Elastic Potential Energy
Simple Explanation
Elastic potential energy (EPE) is the energy stored in a stretched or compressed elastic object, like a spring: EPE = ½kx². Like kinetic energy, this depends on the SQUARE of the extension — stretching a spring twice as far stores four times the energy.
Why Do We Need It?
Elastic potential energy is the energy store behind archery bows, catapults, wind-up clocks, and trampolines — anywhere energy is stored by stretching or compressing something elastic.
Formula
Elastic Potential Energy
EPE = ½kx²
Elastic potential energy is the energy stored in a stretched or compressed elastic object, such as a spring — it grows with the square of the extension, so stretching a spring twice as far stores four times the energy.
- EPE
- — elastic potential energy, in joules (J)
- k
- — the spring constant — a measure of the spring's stiffness, in newtons per metre (N/m)
- x
- — the extension or compression from the natural length, in metres (m)
When to use it: Whenever the energy stored in a stretched or compressed spring needs to be found.
Worked Example
Find the energy stored in a stretched spring
A spring with spring constant 200 N/m is stretched by 0.15 m. Find the elastic potential energy stored.
Why Does This Work?
As a spring stretches, the force needed increases steadily with extension (proportional to x) — since the work done is the AVERAGE force times distance, and the average force is exactly half the final force, the total energy stored ends up proportional to x², not x.
Real-Life Example
Archery bows
An archer pulls back a bowstring before releasing an arrow.
Pulling the string back stores elastic potential energy in the bent bow; releasing the string converts that stored energy almost entirely into the kinetic energy of the launched arrow.
Practice
A spring with spring constant 150 N/m is compressed by 0.1 m. Find the elastic potential energy stored.
MediumCommon mistake
Forgetting to square the extension x — just like with kinetic energy, this is a common algebra slip that gives a far too small answer.
Quick Review
- EPE = ½kx²
- EPE depends on the SQUARE of the extension or compression.
- This is the energy store in bows, catapults, and trampolines.