Elastic Potential Energy
Energy stored in a stretched or compressed spring.
Formula
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Example
Bow stores this before release
How it works
When you stretch or compress a spring, you must do work against the spring’s restoring force. That work is stored as elastic potential energy, and for an ideal spring the force increases linearly with displacement, which is why the stored energy grows with the square of x rather than just x. The spring constant k measures stiffness: a larger k means more force is needed for the same stretch, so more energy is stored.
When to use it
Use this formula whenever you need the energy stored in a spring, rubber-like elastic system, or other object that behaves like an ideal spring. It is common in mechanics problems involving compression, release, oscillations, or any situation where a force changes with displacement.
Worked example, step by step
A spring has spring constant k = 250 N/m and is compressed by x = 0.12 m. U = (1/2)kx^2 U = (1/2)(250)(0.12)^2 U = 125 × 0.0144 U = 1.8 J Final answer: the elastic potential energy stored is 1.8 J.
Common mistakes to avoid
- Forgetting to square the displacement x
- Using the wrong units for k or x, which gives the wrong energy units
- Confusing elastic potential energy with force, since U and kx are not the same quantity
Did You Know?
A stretched bow stores elastic potential energy that becomes the arrow's kinetic energy on release.
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