3.4 Conservation of Energy

Total Mechanical Energy

Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE): E = KE + PE. In a system with no non-conservative forces (like friction), total mechanical energy stays constant. Energy can transform between kinetic and potential forms, but the total remains the same, letting you set initial energy equal to final energy to solve problems.

Conservation of Energy with Non-Conservative Forces

When forces like friction or air resistance act, mechanical energy is not conserved — some energy converts to thermal energy or is dissipated. However, total energy (including all forms) is always conserved. The work-energy theorem extends this: Work done by non-conservative forces equals the change in mechanical energy (W_nc = ΔE_mech).

Energy Bar Charts & System Boundaries

Energy bar charts visually represent KE, PE, and internal/thermal energy at different points, showing how energy shifts while total height (total energy) stays constant. Choosing a system boundary determines which energies and forces are internal (accounted for by conservation) versus external (doing work on the system).

Key terms

Conservation of mechanical energy

In the absence of non-conservative forces, total mechanical energy (KE + PE) remains constant.

Non-conservative force

A force (like friction or air resistance) that removes mechanical energy from a system, converting it to other forms like heat.

Work-energy relation for non-conservative forces

W_nc = ΔE_mech — the work done by non-conservative forces equals the change in mechanical energy.

Energy bar chart

A diagram showing relative amounts of KE, PE, and thermal energy at different points, with total energy height staying constant.

System boundary

The defined boundary of a system that determines which forces/energies are internal (conserved) vs. external (doing work on the system).

Try an AP-style question

A ball is dropped from 20 m. What is its speed just before hitting the ground? (g ≈ 10 m/s²)

1. 20 m/s
2. 14 m/s
3. 200 m/s
4. 10 m/s