AQA GCSE Physics Foundation (8463), Foundation tier · Energy › Energy stores and changes
Practise Changes in energy. 8 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
How to calculate the energy in the kinetic, gravitational potential and elastic potential stores. These are some of the most common calculations on Paper 1: 2 marks for a straight substitution, and 3 to 5 marks when you must convert units, rearrange, or link two stores to find a speed or a height.
Key facts
Kinetic energy: Ek = ½ m v2 (recall)
Gravitational potential energy: Ep = m g h (recall)
Elastic potential energy: Ee = ½ k e2 (on the equations sheet)
Units: E in J, m in kg, v in m/s, g in N/kg, h in m, k in N/m, e in m
g = 9.8 N/kg on Earth (given in the question)
Double v or e → 4 × the energy; double m, h or k → 2 × the energy
Notes
Kinetic energy
A moving object has energy in its kinetic store: Ek = ½ m v2
Ek = kinetic energy in joules (J), m = mass in kilograms (kg), v = speed in metres per second (m/s).
Only the speed is squared. Doubling the mass doubles the kinetic energy; doubling the speed makes it 4 times bigger.
Gravitational potential energy
diagram
Raising an object increases the energy in its gravitational potential store: Ep = m g h
g = gravitational field strength in N/kg (9.8 N/kg on Earth; the question gives you the value to use). h = change in height in metres (m).
Use the vertical height gained or lost, not the distance travelled along a slope.
In Ep = m g h, h is the vertical height gained.
Elastic potential energy
diagram
Stretching or squashing a spring stores energy in its elastic potential store: Ee = ½ k e2 (this equation is on the equations sheet).
k = spring constant in N/m, e = extension (or compression) in metres (m).
The extension e is the increase in length, measured from the original length.
It only works if the limit of proportionality has not been exceeded.
Doubling the extension makes the stored energy 4 times bigger.
How to answer each type of question
Calculate the kinetic energy
2 marksGrade 5
Write Ek = ½ m v2.
Check the mass is in kg and the speed is in m/s.
Substitute, square the speed first, then multiply.
Give the answer with the unit J.
Example. A cyclist and her bicycle have a total mass of 85 kg. She rides at a speed of 6.0 m/s. Calculate the kinetic energy of the cyclist and bicycle.
Show the model answerHide the model answer
Ek = 0.5 × 85 × 6.02 (1) Ek = 1530 J (1)
Don’t lose marks
Squaring the whole of ½ m v instead of just v.
Leaving mass in grams or distances in centimetres.
Using the distance along a slope instead of the vertical height.
Forgetting the square root at the end when finding a speed or an extension.
Rounding the first step (e.g. 1.9 J instead of 1.8816 J), which makes the final answer wrong.
More tips
Memory tricks
Calculator: type 0.5 × m × v and then press x2 straight after the v, so only the speed is squared.
Sense check: a person walking (70 kg at 1.5 m/s) has about 80 J of kinetic energy; a car at motorway speed has hundreds of thousands of joules.
'Squared means 4 times': double the speed or the extension and the energy goes up 4 times.
For a falling object with no energy dissipated the mass cancels out, so v = √(2 g h). Use it to check your answer.
Exam technique
Write the equation, then the substitution, then the answer. The substitution often earns a mark even if you slip later.
Look for 'assume no energy is dissipated': it tells you to set the energy in one store equal to the other.
In a 'show that' question, give your answer to at least one more significant figure than the value you are shown.
Always give a unit: J for energy, m/s for speed, m for a height or an extension.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Recall the kinetic and gravitational energy equationsEk = ½ m v2 and Ep = m g h: the specification says you must be able to recall both.
Grade 4
Calculate gravitational potential energyMultiply mass (kg) × gravitational field strength (N/kg) × height (m) to get the energy in joules.
Grade 5
Calculate kinetic energySquare the speed first, then multiply by the mass and by 0.5.
Grade 5
Calculate elastic potential energy of a springUse Ee = ½ k e2 with the extension in metres, as long as the limit of proportionality is not exceeded.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Calculate the kinetic energy of the runner. Use the equation: kinetic energy = 0.5 × mass × (speed)2
1470 J
Write down the equation that links kinetic energy (Ek), mass (m) and speed (v).
Ek = ½ m v2
Write down the equation that links gravitational field strength (g), gravitational potential energy (Ep), height (h) and mass (m).
Ep = m g h
State the two factors that determine the kinetic energy of a moving object.
Mass and speed.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy5 marks
A runner of mass 60 kg is running at a speed of 7.0 m/s.
(a) Calculate the kinetic energy of the runner. Use the equation: kinetic energy = 0.5 × mass × (speed)2[2]
(b) After the run, the runner lifts a box of mass 12 kg onto a shelf 1.5 m above the floor. Gravitational field strength = 9.8 N/kg Calculate the increase in the gravitational potential energy of the box. Use the equation: gravitational potential energy = mass × gravitational field strength × height[2]
(c) What is the unit of energy? Tick (✓) one box.[1]
joule
kilogram
newton
watt
Show the answer and mark scheme
(a)Answer: 1470 J
Ek = 0.5 × 60 × 7.02
Ek = 1470 (J)
(b)Answer: 176.4 J
Ep = 12 × 9.8 × 1.5
Ep = 176.4 (J)
(c)Answer: joule
Question 2Medium7 marks
A drone is used to take photographs. The drone has a mass of 1.2 kg.
(a) Write down the equation that links kinetic energy (Ek), mass (m) and speed (v).[1]
(b) When the drone is flying horizontally it has 60 J of kinetic energy. Calculate the speed of the drone.[3]
(c) The drone then rises vertically through 25 m at a constant speed. Gravitational field strength = 9.8 N/kg Calculate the increase in the gravitational potential energy of the drone.[2]
(d) Explain why the kinetic energy of the drone does not change as it rises.[1]
Show the answer and mark scheme
(a)Answer: Ek = ½ m v2
Ek = ½ × m × v2 / kinetic energy = 0.5 × mass × (speed)2