Energy Changes in a System (P1.1)
Energy stores
Energy is stored in different ways:
| Store | Example |
|---|---|
| Kinetic | Moving objects |
| Gravitational potential | Object at height |
| Elastic potential | Stretched/compressed spring |
| Thermal (internal) | Hot object |
| Chemical | Food, fuel, batteries |
| Nuclear | Radioactive materials |
| Magnetic | Magnets |
| Electrostatic | Charged objects |
Kinetic energy
Eₖ = ½mv²
where m = mass (kg), v = speed (m/s), Eₖ = energy (J).
Worked example: A 2 kg ball moving at 3 m/s has Eₖ = ½ × 2 × 3² = ½ × 2 × 9 = 9 J.
Gravitational potential energy (GPE)
Eₚ = mgh
where m = mass (kg), g = gravitational field strength (9.8 N/kg on Earth, often 10 N/kg), h = height above reference point (m).
Worked example: A 3 kg book lifted 2 m: Eₚ = 3 × 10 × 2 = 60 J.
Elastic potential energy
Eₑ = ½ke²
where k = spring constant (N/m), e = extension (m).
Specific heat capacity (SHC)
The specific heat capacity (c) of a substance is the energy required to raise the temperature of 1 kg by 1°C (or 1 K).
ΔE = mcΔθ
where m = mass (kg), c = SHC (J/kg°C), Δθ = temperature change (°C).
Worked example: How much energy to heat 2 kg of water (c = 4,200 J/kg°C) by 10°C?
ΔE = 2 × 4,200 × 10 = 84,000 J = 84 kJ
Water has an unusually high SHC → takes a lot of energy to heat up → good coolant.
Power
P = E/t (or P = W/t)
where P = power (W), E = energy (J), t = time (s). Also P = Fv.
Units: 1 W = 1 J/s.
Worked example: A motor does 500 J of work in 10 s: P = 500/10 = 50 W.
Conservation of energy
Energy is never created or destroyed — only transferred between stores or dissipated (often as thermal energy). Total energy is always conserved.
Common exam errors
- Forgetting to square the velocity in Eₖ = ½mv².
- Rearranging ΔE = mcΔθ incorrectly — write the equation first, then substitute.
- Saying energy is "lost" — it is dissipated (spread to thermal store), not destroyed.
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