AQA Physics (8463) 4.1.1.2 · Quantitative
Changes in energy
Triple Science · Higher tier
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To stop a car, the brakes transfer away all its kinetic energy. The car now goes twice as fast.
If you had to guess, do the brakes now have to transfer twice as much energy, or more than twice as much?
Key words
- kinetic energy
- gravitational potential energy
- elastic potential energy
- spring constant
Key knowledge
A moving object has energy in its kinetic store.
kinetic energy = 0.5 × mass × speed²
Ek = ½ m v²
- kinetic energy, Ek, in joules (J)
- mass, m, in kilograms (kg)
- speed, v, in metres per second (m/s)
You need to remember this equation.
An object raised above the ground has energy in its gravitational potential store.
g.p.e. = mass × gravitational field strength × height
Ep = m g h
- gravitational potential energy, Ep, in joules (J)
- mass, m, in kilograms (kg)
- gravitational field strength, g, in newtons per kilogram (N/kg)
- height, h, in metres (m)
You need to remember this equation. The question always gives you g.
A stretched or compressed spring has energy in its elastic potential store.
elastic potential energy = 0.5 × spring constant × extension²
Ee = ½ k e²
- elastic potential energy, Ee, in joules (J)
- spring constant, k, in newtons per metre (N/m)
- extension, e, in metres (m)
This equation is on the equation sheet. It works up to the limit of proportionality.
Speed and extension are squared. Double either one and the energy is four times bigger.
Mass, g, height and k are not squared. Double any of them and the energy doubles.
Wrong: Twice the speed gives twice the kinetic energy.
Right: Twice the speed gives four times the kinetic energy.
Wrong: The box weighs 20 N, so m = 20.
Right: Weight is in newtons. Mass is in kilograms.
Wrong: Putting a speed in km/h or a mass in grams into the equation.
Right: Convert to m/s and kg first.
Key fact
Kinetic energy = ½mv², gravitational potential energy = mgh and elastic potential energy = ½ke². Energy is measured in joules, and speed and extension are squared.
Ignoring air resistance, the gravitational potential energy an object loses equals the kinetic energy it gains.
You can use this to find the speed of a falling object.
- Calculate: work out a number and show each line.
- Describe: name each store in order as it fills or empties.
- Explain: say which store changes, which way, and why.
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