AQA Physics (8463) 4.1.1.2 · Quantitative
Changes in energy
Double a car’s speed, a ball’s height or a spring’s stretch. Which of them doubles the energy stored, and which does far more?
Triple Science · Higher tier
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Twice as fast. How much harder to stop?
To stop a car, its brakes must transfer away all of its kinetic energy, and the brakes get hot. Now the same car is driven at twice the speed.
If you had to guess, do the brakes now have to transfer twice as much energy, or more than twice as much?
Three energy stores each have their own equation. A moving object has energy in its kinetic store. An object raised above the ground has energy in its gravitational potential store. A stretched or compressed spring has energy in its elastic potential store. On the bench, change one quantity at a time and call the factor before the store fills.
The store bench · change 1 of 4
Lift the ball twice as high.
What happens to the energy in the gravitational potential store?
Every equation here works in joules, kilograms, metres, metres per second and newtons per metre. Exam questions often give a quantity in another unit on purpose. Converting it is the first line of your working, before the equation.
Units first
Ready to insert, or convert first?
Each value is from an exam question on these three equations.
Tap a card, then tap the box it belongs in. Tap a placed card to take it back.
Equations
Ek = ½ m v²
kinetic energy (J) = 0.5 × mass (kg) × speed² (m/s)
m = 2Ek ÷ v² · v = √(2Ek ÷ m)
Ep = m g h
gravitational potential energy (J) = mass (kg) × gravitational field strength (N/kg) × height (m). The question always gives g.
h = Ep ÷ (m g)
Ee = ½ k e²
elastic potential energy (J) = 0.5 × spring constant (N/m) × extension² (m). e can be a compression. Valid up to the limit of proportionality.
k = 2Ee ÷ e²
Think again · weight is not mass
“The box weighs 20 N, so m = 20.”
Spot the flaw
IdentifyA box of weight 20 N is lifted 3.0 m. A student writes Ep = 20 × 9.8 × 3.0 = 588 J. What has gone wrong?
Command words in this lesson
- Calculate
- Work out a number. Write each line: convert, equation, substitute, rearrange, answer with its unit.
- Explain
- Say which store changes, which way, and why: height, speed or extension.
- Describe
- Name each store in order as it fills or empties. Reasons are optional.
Key note · AQA 4.1.1.2 (8463)
Changes in energy
- Ek = ½mv² (kinetic).
- Ep = mgh (gravitational PE, g = 9.8 N/kg Earth).
- Ee = ½ke² (elastic PE).
- Doubling speed → ×4 kinetic energy.
- Doubling extension → ×4 elastic PE.
- All three equations need mass in kg and distance in m.
Photograph this card. Tomorrow, cover it and say each line first.
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Stuck on which quantity to square, or which unit to convert?
The bench uses g = 9.8 N/kg and treats each store on its own: no energy is dissipated, and the spring stays within its limit of proportionality. Bars are drawn to scale within each change, not between changes.