Elastic Potential Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Elastic Potential Energy.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Energy stored in an elastic object that has been stretched or compressed from its natural length.

A stretched rubber band 'wants' to snap back—that desire is stored energy.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The energy depends on how much you stretch AND how stiff the spring is.

Common stuck point: Displacement x is from the natural (unstretched) length, not total length.

Sense of Study hint: When solving an elastic potential energy problem, first identify the spring constant k and the displacement x from the spring's natural (relaxed) length. Then substitute into PE = \frac{1}{2}kx^2. Finally, remember that x is always measured from the equilibrium position and the energy is always positive regardless of stretch or compression direction.

Worked Examples

Example 1

easy
A spring with spring constant k = 400 \text{ N/m} is compressed by 0.05 \text{ m}. How much elastic potential energy is stored in the spring?

Solution

  1. 1
    Use the elastic potential energy formula: PE_{\text{elastic}} = \frac{1}{2}kx^2.
  2. 2
    PE = \frac{1}{2}(400)(0.05)^2 = \frac{1}{2}(400)(0.0025) = 0.5 \text{ J}
  3. 3
    This energy is available to be converted to kinetic energy when the spring is released.

Answer

PE_{\text{elastic}} = 0.5 \text{ J}
Elastic potential energy is stored in deformed elastic objects such as springs, rubber bands, and bows. It depends on the square of the deformation, so doubling the compression quadruples the stored energy.

Example 2

medium
A toy dart gun has a spring (k = 250 \text{ N/m}) compressed by 0.08 \text{ m}. If the dart has a mass of 0.01 \text{ kg}, what speed does the dart have when it leaves the gun?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A bungee cord (k = 50 \text{ N/m}) stretches 4 \text{ m} beyond its natural length when a jumper reaches the lowest point. How much elastic PE is stored?

Example 2

hard
A 0.2 \text{ kg} ball is launched vertically by a spring (k = 500 \text{ N/m}) compressed by 0.1 \text{ m}. How high does the ball rise above the release point? Use g = 9.8 \text{ m/s}^2.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

potential energyspring force