AQA GCSE Combined Science (8464), Higher tier · Physics › Energy › Energy changes in a system, and the ways energy is stored
Practise Changes in energy. 14 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.
Grade by grade
What you need to be able to do, from the first marks up to the top 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.
4
Calculate gravitational potential energyMultiply mass (kg) × gravitational field strength (N/kg) × height (m) to get the energy in joules.
5
Calculate kinetic energySquare the speed first, then multiply by the mass and by 0.5.
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.
6
Convert units before you substituteChange grams to kilograms, centimetres to metres and kilojoules to joules first.
7
Rearrange to find speed, height or extensionE.g. h = Ep ÷ (m × g), or v = √(2Ek ÷ m), taking the square root last.
8
Link energy stores in multi-step problemsUse 'energy lost from one store = energy gained by another' to find a speed or a height.
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.
To find the speed, rearrange: \(v = \sqrt{\dfrac{2E_k}{m}}\) grade 7+
Gravitational potential energy
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.
Elastic potential energy
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).
It only works if the limit of proportionality has not been exceeded.
Doubling the extension makes the stored energy 4 times bigger.
Linking two stores grade 7+
If no energy is dissipated, the energy lost from one store equals the energy gained by another.
A falling object: gravitational potential energy lost = kinetic energy gained. A spring firing a ball: elastic potential energy of the spring = kinetic energy of the ball.
Work in two steps: calculate the energy in the first store, then put that value into the equation for the second store.
In real life some energy is dissipated by air resistance or friction, so the kinetic energy gained is less than this.
Cheatsheet
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
No energy dissipated: energy lost from one store = energy gained by another grade 7+
\(v = \sqrt{\dfrac{2E_k}{m}}\) and \(e = \sqrt{\dfrac{2E_e}{k}}\) grade 7+
How to answer each type of question
Calculate the kinetic energy
2 marks5
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 answer
Ek = 0.5 × 85 × 6.02 (1) Ek = 1530 J (1)
Calculate the gravitational potential energy (with unit conversions)
2 marks6
Convert grams to kg and centimetres to m.
Use the vertical change in height.
Substitute into Ep = m g h, using the value of g given in the question.
Example. A student lifts a bag of mass 2400 g from the floor onto a shelf 150 cm above the floor. gravitational field strength = 9.8 N/kg Calculate the increase in the gravitational potential energy store of the bag.
Show the model answer
Ep = 2.4 × 9.8 × 1.5 (1) Ep = 35 J (35.28 J) (1)
Calculate the elastic potential energy
2 marks6
Convert the extension to metres.
Substitute into Ee = ½ k e2, squaring only the extension.
Give the answer with the unit J.
Example. A spring has a spring constant of 40 N/m. It is stretched by 15 cm. The limit of proportionality is not exceeded. Calculate the elastic potential energy stored in the spring.
Show the model answer
Ee = 0.5 × 40 × 0.152 (1) Ee = 0.45 J (1)
Calculate a speed by linking two energy stores
4 marks8
Calculate the energy in the first store (here Ep = m g h).
Set it equal to the energy gained by the second store (here Ek = ½ m v2).
Rearrange to find v2.
Take the square root, rounding only at the end.
Example. A ball of mass 0.060 kg is dropped from a height of 3.2 m. Assume that no energy is dissipated as the ball falls. gravitational field strength = 9.8 N/kg Calculate the speed of the ball just before it hits the ground.
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.
Where marks are lost
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.
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.
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
(b)Answer: 10 m/s
60 = 0.5 × 1.2 × v2
v2 = 100
v = 10 (m/s)
(c)Answer: 294 J
Ep = 1.2 × 9.8 × 25
Ep = 294 (J)
(d)Answer: Its speed (and mass) stay the same.
the speed (and mass) of the drone is constant
Question 3Hard9 marks
A toy launcher uses a compressed spring to fire a small ball horizontally. The spring constant of the spring is 250 N/m. The spring is compressed by 8.0 cm before the ball is released. The mass of the ball is 20 g.
(a) Calculate the elastic potential energy stored in the spring. Use the Physics Equations Sheet.[3]
(b) Calculate the maximum possible speed of the ball as it leaves the launcher. Give your answer to 2 significant figures.[3]
(c) The actual speed of the ball as it leaves the launcher is 7.5 m/s. Calculate the percentage of the elastic potential energy that is transferred to the kinetic energy store of the ball.[3]