# Work, energy and power

> CIE A-Level Physics · CIE A-Level 9702
> Source: https://www.owlsprep.com/study/cie-9702-u5-overview/
> Weight: n/a

This unit introduces core foundational concepts of work, energy and power for all areas of physics. You will learn how energy transfers and transforms in mechanical systems, and apply these ideas to solve common exam problems.

**Prerequisites:** [Forces and Newton's laws of motion](https://www.owlsprep.com/study/cie-9702-u4-forces-overview/)

## Learning objectives

- Calculate work done by constant forces for different orientations of force and displacement
- Derive and apply formulas for gravitational potential energy and kinetic energy
- Apply the principle of conservation of energy to solve mechanical problems
- Calculate power and energy efficiency for real-world energy transfer systems

## Unit at a glance

This unit follows a logical learning arc that builds on your prior knowledge of forces and motion. We start by defining work, the measure of energy transferred by a force, then move to classifying the two most common forms of mechanical energy: gravitational potential energy and kinetic energy. Next we cover the overarching principle of conservation of energy that governs all physical processes, before ending with rate of energy transfer (power) and efficiency of energy use.

Every concept in this unit builds on the previous one, so we recommend completing the sub-topics in the order listed below.

Sub-topics in this unit:
- [Work done by a force](https://www.owlsprep.com/study/cie-9702-u5-work-done-by-a-force/) — Learn the definition of work and calculate work done by constant forces at any angle to displacement.
- [Gravitational potential energy and kinetic energy](https://www.owlsprep.com/study/cie-9702-u5-gravitational-potential-energy-and-kinetic/) — Derive and apply formulas for gravitational potential energy and kinetic energy for moving objects.
- [Conservation of energy](https://www.owlsprep.com/study/cie-9702-u5-conservation-of-energy/) — Apply the principle of conservation of energy to solve problems involving energy transfer.
- [Power](https://www.owlsprep.com/study/cie-9702-u5-power/) — Learn the definition of power and calculate the rate of energy transfer for mechanical systems.
- [Energy efficiency](https://www.owlsprep.com/study/cie-9702-u5-energy-efficiency/) — Calculate the efficiency of energy transfers and explain why energy is lost in real processes.

## Common pitfalls

- **Wrong:** Forgetting to include the angle between force and displacement when calculating work.
  - Why it fails: The simplified formula $W = Fs$ only works when force is parallel to displacement. For other angles, work is smaller than this value.
  - Correct: Always use the full formula $W = Fs\cos\theta$ where $\theta$ is the angle between force and displacement.
- **Wrong:** Assuming total kinetic energy stays constant when applying conservation of energy.
  - Why it fails: Conservation of energy says total energy is constant, not that any single form of energy is constant.
  - Correct: Always account for all forms of energy (potential, heat, sound, etc.) when setting up your energy balance equation.

## Cheatsheet

| Concept | Key Formula / Relationship |
| --- | --- |
| Work done by constant force | $W = Fs\cos\theta$ |
| Kinetic energy | $E_k = \frac{1}{2}mv^2$ |
| Change in gravitational potential energy (near surface) | $\Delta E_p = mgh$ |
| Conservation of energy | Total initial energy = Total final energy |
| Power | $P = \frac{E}{t} = Fv$ (for constant parallel force) |
| Energy efficiency | $\text{Efficiency} = \frac{\text{useful output energy}}{\text{total input energy}} \times 100\%$ |

## What's next

Begin your study of this unit with the first sub-topic on work done by a force, which lays the foundation for all other energy concepts covered here. Once you complete all sub-topics in this unit, move on to the next unit on momentum, which continues building your core mechanics knowledge for CIE A-Level Physics.

- [Work done by a force](https://www.owlsprep.com/study/cie-9702-u5-work-done-by-a-force/)
- [Gravitational potential energy and kinetic energy](https://www.owlsprep.com/study/cie-9702-u5-gravitational-potential-energy-and-kinetic/)
- [Conservation of Energy](https://www.owlsprep.com/study/cie-9702-u5-conservation-of-energy/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/cie-9702-u5-overview/