New
New
Year 10
Edexcel
Higher

# Calculating the energy of springs (E = 1/2 kx²)

I can calculate the energy a spring has because it is stretched.

New
New
Year 10
Edexcel
Higher

# Calculating the energy of springs (E = 1/2 kx²)

I can calculate the energy a spring has because it is stretched.

## Lesson details

### Key learning points

1. Doubling the stiffness of a spring doubles the energy it has because it is stretched.
2. The spring constant is measured in newtons per metre (N/m).
3. Doubling the extension of a spring increases the energy it has, because it is stretched, by four times.
4. The energy a spring has because it is stretched equals 1/2 × spring constant × (extension)².

### Common misconception

When calculating energy in the elastic store, pupils often work out (½ times spring constant tmes extension) and then square everything, rather than just the extension.

Scaffold calculations to show how elastic energy is calculated, taking pupils through how to do this on their calculators without making a mistake.

### Keywords

• Elastic store - If an elastic object is stretched, compressed or bent out of shape, there is energy in the elastic store.

• Compress - To make something smaller using forces, e.g. a spring gets shorter when it is compressed.

• Extension - The increase in length from the original length of a spring when it is stretched.

• Spring constant - A measure of how stiff a spring is and how hard it is to stretch or compress.

Do some quick calculations on calculators with pupils using mini–whiteboards to show their answers, in order to quickly identify those not squaring extension correctly on their calculators.
Teacher tip

### Equipment

Mini-whiteboards.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Which of the following describe work done?
Correct answer: work done = force × distance moved in direction of force
work done = force ÷ distance moved in direction of force
work done = amount of force used
Correct answer: work done = amount of energy transferred
Q2.
A pupil stretches a spring. Which of the following statements is correct?
Correct answer: The size of the force increases as the extension increases.
The size of the force decreases as the extension increases.
The size of the force stays the same as the extension increases.
Q3.
Which of the following can be used to describe the spring constant of a spring?
Correct answer: It is a measure of how stiff a spring is.
It is the length of a spring when it is stretched.
Correct answer: It is the amount of force per metre of extension.
It is the amount of extension per newton of force.
Q4.
Which of the following is a unit of energy?
watts
newtons
degrees Celsius
Q5.
Two springs, A and B, are equal in length. Identical masses are hung from the springs which do not stretch beyond their limits of proportionality. Which of the following statements are correct?
Spring A has a higher spring constant than spring B.
Correct answer: Spring B has a higher spring constant than spring A.
Spring A is stiffer than spring B.
Correct answer: Spring B is stiffer than spring A.
Q6.
A pupil wants to calculate a kinetic energy using the formula: kinetic energy = $$\frac{1}{2}mv^2$$. Which of the following calculations will give them the correct answer?
Correct answer: Square $$v$$, then multiply by $$m$$, then divide by 2.
Divide $$m$$ by 2, then multiply by $$v$$, then square.
Multiply $$m$$ by $$v$$, then square, then multiply by ½ .
Correct answer: Square $$v$$, then multiply by ½, then multiply by $$m$$.

## Exit quiz

### 6 Questions

Q1.
Which of the following words means ‘make something smaller using forces’?
deform
expand
extend
compound
Q2.
A spring has a length of 10 cm. Starting with the least energy transferred to the elastic store, sort the following deformations into order of increasing energy.
1 - The spring is stretched from 10 cm to 12 cm long.
2 - The spring is stretched from 15 cm to 17 cm long.
3 - The spring is stretched from 15 cm to 18 cm long.
4 - The spring is stretched from 10 cm to 18 cm long.
Q3.
A pupil stretches a spring. The work done by the pupil is equal to …
Correct answer: extension × average force.
extension × force at the start.
extension × force at the end.
Q4.
A spring of length 6.0 cm has spring constant 960 N/m. How much energy does it gain if it is stretched to 8.0 cm?
3.1 J
92 J
180 J
Q5.
A spring is stretched by 4.0 cm, transferring 96 J of energy to the elastic store. What is the spring constant of the spring?
490 N/m
4800 N/m
30 000 N/m