What is the principle of energy conservation in Physics?

The principle of energy conservation states that energy cannot be created or destroyed; it can only be transformed from one form to another. In a closed system, the total energy remains constant. This principle is fundamental in Physics and is crucial for solving problems related to Work, Energy, and Power, especially in the Cambridge International A Levels curriculum.

How does energy conservation apply to mechanical systems?

In mechanical systems, energy conservation means that the total mechanical energy (the sum of kinetic and potential energy) remains constant if only conservative forces, like gravity, are acting. For example, in a pendulum, energy is continuously converted between kinetic and potential forms, but the total energy remains constant, assuming no energy is lost to friction or air resistance.

Why is energy conservation important in solving Physics problems?

Energy conservation is crucial in solving Physics problems because it provides a powerful tool for analyzing systems without needing to know all the forces involved. By applying the conservation of energy principle, students can predict the behavior of systems, calculate unknown quantities, and understand energy transformations, which are key skills in the Cambridge International A Levels Physics syllabus.

Can you provide an example of energy conservation in everyday life?

A common example of energy conservation in everyday life is a roller coaster. At the highest point, the roller coaster has maximum potential energy and minimum kinetic energy. As it descends, potential energy is converted into kinetic energy, increasing its speed. Throughout the ride, the total energy (ignoring friction and air resistance) remains constant, illustrating the conservation of energy principle.

How do non-conservative forces affect energy conservation?

Non-conservative forces, such as friction and air resistance, cause energy to be transformed into non-mechanical forms, like heat, which are not recoverable as mechanical energy. In such cases, the total mechanical energy is not conserved. However, the total energy, including all forms, remains constant. Understanding this distinction is important for Cambridge International A Levels students when analyzing real-world systems where energy losses occur.

Why is "Saying force perpendicular to motion does work" a common mistake in Energy conservation?

Why it happens: Confusing force with work. How to avoid it: Force at 90° to motion does ZERO work. e.g. normal reaction on a horizontal surface; centripetal force in circular motion. Source: 9702 Examiner Reports 2022-2024

Why is "Calculating efficiency > 100%" a common mistake in Energy conservation?

Why it happens: Wrong direction of fraction. How to avoid it: USEFUL OUTPUT divided by TOTAL INPUT. Output cannot exceed input — second law of thermodynamics. Source: 9702 Examiner Reports 2022-2024

Work, Energy and PowerCambridge International A Levels Physics (9702)

Energy conservation

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Energy Conservation Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Work, energy, power and efficiency. Conservation of energy.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

5.1.1 — Compute work done.
5.1.2 — Apply conservation of energy.
5.1.3 — Compute power and efficiency.

Work

$W = Fd\cos\theta$ .

Definition. Energy transferred when force moves its point of application.

Formula. $W = F d \cos\theta$ where $\theta$ is angle between force and displacement.

Special cases.

$\theta = 0°$ : $W = Fd$ (force along motion).
$\theta = 90°$ : $W = 0$ (force perpendicular to motion).
$\theta = 180°$ : $W = -Fd$ (force opposite, e.g. friction → negative work).

Units. Joule (J) = N·m.

Example. 40 N horizontal force pushes crate 5 m on level floor: $W = 40 \times 5 = 200$ J.

Cambridge tip. Mark scheme rewards sign when force opposes motion (negative work).

$W = Fd\cos\theta$ .
Perpendicular: $W = 0$ .
Friction: negative work.

See the full worked example for energy conservation →

Conservation of energy

Total energy constant.

Principle. Energy cannot be created or destroyed; it transfers between forms.

Common transformations.

Falling: GPE → KE.
Spring released: EPE → KE.
Heat engine: heat → mechanical work + waste heat.
Brake: KE → thermal (heat in brake disks).

Sankey diagrams. Width proportional to energy. Show useful vs wasted.

Example. Brake decelerates car: KE → friction heat in brakes.

Cambridge tip. Mark scheme awards 'energy conserved' or 'energy transferred from X to Y' phrasing.

Energy conserved overall.
Transformations between forms.
Use Sankey diagrams.

Power and efficiency

Rate and useful proportion.

Power. $P = W/t$ (average) or $P = Fv$ (instantaneous, constant $F$ along $v$ ).

Units. Watt (W) = J/s.

Efficiency. Useful energy/work output divided by total energy/work input: $\eta = \frac{P_{\text{out, useful}}}{P_{\text{in, total}}}$

Expressed as decimal or percentage. Always $\leq 1$ or $100\%$ .

Example. Motor lifts 50 kg through 4 m in 8 s. $W = mgh = 1962$ J. $P = 1962/8 = 245$ W.

Example efficiency. 1.5 kW useful from 5.0 kW input: $\eta = 30\%$ . Rest (70%) is heat + sound.

Cambridge tip. State where energy lost goes (typically heat).

$P = W/t = Fv$ .
Efficiency $\leq 100\%$ .
Lost energy → heat / sound.

See the full worked example for energy conservation →

How it’s examined

Work-energy-power appears every paper. Most-tested: work done (5 marks), power calculation (5-7 marks), efficiency (6 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Energy conservation, ready to print or save as PDF.

Step-by-step worked examples — Energy conservation

Step-by-step solutions to past-paper-style questions on energy conservation, written exactly the way a tutor would explain them at the board.

1Work done by a constant force (5 marks)
Extended• Adapted from 9702/22 May/Jun 2024• work
Question
A 40 N horizontal force pushes a crate 5.0 m across a level floor. Find work done by the force. (5 marks)
Step-by-step solution
1. Step 1
  $W = Fd\cos\theta$ with $\theta = 0°$ .
  $W = 40 \times 5.0 \times 1 = 200 \text{ J}$
Answer
$W = 200$ J.
2Power from work (5 marks)
Extended• power
Question
A motor lifts a 50 kg load through 4.0 m in 8.0 s at constant velocity. Find average power output. Take $g = 9.81$ . (5 marks)
Step-by-step solution
1. Step 1
  Work done against gravity.
  $W = mgh = 50 \times 9.81 \times 4.0 = 1962 \text{ J}$
2. Step 2
  Power.
  $P = W/t = 1962/8.0 \approx 245 \text{ W}$
Answer
$P \approx 245$ W.
3Efficiency (6 marks)
Extended• efficiency
Question
A petrol engine consumes fuel at a rate of 5.0 kW input. Useful mechanical output is 1.5 kW. Find the efficiency. Where does the rest go? (6 marks)
Step-by-step solution
1. Step 1
  Efficiency = useful output / total input.
  $\eta = \dfrac{1.5}{5.0} = 0.30 = 30\%$
2. Step 2
  Rest (70%) is dissipated as HEAT (exhaust, friction, engine cooling), some as SOUND.
Answer
$\eta = 30\%$ . 70% lost as heat/sound.

Key Formulae — Energy conservation

The formulae you need to memorise for energy conservation on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Work done
$W = Fd\cos\theta$
$F$
force
$d$
displacement
$\theta$
angle between $F$ and $d$
When to use
Constant force. Units: J = N·m. Zero when force perpendicular to motion.
Power
$P = \dfrac{W}{t} = Fv$
When to use
Rate of doing work. Units: W = J/s. $P = Fv$ when force along motion at constant speed.
Efficiency
$\eta = \dfrac{\text{useful output}}{\text{total input}} \times 100\%$
When to use
Always $\leq 100\%$ . Energy lost typically as heat or sound.

Key Definitions and Keywords — Energy conservation

Definitions to memorise and the exact keywords mark schemes credit for energy conservation answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Work
Examiner keyword
Energy transferred when a force moves its point of application in the direction of the force. $W = Fd\cos\theta$ .
Energy
Examiner keyword
Capacity to do work. Scalar. Units: J.
Power
Examiner keyword
Rate of doing work (or transferring energy). Scalar. Units: W = J/s.
Conservation of energy
Examiner keyword
Total energy of an isolated system is constant. Energy may transfer between forms but never created or destroyed.
Efficiency
Examiner keyword
Ratio of useful energy output to total energy input. $\leq 1$ .

Common Mistakes and Misconceptions — Energy conservation

The traps other students keep falling into on energy conservation questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Saying force perpendicular to motion does work
9702 Examiner Reports 2022-2024
Why it happens
Confusing force with work.
How to avoid it
Force at $90°$ to motion does ZERO work. e.g. normal reaction on a horizontal surface; centripetal force in circular motion.
✕Calculating efficiency > 100%
9702 Examiner Reports 2022-2024
Why it happens
Wrong direction of fraction.
How to avoid it
USEFUL OUTPUT divided by TOTAL INPUT. Output cannot exceed input — second law of thermodynamics.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Energy conservation — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Work, Energy and PowerCambridge International A Levels Physics (9702)

Energy conservation

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

PreviousNext

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Study Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Energy conservation, ready to print or save offline.

Energy Conservation Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Work, energy, power and efficiency. Conservation of energy.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

5.1.1 — Compute work done.
5.1.2 — Apply conservation of energy.
5.1.3 — Compute power and efficiency.

Work

$W = Fd\cos\theta$ .

Definition. Energy transferred when force moves its point of application.

Formula. $W = F d \cos\theta$ where $\theta$ is angle between force and displacement.

Special cases.

$\theta = 0°$ : $W = Fd$ (force along motion).
$\theta = 90°$ : $W = 0$ (force perpendicular to motion).
$\theta = 180°$ : $W = -Fd$ (force opposite, e.g. friction → negative work).

Units. Joule (J) = N·m.

Example. 40 N horizontal force pushes crate 5 m on level floor: $W = 40 \times 5 = 200$ J.

Cambridge tip. Mark scheme rewards sign when force opposes motion (negative work).

$W = Fd\cos\theta$ .
Perpendicular: $W = 0$ .
Friction: negative work.

See the full worked example for energy conservation →

Conservation of energy

Total energy constant.

Principle. Energy cannot be created or destroyed; it transfers between forms.

Common transformations.

Falling: GPE → KE.
Spring released: EPE → KE.
Heat engine: heat → mechanical work + waste heat.
Brake: KE → thermal (heat in brake disks).

Sankey diagrams. Width proportional to energy. Show useful vs wasted.

Example. Brake decelerates car: KE → friction heat in brakes.

Cambridge tip. Mark scheme awards 'energy conserved' or 'energy transferred from X to Y' phrasing.

Energy conserved overall.
Transformations between forms.
Use Sankey diagrams.

Power and efficiency

Rate and useful proportion.

Power. $P = W/t$ (average) or $P = Fv$ (instantaneous, constant $F$ along $v$ ).

Units. Watt (W) = J/s.

Efficiency. Useful energy/work output divided by total energy/work input: $\eta = \frac{P_{\text{out, useful}}}{P_{\text{in, total}}}$

Expressed as decimal or percentage. Always $\leq 1$ or $100\%$ .

Example. Motor lifts 50 kg through 4 m in 8 s. $W = mgh = 1962$ J. $P = 1962/8 = 245$ W.

Example efficiency. 1.5 kW useful from 5.0 kW input: $\eta = 30\%$ . Rest (70%) is heat + sound.

Cambridge tip. State where energy lost goes (typically heat).

$P = W/t = Fv$ .
Efficiency $\leq 100\%$ .
Lost energy → heat / sound.

See the full worked example for energy conservation →

How it’s examined

Work-energy-power appears every paper. Most-tested: work done (5 marks), power calculation (5-7 marks), efficiency (6 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Energy conservation, ready to print or save as PDF.

Step-by-step worked examples — Energy conservation

Step-by-step solutions to past-paper-style questions on energy conservation, written exactly the way a tutor would explain them at the board.

1Work done by a constant force (5 marks)
Extended• Adapted from 9702/22 May/Jun 2024• work
Question
A 40 N horizontal force pushes a crate 5.0 m across a level floor. Find work done by the force. (5 marks)
Step-by-step solution
1. Step 1
  $W = Fd\cos\theta$ with $\theta = 0°$ .
  $W = 40 \times 5.0 \times 1 = 200 \text{ J}$
Answer
$W = 200$ J.
2Power from work (5 marks)
Extended• power
Question
A motor lifts a 50 kg load through 4.0 m in 8.0 s at constant velocity. Find average power output. Take $g = 9.81$ . (5 marks)
Step-by-step solution
1. Step 1
  Work done against gravity.
  $W = mgh = 50 \times 9.81 \times 4.0 = 1962 \text{ J}$
2. Step 2
  Power.
  $P = W/t = 1962/8.0 \approx 245 \text{ W}$
Answer
$P \approx 245$ W.
3Efficiency (6 marks)
Extended• efficiency
Question
A petrol engine consumes fuel at a rate of 5.0 kW input. Useful mechanical output is 1.5 kW. Find the efficiency. Where does the rest go? (6 marks)
Step-by-step solution
1. Step 1
  Efficiency = useful output / total input.
  $\eta = \dfrac{1.5}{5.0} = 0.30 = 30\%$
2. Step 2
  Rest (70%) is dissipated as HEAT (exhaust, friction, engine cooling), some as SOUND.
Answer
$\eta = 30\%$ . 70% lost as heat/sound.

Key Formulae — Energy conservation

The formulae you need to memorise for energy conservation on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Work done
$W = Fd\cos\theta$
$F$
force
$d$
displacement
$\theta$
angle between $F$ and $d$
When to use
Constant force. Units: J = N·m. Zero when force perpendicular to motion.
Power
$P = \dfrac{W}{t} = Fv$
When to use
Rate of doing work. Units: W = J/s. $P = Fv$ when force along motion at constant speed.
Efficiency
$\eta = \dfrac{\text{useful output}}{\text{total input}} \times 100\%$
When to use
Always $\leq 100\%$ . Energy lost typically as heat or sound.

Key Definitions and Keywords — Energy conservation

Work
Examiner keyword
Energy transferred when a force moves its point of application in the direction of the force. $W = Fd\cos\theta$ .
Energy
Examiner keyword
Capacity to do work. Scalar. Units: J.
Power
Examiner keyword
Rate of doing work (or transferring energy). Scalar. Units: W = J/s.
Conservation of energy
Examiner keyword
Total energy of an isolated system is constant. Energy may transfer between forms but never created or destroyed.
Efficiency
Examiner keyword
Ratio of useful energy output to total energy input. $\leq 1$ .

Common Mistakes and Misconceptions — Energy conservation

The traps other students keep falling into on energy conservation questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Saying force perpendicular to motion does work
9702 Examiner Reports 2022-2024
Why it happens
Confusing force with work.
How to avoid it
Force at $90°$ to motion does ZERO work. e.g. normal reaction on a horizontal surface; centripetal force in circular motion.
✕Calculating efficiency > 100%
9702 Examiner Reports 2022-2024
Why it happens
Wrong direction of fraction.
How to avoid it
USEFUL OUTPUT divided by TOTAL INPUT. Output cannot exceed input — second law of thermodynamics.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Energy conservation — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Energy conservation

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Work done by a constant force (5 marks)

2Power from work (5 marks)

3Efficiency (6 marks)

Work done

Power

Efficiency

Work

Energy

Power

Conservation of energy

Efficiency

✕Saying force perpendicular to motion does work

✕Calculating efficiency > 100%

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Energy conservation — frequently asked questions

Energy conservation

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Work done by a constant force (5 marks)

2Power from work (5 marks)

3Efficiency (6 marks)

Work done

Power

Efficiency

Work

Energy

Power

Conservation of energy

Efficiency

✕Saying force perpendicular to motion does work

✕Calculating efficiency > 100%

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Energy conservation — frequently asked questions