Energy stores, kinetic and potential energy
Energy is stored in different ways and moves between stores when something happens. Three of the stores have equations you must know and use: kinetic, gravitational potential and elastic potential.
Part 1 of 3: Learn it
In short
- Eₖ = ½mv², with m in kg and v in m/s.
- Eₚ = mgh: the change in height times mass times gravitational field strength.
- Energy cannot be created or destroyed, only transferred between stores.
Where this is in your specification
Spec points: AQA 4.1.1.1 and 4.1.1.2 (Combined Trilogy 6.1.1.1 and 6.1.1.2), Edexcel Topic 3, OCR P7.1
| Board | Topic: Energy stores, transfers and efficiency |
|---|---|
| AQA 8463 | 4.1 (8463); 6.1 (8464) |
| Edexcel 1PH0 | Topics 3 and 8 (specific heat capacity: Topic 14) |
| OCR J249 | P7 and P8.2; P5 and P6.2 (specific heat capacity: P1.2) |
| Eduqas C420 | 1.1 to 1.3 |
| Cambridge IGCSE 0625 | 1.7, 2.3 |
| National 5 C857 75 | Dynamics: energy; Properties of matter: specific heat capacity |
Stores and transfers
Energy stores: kinetic, gravitational potential, elastic potential, thermal, chemical, magnetic, electrostatic and nuclear. Energy moves between them by four pathways: mechanically (a force doing work), electrically (a current), by heating, and by radiation (light or sound waves).
A ball thrown upwards: the kinetic store empties and the gravitational potential store fills as it rises; on the way down it happens in reverse.
The three equations
| Symbol | Quantity | Unit |
|---|---|---|
| Eₖ, Eₚ, Eₑ | kinetic, gravitational potential, elastic potential energy | J |
| m | mass | kg |
| v | speed | m/s |
| g | gravitational field strength (9.8 N/kg on Earth) | N/kg |
| h | change in height | m |
| k | spring constant | N/m |
| e | extension | m |
The elastic equation only works while the spring is not stretched past its limit of proportionality.
Conservation of energy
In a closed system the total energy stays the same. If air resistance is small, the gravitational potential energy lost by a falling object equals the kinetic energy it gains, so mgh = ½mv². The mass cancels, which is why a heavy and a light ball dropped together land at the same time.
A 2 kg object has 64 J of kinetic energy. How fast is it moving?
Show the answer
64 = 0.5 × 2 × v², so v² = 64 and v = 8 m/s.
Part 2 of 3: See it worked
Worked examples
Example 1
A car of mass 1200 kg travels at 15 m/s. Calculate its kinetic energy.
- v² = 15² = 225
- Eₖ = 0.5 × 1200 × 225
Answer: 135 000 J (135 kJ).
Example 2
A 0.4 kg ball is dropped from 5.0 m. Ignoring air resistance, how fast is it moving just before it lands? (g = 9.8 N/kg)
- Eₚ lost = 0.4 × 9.8 × 5.0 = 19.6 J
- This becomes kinetic: 19.6 = 0.5 × 0.4 × v²
- v² = 19.6 ÷ 0.2 = 98, so v = √98 = 9.9 m/s
Answer: About 9.9 m/s.
Example 3
A spring with spring constant 40 N/m is stretched by 15 cm. How much energy does it store?
- e = 15 cm = 0.15 m
- Eₑ = 0.5 × 40 × 0.15²
- = 0.5 × 40 × 0.0225
Answer: 0.45 J.
Common mistakes
- Squaring the whole of ½mv instead of only v.
- Leaving mass in grams or extension in centimetres.
- Using total height instead of the change in height.
- Saying energy is used up. It is transferred, and some is often dissipated to the surroundings.
How much gravitational potential energy does a 50 kg student gain climbing 3 m of stairs? (g = 9.8 N/kg)
Show the answer
50 × 9.8 × 3 = 1470 J.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
A 2 kg object has 64 J of kinetic energy. How fast is it moving?
64 = 0.5 × 2 × v², so v² = 64 and v = 8 m/s.
How much gravitational potential energy does a 50 kg student gain climbing 3 m of stairs? (g = 9.8 N/kg)
50 × 9.8 × 3 = 1470 J.
A ball is thrown straight up. Which energy store fills as it rises?
The gravitational potential store, while the kinetic store empties.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Estos apuntes están en inglés porque siguen los programas de examen del Reino Unido.
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