Efficiency Examples: 46 Problems with Answers

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 \text{ J}

of input energy and produces

350 \text{ J}

of useful output. What is its efficiency?

Answer

η = 70 %

First step

Use the efficiency formula:

\eta = \frac{\text{useful output}}{\text{total input}} \times 100\%

Full solution

2
Substitute the given values: $\eta = \frac{350}{500} \times 100\%$ .
3
$η = 70 %$

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\%

efficiency lifts a

200 \text{ kg}

load by

10 \text{ m}

. How much electrical energy is consumed? Use

g = 10 \text{ m/s}^2

Example 3

medium

An electric motor is

70\%

efficient. It must do

1400

J of useful work. How much input energy is required?

Example 4

medium

A two-stage process: stage 1 is

60\%

efficient, stage 2 is

70\%

efficient. Find overall efficiency.

Example 5

hard

A pump lifts

300

kg of water

20

m in

40

s, drawing

2000

W from the grid. Use

g = 10

m/s

^2

. Find efficiency.

Example 6

hard

A power plant outputs

700

MW and operates at

35\%

efficiency. How many tonnes of coal per hour does it burn if coal yields

30

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 \text{ J}

and generates

350{,}000 \text{ J}

of electrical energy. What is the efficiency?

Example 2

hard

A car engine has an efficiency of

25\%

and a petrol pump has an efficiency of

90\%

. The pump delivers

40 \text{ litres}

of fuel containing

1.4 \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 = 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 = 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

400

J and produces

120

J of useful output. Find efficiency.

Example 24

easy

Express an efficiency of

0.65

as a percentage.

Example 25

easy

A motor consumes

150

J of input and wastes

30

J as heat. Find its efficiency.

Example 26

easy

200

W bulb produces

50

W of light. Find its efficiency.

Example 27

medium

A pulley system lifts a

40

kg mass

3

m using

1500

J of input work. Use

g = 10

m/s

^2

. Find the efficiency.

Example 28

medium

A car engine takes in

5000

J of chemical energy and converts

1750

J to kinetic energy. Find efficiency.

Example 29

medium

A wind turbine receives

20

MW of wind power and outputs

8

MW of electrical power. Find efficiency.

Example 30

medium

A 500 W heater is

95\%

efficient at converting electrical to thermal energy. How much heat is delivered to the room in

10

minutes?

Example 31

medium

A motor delivers

720

J of useful work and wastes

480

J as heat. Find efficiency.

Example 32

medium

An LED bulb is

35\%

efficient and produces

7

W of visible light. Find the electrical power input.

Example 33

hard

A coal plant burns coal at

9000

MJ/kg and is

33\%

efficient. How much electrical energy does

1

tonne (

1000

kg) of coal produce?

Example 34

hard

A 75% efficient engine produces

1500

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

T_H = 600

K and cold reservoir

T_C = 300

K. Find the maximum (Carnot) efficiency.

Example 36

hard

A pulley system requires

500

N of effort to lift a

1500

N load through a height of

1

m using

5

m of rope movement. Find efficiency.

Example 37

hard

Three serial stages have efficiencies

90\%

80\%

70\%

. Find overall efficiency.

Example 38

hard

A heat pump uses

200

J of work to transfer

700

J of heat into a house. Find the coefficient of performance (heat-pump 'efficiency' analog).

Example 39

challenge

A motor drives a

0.5

kg projectile to

20

m/s using

250

J of electrical input (ignore air resistance). Find efficiency.

Example 40

challenge

A car gets

25\%

engine efficiency,

90\%

transmission efficiency, and

95\%

wheel-to-road efficiency. Find overall efficiency.

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Related Concepts

Energy Work Power

Background Knowledge

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

energywork