igcse Energy, Work & Power
Key Ideas
- Energy is the ability to do work. Unit: joule (J).
- Work is energy transferred when a force moves an object. Unit: joule (J).
- Power is the rate of doing work or transferring energy. Unit: watt (W).
Core Formulas
Work (W) = Force (F) × distance (d) (force in the direction of motion)
Power (P) = Work (W) ÷ time (t) = Energy transferred (E) ÷ time (t)
Kinetic energy (E_k) = 1/2 × m × v^2
Change in gravitational potential energy (ΔE_p) = m × g × Δh
Directions Matter
If the force is not along the direction of motion, use W = F × d × cos(theta).
Units & Symbols
| Quantity | Symbol | Unit | Notes |
|---|---|---|---|
| Work | W | J | 1 J = 1 N·m |
| Energy | E | J | Same unit as work |
| Power | P | W | 1 W = 1 J/s |
| Mass | m | kg | — |
| Speed | v | m/s | — |
| Gravity | g | N/kg | ≈ 9.8 N/kg |
| Height change | Δh | m | — |
| Time | t | s | — |
| Force | F | N | — |
| Distance (along force) | d | m | — |
Efficiency
How well a device converts input energy (or power) into useful output.
Efficiency (%) = (useful energy out ÷ total energy in) × 100%
Efficiency (%) = (useful power out ÷ total power in) × 100%
Common Mistakes
- Mixing energy and power in the same calculation.
- Forgetting to convert minutes or hours to seconds when using power.
- Using total distance instead of distance moved in the force direction.
Worked Examples
1) Work Done by a Force
A box is pushed with a constant force of 50 N over 6.0 m along a level floor.
Work: W = F × d = 50 × 6.0 = 300 J.
2) Power from Energy per Time
An electric motor lifts 800 J of energy every 4 s.
Power: P = E ÷ t = 800 ÷ 4 = 200 W.
3) Gravitational Potential Energy
A 2.5 kg book is raised by 1.2 m.
ΔE_p: = m × g × Δh = 2.5 × 9.8 × 1.2 ≈ 29 J.
4) Kinetic Energy
A 1,000 kg car travels at 12 m/s.
E_k: = 1/2 × 1000 × 12^2 = 72,000 J.
5) Efficiency
A device takes 2,000 J of electrical energy and delivers 1,400 J of useful output.
Efficiency: = (1400 ÷ 2000) × 100% = 70%.
Energy Transfers & Sankey Idea
In any process, total energy is conserved. Useful energy appears in the intended form; the rest is usually lost as heat or sound.
Sankey diagrams help show how input energy splits into useful and wasted outputs. Arrow width represents the amount of energy.
Quick Practice
- A 600 N student climbs 5.0 m of stairs in 8.0 s. Find the work done and average power.
- A 60 W lamp is on for 3 hours. How much energy does it use in joules?
- A 0.40 kg ball speeds up from 5 m/s to 9 m/s. Find the increase in kinetic energy.
Summary: Work links force and distance, energy measures capacity to do work, and power measures how fast it happens. Use consistent units and always check the direction of the force.