What you'll learn
This revision guide covers kinetic and gravitational potential energy calculations as required for AQA GCSE Physics. You'll learn how to apply the key equations, convert between energy stores, and solve multi-step problems involving energy transfers. These calculations appear regularly in both Paper 1 and Paper 2, often combined with work done, power, and efficiency questions.
Key terms and definitions
Kinetic energy — the energy an object possesses due to its motion, measured in joules (J)
Gravitational potential energy — the energy stored in an object due to its position in a gravitational field, measured in joules (J)
Gravitational field strength (g) — the force per kilogram acting on a mass in a gravitational field, measured in newtons per kilogram (N/kg); on Earth's surface g = 9.8 N/kg (often approximated to 10 N/kg in calculations)
Energy store — a way of describing where energy is located within a system (e.g. kinetic energy store, gravitational potential energy store, elastic potential energy store)
Conservation of energy — the principle that energy cannot be created or destroyed, only transferred from one store to another
Work done — energy transferred when a force moves an object through a distance, measured in joules (J)
Mass — the amount of matter in an object, measured in kilograms (kg)
Velocity — the speed of an object in a particular direction, measured in metres per second (m/s)
Core concepts
The kinetic energy equation
The kinetic energy stored in a moving object can be calculated using:
Ek = ½mv²
Where:
- Ek = kinetic energy in joules (J)
- m = mass in kilograms (kg)
- v = velocity in metres per second (m/s)
Key points about this equation:
- Velocity is squared, so doubling the speed quadruples the kinetic energy
- A small increase in velocity produces a large increase in kinetic energy
- This explains why stopping distances increase dramatically at higher speeds
- The equation applies to any moving object, from electrons to spacecraft
Rearranging the kinetic energy equation:
To find mass: m = 2Ek ÷ v²
To find velocity: v = √(2Ek ÷ m)
The gravitational potential energy equation
The gravitational potential energy stored when an object is raised above ground level can be calculated using:
Ep = mgh
Where:
- Ep = gravitational potential energy in joules (J)
- m = mass in kilograms (kg)
- g = gravitational field strength in newtons per kilogram (N/kg)
- h = height in metres (m)
Key points about this equation:
- Height is measured vertically from a reference point (usually ground level)
- On Earth's surface, g = 9.8 N/kg (or 10 N/kg for simpler calculations)
- The equation assumes g is constant (valid for heights small compared to Earth's radius)
- Gravitational potential energy increases linearly with height
Rearranging the gravitational potential energy equation:
To find mass: m = Ep ÷ (gh)
To find height: h = Ep ÷ (mg)
To find gravitational field strength: g = Ep ÷ (mh)
Energy transfers between stores
Energy frequently transfers between kinetic and gravitational potential energy stores. Understanding these transfers is essential for GCSE exam questions.
Object falling freely:
When an object falls (ignoring air resistance):
- Gravitational potential energy decreases
- Kinetic energy increases
- Total mechanical energy remains constant
- At any point: initial Ep = final Ek + remaining Ep
Object thrown upwards:
When an object is thrown upwards:
- Kinetic energy decreases as it rises
- Gravitational potential energy increases
- At maximum height, all kinetic energy has transferred to gravitational potential energy (velocity = 0)
- As it falls back down, energy transfers back to kinetic store
With energy dissipation:
In real situations, some energy dissipates to thermal stores due to:
- Air resistance (drag forces)
- Friction
- Sound production
This means: initial total energy = final total energy + energy dissipated
Units and standard form
Ensuring correct units is critical for earning marks:
Mass must be in kilograms (kg):
- Convert grams to kg by dividing by 1000
- Example: 250 g = 0.25 kg
Velocity must be in metres per second (m/s):
- Convert km/h by dividing by 3.6
- Example: 72 km/h = 20 m/s
Height must be in metres (m):
- Convert centimetres by dividing by 100
- Convert kilometres by multiplying by 1000
Energy values often require standard form:
- Example: 4,500,000 J = 4.5 × 10⁶ J
- Example: 0.0025 J = 2.5 × 10⁻³ J
Combined energy calculations
GCSE questions often require multiple steps combining both equations.
Typical multi-step scenarios:
Roller coaster problems — converting between gravitational potential energy at the top and kinetic energy at the bottom
Pendulum motion — energy transfers between kinetic (maximum at lowest point) and gravitational potential (maximum at highest points)
Vehicle braking — calculating kinetic energy that must be dissipated to stop
Hydroelectric power — water falling from height converts gravitational potential energy to kinetic energy
Problem-solving strategy:
- Identify what type of energy the object has initially
- Identify what type of energy the object has finally
- Write down the relevant equation(s)
- Substitute values with correct units
- Calculate the answer
- Check the answer is reasonable
Efficiency and energy dissipation
Real energy transfers are never 100% efficient. Some energy always dissipates to less useful stores.
Efficiency equation:
Efficiency = (useful energy transferred ÷ total energy supplied) × 100%
When an object falls in air:
- Not all gravitational potential energy converts to kinetic energy
- Some dissipates due to air resistance (thermal and sound stores)
- Actual velocity reached is less than calculated assuming no air resistance
Example: A stone of mass 2 kg falls 10 m. Calculate:
- Theoretical kinetic energy gained (no air resistance): Ep = 2 × 10 × 10 = 200 J
- If actual kinetic energy measured is 180 J
- Energy dissipated = 200 - 180 = 20 J
- Efficiency = (180 ÷ 200) × 100% = 90%
Worked examples
Example 1: Calculating kinetic energy
Question: A car of mass 1200 kg is travelling at 25 m/s. Calculate the kinetic energy of the car. [3 marks]
Solution:
Step 1: Write the equation Ek = ½mv²
Step 2: Substitute values Ek = ½ × 1200 × 25² [1 mark]
Step 3: Calculate Ek = ½ × 1200 × 625 Ek = 375,000 J [1 mark]
Step 4: Express in standard form if appropriate Ek = 3.75 × 10⁵ J [1 mark]
Mark scheme notes: Award 1 mark for correct equation (may be in symbols or words), 1 mark for correct substitution, 1 mark for correct answer with unit.
Example 2: Calculating height from gravitational potential energy
Question: A climber of mass 70 kg gains 21,000 J of gravitational potential energy. Calculate the vertical height climbed. Use g = 10 N/kg. [4 marks]
Solution:
Step 1: Write the equation Ep = mgh [1 mark]
Step 2: Rearrange for h h = Ep ÷ (mg) [1 mark]
Step 3: Substitute values h = 21,000 ÷ (70 × 10) h = 21,000 ÷ 700 [1 mark]
Step 4: Calculate h = 30 m [1 mark]
Mark scheme notes: Award marks for correct equation, correct rearrangement, correct substitution, and correct answer with unit.
Example 3: Energy transfer during a fall
Question: A coconut of mass 1.5 kg falls from a tree from a height of 8.0 m. Assuming no energy is dissipated, calculate: (a) The gravitational potential energy lost [2 marks] (b) The velocity of the coconut just before it hits the ground [4 marks] Use g = 10 N/kg.
Solution:
(a) Gravitational potential energy lost
Ep = mgh [1 mark] Ep = 1.5 × 10 × 8.0 Ep = 120 J [1 mark]
(b) Velocity just before impact
Step 1: Recognise energy transfer All gravitational potential energy converts to kinetic energy Therefore: Ek = 120 J [1 mark]
Step 2: Write equation and rearrange Ek = ½mv² v² = 2Ek ÷ m v = √(2Ek ÷ m) [1 mark]
Step 3: Substitute v = √(2 × 120 ÷ 1.5) v = √(240 ÷ 1.5) v = √160 [1 mark]
Step 4: Calculate v = 12.6 m/s (or 13 m/s to 2 sig figs) [1 mark]
Mark scheme notes: Part (a) requires equation and calculation. Part (b) requires recognition of energy conservation, correct rearrangement, substitution, and final answer.
Common mistakes and how to avoid them
Forgetting to square the velocity — Students often calculate Ek = ½ × m × v instead of Ek = ½ × m × v². Always check you've squared the velocity before multiplying.
Using incorrect units — Converting mass from grams to kilograms is frequently forgotten. Always check units before substituting: mass in kg, velocity in m/s, height in m.
Confusing speed and velocity squared — If velocity is 5 m/s, then v² = 25, not 10. Write out the squaring step clearly: v² = 5² = 25.
Not rearranging equations correctly — When finding velocity from kinetic energy, remember to take the square root at the end: v = √(2Ek ÷ m), not v = 2Ek ÷ m.
Assuming all energy transfers are 100% efficient — Unless told to ignore air resistance or friction, acknowledge that some energy dissipates. The question will usually specify whether to ignore resistive forces.
Mixing up g and 10 — g = 9.8 N/kg on Earth, but GCSE questions often say "use g = 10 N/kg" for simpler calculations. Always use the value given in the question.
Exam technique for kinetic and potential energy calculations
Show your working clearly — Even if your final answer is wrong, you can gain method marks for correct equations and substitution. Write out each step on a separate line.
Include units in your final answer — Energy answers need joules (J). Velocity needs m/s. Height needs metres (m). Many students lose the final mark by omitting units.
Use the equation sheet strategically — Both equations (Ek = ½mv² and Ep = mgh) appear on the AQA Physics equation sheet. You don't need to memorise them, but you must know when to use each one and how to rearrange them.
Check if standard form is expected — For large energy values (above 100,000 J), examiners often expect standard form. Convert your answer: 450,000 J = 4.5 × 10⁵ J.
Quick revision summary
Energy calculations use two key equations: kinetic energy (Ek = ½mv²) and gravitational potential energy (Ep = mgh). Kinetic energy depends on mass and velocity squared; doubling speed quadruples kinetic energy. Gravitational potential energy depends on mass, height, and gravitational field strength (g = 10 N/kg on Earth). Energy transfers between these stores following conservation of energy principles. Always use correct units (kg, m/s, m, J) and show full working for maximum marks. Real transfers involve some energy dissipation to thermal stores through friction and air resistance.