Mechanical Energy Examples in Physics

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

The total of kinetic energy and potential energy in a mechanical system at any given moment.

The combined 'useful' energy for mechanical motion — kinetic plus all forms of potential 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: In ideal conditions (no friction), mechanical energy is conserved.

Common stuck point: Friction converts mechanical energy to thermal energy—ME decreases, but total energy is still conserved.

Sense of Study hint: When solving a mechanical energy problem, first identify all forms of kinetic and potential energy at the initial and final states. Then apply ME = KE + PE at each state. Finally, if no non-conservative forces (like friction) act, set ME_i = ME_f to solve for the unknown.

Worked Examples

Example 1

easy
A 1 \text{ kg} ball at height 5 \text{ m} moves at 6 \text{ m/s}. What is its total mechanical energy? Use g = 10 \text{ m/s}^2.

Solution

  1. 1
    KE: \frac{1}{2}mv^2 = \frac{1}{2}(1)(36) = 18 \text{ J}.
  2. 2
    PE: mgh = 1 \times 10 \times 5 = 50 \text{ J}.
  3. 3
    Total: E = KE + PE = 18 + 50 = 68 \text{ J}

Answer

E = 68 \text{ J}
Mechanical energy is the sum of kinetic and potential energy. In the absence of friction and other non-conservative forces, it remains constant.

Example 2

medium
A 2 \text{ kg} object slides down a frictionless ramp from 8 \text{ m} high. What is its speed at the bottom? 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 ball with 68 \text{ J} of mechanical energy is at height 3 \text{ m}. Its mass is 1 \text{ kg}. What is its speed? Use g = 10 \text{ m/s}^2.

Example 2

easy
A 4 \text{ kg} projectile has 200 \text{ J} of kinetic energy at a height of 5 \text{ m}. What is its mechanical energy? Use g = 10 \text{ m/s}^2.
← Back to Mechanical Energy Formula Explained Practice Mode

Background Knowledge

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

kinetic energypotential energy