Conservation of Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Conservation of 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

A fundamental law of physics stating that the total energy of an isolated system remains constant over time — energy can be transferred between objects.

Energy is like money—you can spend it, save it, or change its form, but you can't make more out of nothing.

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 total energy in a closed system always remains constant — it changes form but never disappears.

Common stuck point: Energy 'lost' to friction isn't destroyed — it converts to thermal energy, which is harder to recover.

Sense of Study hint: When applying conservation of energy, first list all forms of energy at the initial state (KE, PE, thermal, etc.) and all forms at the final state. Then set total initial energy equal to total final energy, plus any energy added or removed by external work or heat. Finally, solve for the unknown quantity.

Worked Examples

Example 1

medium
A 2 \text{ kg} ball is dropped from 20 \text{ m}. What is its speed just before hitting the ground? Use g = 10 \text{ m/s}^2.

Solution

  1. 1
    At the top: PE = mgh = 2 \times 10 \times 20 = 400 \text{ J}, KE = 0.
  2. 2
    At the bottom: all PE converts to KE. \frac{1}{2}mv^2 = 400
  3. 3
    v = \sqrt{\frac{2 \times 400}{2}} = \sqrt{400} = 20 \text{ m/s}

Answer

v = 20 \text{ m/s}
Conservation of energy states that total mechanical energy is constant in the absence of non-conservative forces. PE at the top equals KE at the bottom.

Example 2

hard
A roller coaster car (500 \text{ kg}) starts from rest at 30 \text{ m} high and descends to 10 \text{ m}. What is its speed at 10 \text{ m}? Use g = 10 \text{ m/s}^2.

Practice Problems

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

Example 1

medium
A pendulum of length 2 \text{ m} is released from a height 0.5 \text{ m} above its lowest point. What is its speed at the lowest point? Use g = 10 \text{ m/s}^2.

Example 2

hard
A skier (60 \text{ kg}) starts from rest at the top of a 25 \text{ m} hill and reaches the bottom at 18 \text{ m/s}. How much energy was lost to friction? Use g = 10 \text{ m/s}^2.
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Background Knowledge

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

kinetic energypotential energy