Potential Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of 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 a system due to the position or configuration of its parts, ready to be converted into kinetic or other forms of energy.

Energy waiting to be released—like a stretched rubber band or a ball held high.

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: Potential energy is relative—you need to define a reference point (like the ground).

Common stuck point: PE can be negative if the object is below your chosen reference point — the reference is arbitrary.

Sense of Study hint: When solving a potential energy problem, first identify the type of PE involved (gravitational, elastic, or other). Then choose a reference point — for gravitational PE, pick a convenient zero-height level. Finally, calculate PE using the appropriate formula (mgh for gravitational, \frac{1}{2}kx^2 for elastic) and be consistent with the reference point throughout.

Worked Examples

Example 1

easy
A spring with spring constant k = 200 \text{ N/m} is compressed by 0.1 \text{ m}. What is the elastic potential energy stored?

Solution

  1. 1
    Use the elastic PE formula: PE = \frac{1}{2}kx^2.
  2. 2
    Square the compression distance: (0.1)^2 = 0.01.
  3. 3
    PE = \frac{1}{2}(200)(0.01) = 1 \text{ J}

Answer

PE = 1 \text{ J}
Elastic potential energy is stored in deformed elastic objects like springs. It depends on the spring constant and the square of the deformation.

Example 2

medium
A 0.3 \text{ kg} ball on a compressed spring (k = 800 \text{ N/m}, compressed 0.15 \text{ m}) is released. What speed does the ball reach?

Practice Problems

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

Example 1

medium
A spring (k = 500 \text{ N/m}) is stretched 0.2 \text{ m}. How much work was done to stretch it?

Example 2

easy
A bungee cord has an effective spring constant k = 100 \text{ N/m}. If it stretches 3 \text{ m} beyond its natural length, how much elastic potential energy is stored?
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Background Knowledge

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

energy