasted.

Example 23

easy
A device takes in 400400 J and produces 120120 J of useful output. Find efficiency.

Example 24

easy
Express an efficiency of 0.650.65 as a percentage.

Example 25

easy
A motor consumes 150150 J of input and wastes 3030 J as heat. Find its efficiency.

Example 26

easy
A 200200 W bulb produces 5050 W of light. Find its efficiency.

Example 27

medium
A pulley system lifts a 4040 kg mass 33 m using 15001500 J of input work. Use g=10g = 10 m/s2^2. Find the efficiency.

Example 28

medium
A car engine takes in 50005000 J of chemical energy and converts 17501750 J to kinetic energy. Find efficiency.

Example 29

medium
A wind turbine receives 2020 MW of wind power and outputs 88 MW of electrical power. Find efficiency.

Example 30

medium
A 500 W heater is 95%95\% efficient at converting electrical to thermal energy. How much heat is delivered to the room in 1010 minutes?

Example 31

medium
A motor delivers 720720 J of useful work and wastes 480480 J as heat. Find efficiency.

Example 32

medium
An LED bulb is 35%35\% efficient and produces 77 W of visible light. Find the electrical power input.

Example 33

hard
A coal plant burns coal at 90009000 MJ/kg and is 33%33\% efficient. How much electrical energy does 11 tonne (10001000 kg) of coal produce?

Example 34

hard
A 75% efficient engine produces 15001500 J of useful work each cycle. How much heat is rejected to the environment per cycle?

Example 35

hard
A Carnot engine operates between hot reservoir TH=600T_H = 600 K and cold reservoir TC=300T_C = 300 K. Find the maximum (Carnot) efficiency.

Example 36

hard
A pulley system requires 500500 N of effort to lift a 15001500 N load through a height of 11 m using 55 m of rope movement. Find efficiency.

Example 37

hard
Three serial stages have efficiencies 90%90\%, 80%80\%, 70%70\%. Find overall efficiency.

Example 38

hard
A heat pump uses 200200 J of work to transfer 700700 J of heat into a house. Find the coefficient of performance (heat-pump 'efficiency' analog).

Example 39

challenge
A motor drives a 0.50.5 kg projectile to 2020 m/s using 250250 J of electrical input (ignore air resistance). Find efficiency.

Example 40

challenge
A car gets 25%25\% engine efficiency, 90%90\% transmission efficiency, and 95%95\% wheel-to-road efficiency. Find overall efficiency.
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Related Concepts

EnergyWorkPower

Background Knowledge

These ideas may be useful before you work through the harder examples.

energywork