Changes in energy — AQA GCSE Physics
Test yourself on Changes in energy with AQA GCSE practice questions.
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Changes in energy explained
Three equations cover this content. The kinetic store of a moving object is Eₖ = ½ m v², so doubling the speed quadruples the energy; a 0.020 kg aeroplane at 6.0 m/s stores 0.36 J.
Read the full explanation
The elastic potential store of a spring is Eₑ = ½ k e², with e the extension in metres, not the total length; a spring of constant 50 N/m stretched 0.12 m stores 0.36 J. The gravitational potential store is Eₚ = m g h with g = 9.8 N/kg. Questions usually chain them: energy stored in the spring becomes the kinetic store of the launched object, so set ½ k e² equal to ½ m v² and solve for v. Watch the squares all the way through, because both the extension and the speed are squared, so halving the extension quarters the energy stored in the spring.
height, h, in metres, m
Height in the gravitational potential energy equation is the vertical distance moved, measured in metres, and it must be vertical: a ramp 5 m long rising 2 m gives h = 2 m. The equation is Eₚ = m g h, with mass in kilograms and gravitational field strength g = 9.8 N/kg near the Earth surface. So lifting a 60 kg student 4.5 m up a staircase fills the gravitational store with 60 × 9.8 × 4.5 = 2646 J. Only the change in height counts, so a ball that rises 3 m and falls back to the start has no net change. On the Moon the same lift stores far less because g is about 1.6 N/kg. Height questions often pair with the kinetic store, as in a falling object where m g h becomes ½ m v² and the mass cancels from both sides.
Your focus
- Calculate the kinetic store of a moving object and explain why doubling its speed multiplies that store by four.
- Work out the energy stored in a stretched spring from its spring constant and extension.
- Solve a launch problem by equating the elastic store before release to the kinetic store afterwards.
Show all 7 objectives
- Identify the vertical height change in a ramp, staircase or cliff problem and explain why the slope length is not used.
- Calculate the gravitational potential store gained by a named object using g = 9.8 N/kg.
- Rearrange Eₚ = m g h to find the height reached when the energy transferred is given.
- Explain why the same lift on the Moon stores about six times less energy.
Changes in energy exam tips
Marking Points
- one mark for a correct substitution into ½ k e² using the extension rather than the length
- one mark for equating the elastic store to the kinetic store when the object is released
- one mark for a correct rearrangement to make the speed the subject
- one mark for the final value with the unit, for example 6.0 m/s
- one mark for identifying the vertical height change rather than the distance travelled along a slope
- one mark for substituting mass in kilograms and g = 9.8 N/kg into Eₚ = m g h
- one mark for the energy given in joules
- one mark for a rearrangement to find height or mass when the energy is the quantity given
Examiner Tips
- 💡Always write down the formula you are using before substituting numbers, such as Eₖ = ½ m v², to ensure you pick up the first mark even if your calculation goes wrong.
- 💡Carry an unrounded intermediate energy into the second stage, then round only the final speed.
- 💡Underline the vertical height in the question before you start, especially on ramp and staircase problems.
- 💡Where a question gives weight rather than mass, use energy = weight × height, because weight already contains g.
- 💡Keep g = 9.8 N/kg unless the paper tells you otherwise.
Common Mistakes
- squaring only part of the expression, so calculating ½ × m × v instead of ½ × m × v²
- putting the natural length of the spring into the equation in place of the extension
- forgetting to convert kJ to J, which throws the spring constant out by a factor of 1000
- using the length of a ramp or the distance run rather than the vertical rise
- leaving the mass in grams, which makes the stored energy 1000 times too large
- quoting the height in centimetres so the answer is out by a factor of 100
- using a weight in newtons in place of the mass in kilograms, so g gets counted twice