AQA GCSE PHYSICS · PAPER 1 · FOUNDATION & HIGHER
Kinetic, elastic and gravitational potential energy
Energy · Lesson 2 of 7
Warm-up
Answer each one, then check.
1. Write the unit for mass.
Kilograms (kg)
2. Convert 6.0 cm to metres.
0.060 m
3. Work out 4².
16
4. What does g stand for in E_p = mgh?
Gravitational field strength
5. What is the unit of speed?
Metres per second (m/s)
Learning Objectives
1. Recall and apply the equation for kinetic energy.
2. Recall and apply the equation for elastic potential energy.
3. Apply the equation for gravitational potential energy.
4. Use energy conservation to find speeds and heights.
5. Convert units and give answers to an appropriate number of significant figures.
Three Energy Equations
E_k = ½mv² E_e = ½ke² E_p = mgh
Learn the first two. E_p = mgh is on the equation sheet, and the value of g (9.8 N/kg) is always given in the question.
Three Stores, Three Equations
|
Check the units before you substitute. |
Diagrams of a moving car, a stretched spring and a raised object with their energy equations.
Quantities and Units
Always use these units.
|
Quantity |
Symbol |
Unit |
|---|---|---|
|
Kinetic energy |
E_k |
joules (J) |
|
Elastic potential energy |
E_e |
joules (J) |
|
Gravitational potential energy |
E_p |
joules (J) |
|
Mass |
m |
kilograms (kg) |
|
Speed |
v |
metres per second (m/s) |
|
Spring constant |
k |
newtons per metre (N/m) |
|
Extension |
e |
metres (m) |
|
Gravitational field strength |
g |
newtons per kilogram (N/kg) |
|
Height |
h |
metres (m) |
Kinetic Energy
|
A car of mass 1200 kg travels at 15 m/s. Calculate its kinetic energy. |
1. Write the equation
E_k = ½mv²
2. Substitute
E_k = 0.5 × 1200 × 15²
3. Square first
15² = 225
4. Answer
E_k = 135 000 J
Answer: Kinetic energy = 135 000 J (or 135 kJ).
Elastic Potential Energy
|
A spring has a spring constant of 40 N/m. It is stretched by 25 cm. Calculate the elastic potential energy stored. |
1. Convert the extension
25 cm = 0.25 m
2. Substitute
E_e = 0.5 × 40 × 0.25²
3. Answer
E_e = 1.25 J
Answer: 1.25 J
Gravitational Potential Energy
|
A 2.0 kg book is lifted 3.0 m onto a shelf. g = 9.8 N/kg. Calculate the gain in gravitational potential energy. |
1. Write the equation
E_p = mgh
2. Substitute
E_p = 2.0 × 9.8 × 3.0
3. Answer
E_p = 58.8 J
Answer: 58.8 J (about 59 J)
Using Energy Conservation
|
A roller coaster car starts from rest at a height of 20 m. Ignoring friction, find its speed at the bottom. g = 9.8 N/kg. |
1. Gravitational potential lost equals kinetic gained
mgh = ½mv²
2. The mass cancels
v² = 2gh = 2 × 9.8 × 20 = 392
3. Square root
v = 19.8 m/s
Answer: 19.8 m/s
Common Mistakes
Marks are often lost here.
▸ Squaring. Square only the speed or extension, not the whole of ½mv.
▸ Units. Convert cm to m and g to kg before substituting.
▸ Halving. Do not forget the 0.5 in the kinetic and elastic equations.
▸ Significant figures. Give the answer to the same number of s.f. as the least accurate data, usually 2 or 3.
Key Terms
|
Kinetic energy Energy stored in the movement of an object. |
Elastic potential energy Energy stored in a stretched or compressed object. |
|
Gravitational potential energy Energy stored in an object raised above the ground. |
Spring constant How stiff a spring is; force needed per metre of extension. |
|
Extension The increase in length of a spring. |
Gravitational field strength The force on each kilogram; 9.8 N/kg on Earth. |
Your Task: Energy Race
12 minutes
|
Calculate each. (a) A 0.50 kg ball moving at 8.0 m/s. (b) A spring with k = 100 N/m stretched by 0.10 m. (c) A 60 kg climber 15 m up a cliff (g = 9.8 N/kg). 1. Write the equation. 2. Substitute and calculate. 3. Add the unit. |
A good answer shows: (a) 16 J (b) 0.50 J (c) 8820 J (about 8800 J).
Can I...?
☐ Recall the kinetic energy equation.
☐ Recall the elastic potential energy equation.
☐ Use the gravitational potential energy equation.
☐ Convert cm to m.
☐ Square the correct quantity.
☐ Use conservation of energy to find a speed.
☐ Give units and sensible significant figures.
☐ Rearrange an equation.
Summary
✓ E_k = ½mv².
✓ E_e = ½ke², with e in metres.
✓ E_p = mgh, with g given.
✓ Energy lost from one store is gained by another if no energy is dissipated.
|
EXAM FOCUS A 0.40 kg ball moves at 12 m/s. Calculate its kinetic energy. (2 marks) Write the equation, substitute, then give the unit. |