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In Ee = ½ke², k is the spring constant, a measure of how stiff the spring is, in newtons per metre (N/m). Free GCSE Physics notes and 13 FAQs.
Elastic Potential Energy is part of Forces and elasticity in GCSE AQA Higher Physics.
3 min
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GCSE AQA Higher
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In Ee = ½ke², k is the spring constant, a measure of how stiff the spring is, in newtons per metre (N/m). Free GCSE Physics notes and 13 FAQs.
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Use this lesson to stay inside Forces and elasticity while connecting the detail back to the wider Forces topic.
Read the core explanations from Elastic Potential Energy before testing yourself from memory.
Picture pulling back a catapult or stretching a rubber band. You're doing work against the elastic forces, and that energy doesn't just disappear - it gets stored. When you release it, that stored energy converts back into kinetic energy, launching your projectile forward.
This stored energy depends on two key factors: how stiff the spring is (its spring constant) and how much you've stretched it (the extension). The stiffer the spring or the more you stretch it, the more energy gets stored.
Before we can calculate elastic potential energy, we need to understand the three variables involved. Each one tells us something different about the spring and how it behaves.
A stiff spring (high k value) needs more force to stretch it the same distance as a weak spring (low k value). Extension is always measured from the spring's natural length - not the total length when stretched.
Now we can put these variables together. The energy stored in a spring depends on both how stiff it is and how much it's stretched - but there's a twist.
Notice the extension is squared - this means doubling the extension gives four times the stored energy. The ½ factor comes from the fact that the force increases gradually as you stretch the spring, not all at once.
Let's see how this formula works in practice. These are the types of calculations you'll face in your exam, so pay attention to the method and units.
Worked example: Calculating Elastic Potential Energy
A spring with spring constant 200 N/m is stretched by 0.05 m. Calculate the elastic potential energy stored. [3 marks]
Answer: 0.25 J
Worked example: Finding Spring Constant from Energy
A spring stores 8 J of elastic potential energy when extended by 0.2 m. Calculate the spring constant. [3 marks]
Answer: 400 N/m
In the required practical, hang a spring from a clamp stand, measure its original length, then add known masses one at a time. Record the new length each time, calculate the extension, and convert the mass to force using F = mg. Repeat readings, plot force against extension, and only use data up to the limit of proportionality when applying Hooke’s law.
Elastic potential energy questions are easier if you convert centimetres to metres first, square the extension carefully, and remember that the formula works for both stretching and compression. In practical work, mention repeat readings, a ruler at eye level, and the limit of proportionality for full-mark explanations.
Mark-winning phrases: Use 'elastic potential energy' not just 'energy'. State 'measured in joules' for energy questions. For practical questions, mention 'repeat readings and calculate mean' for reliability.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
Elastic potential energy is the energy stored in a stretched or compressed elastic object, like a spring, measured in joules (J). It depends on the spring constant and the extension, and it converts back into kinetic energy when released, as in a catapult.
The energy stored in a stretched spring is found with Ee = ½ke². A spring with spring constant 200 N/m stretched by 0.05 m stores ½ × 200 × 0.0025 = 0.25 J; a spring storing 8 J at 0.2 m has k = 400 N/m.
If the extension doubles, the elastic potential energy stored becomes four times bigger, because the extension is squared in Ee = ½ke². A stiffer spring or a bigger extension stores more energy.
The ½ factor in Ee = ½ke² comes from the fact that the force increases gradually as the spring is stretched, not all at once. So the energy stored is not simply the final force × the extension; the extension is also squared in the formula.
Hang a spring from a clamp stand, measure its original length, then add known masses one at a time and record the new length. Calculate each extension, convert mass to force using F = mg, repeat readings, and plot force against extension.
In Ee = ½ke², k is the spring constant, a measure of how stiff the spring is: the force needed per metre of extension, measured in newtons per metre (N/m). Ee is elastic potential energy in joules and e is extension in metres.
A spring that stores 8 J of elastic potential energy when extended by 0.2 m has a spring constant of 400 N/m. Rearranging Ee = ½ke² gives k = (2 × 8) ÷ 0.2² = 16 ÷ 0.04 = 400 N/m.
The elastic potential energy formula Ee = ½ke² works for both stretching and compression. Centimetres should be converted to metres first and the extension squared carefully.
The elastic potential energy stored depends on how stiff the spring is (its spring constant) and how much it is stretched (the extension). The stiffer the spring or the more it is stretched, the more energy is stored.
When a catapult is released, the elastic potential energy stored by doing work against the elastic forces converts back into kinetic energy, launching the projectile forward.
Extension is always measured from the spring's natural length, not the total length when stretched. It is the increase in length of a spring when a force is applied, measured in metres.
Full marks on the spring practical come from mentioning repeat readings and calculating a mean, reading the ruler at eye level, and using only data up to the limit of proportionality when applying Hooke's law.
In the springs practical, a spring is hung from a clamp stand, its original length measured, and known masses added one at a time. The new length is recorded each time, the extension calculated, mass converted to force with F = mg, and a graph of force against extension drawn.