Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Why this shows up in the exam
NEET tests your understanding of how energy is stored and calculated in elastic systems.
How NEET tests this
Learn the idea
Elastic potential energy is the energy a spring stores when its length changes, and it depends on the square of the displacement, not on whether the spring is compressed or stretched.
🧠 Memory hook: Think of a spring as a ‘half‑kite’ (½ k) that flies farther the more you pull – the distance squared (x²) decides its height (energy).
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Restoring force of an ideal spring: F = –k x
- Elastic potential energy: U = ½ k x²
- x is the magnitude of displacement from the natural length (positive for both compression and extension)
- Energy is always positive because of the x² term
- k (N m⁻¹) measures the stiffness of the spring
How to approach it
- 1Read the question and note the given displacement (or a ratio of displacements)
- 2Write U = ½ k x²; if k is unknown but cancels, use the square‑law directly
- 3For comparative questions, remember that doubling x quadruples U
- 4Check whether the statement concerns compression or extension – the formula works for both
Worked example — watch it click
Assertion A: A spring has potential energy, both when it is compressed or stretched. Reason R: In compressing or stretching, work is done on the spring against the restoring force.
- ✅If both assertion and reason are true, and reason is the correct explanation of assertion.
- B)If both assertion and reason are true, but reason is not the correct explanations of assertion.
- C)If assertion is true, but reason is false.
- D)If both assertion and reason are false.
The concept behind this problem
The example asks you to link the fact that a spring stores energy in any deformation with the reason that work must be done against the restoring force, testing the core idea that the stored energy originates from that work.
Step by step
- 1Assertion A is true: A spring stores elastic potential energy U = ½kx² whether compressed (x < 0) or stretched (x > 0), since x² is always positive.
- 2Reason R is true: Work is done against the restoring force F = -kx in both compression and stretching, and this work is stored as potential energy.
- 3The reason correctly explains why the assertion is true.
Watch out
Students often forget that the reason must explain the assertion and mistakenly claim the work done by the spring, not on it, is the source of the energy.
Common slip-ups that cost marks
- •Using the sign of x and getting a negative energy
- •Assuming the work done by the spring equals the stored energy (it is the work done on the spring)
- •Mixing up k with the force value instead of the constant
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
Assertion A: A spring has potential energy, both when it is compressed or stretched. Reason R: In compressing or stretching, work is done on the spring against the restoring force.
Push further
More challenging5 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.
When a spring is stretched by 5 cm, its potential energy is 25 J. If the same spring is stretched by 15 cm, what is the new potential energy stored in it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.
Work by a Constant Force
For a constant force, work is the scalar product of force and displacement, so its sign is set by the angle between those vectors and not by force magnitude alone.