Conservation of Energy

Conservation of energy means energy cannot be created or destroyed; it only moves between stores or transfers from one place to another. The total energy in a closed system stays the same.

Energy stores and transfers

Common energy stores: kinetic (moving), gravitational potential (due to height), elastic (stretched/squashed), chemical (batteries, fuels), internal/thermal (hot objects), nuclear, and electrostatic.

Ways energy transfers: by forces doing mechanical work, by electrical work (currents), by heating, and by waves (light, sound).

Key idea (system thinking)

Choose a system (for example, a ball and Earth). Track energy as it shifts between stores. Some energy often becomes internal (thermal) in surroundings due to friction or air resistance.

Useful equations for applying conservation

Kinetic energy: $$E_k = \tfrac{1}{2} m v^2$$

Change in gravitational potential energy: $$\Delta E_p = m g \, \Delta h$$

Mechanical work done by a force (energy transferred): $$W = F d = \Delta E$$

Sankey diagrams and efficiency

A Sankey diagram shows energy in arrows. The arrow width shows the amount of energy. The main forward arrow is useful energy; split side arrows show wasted energy (often to thermal). Efficiency tells what fraction is useful.

Common misconceptions

• “Energy is used up.” Energy is not destroyed; it spreads out, often warming the surroundings.
• Energy vs power. Energy is measured in joules (J). Power is the rate of transfer in watts (W).
• Speed in free fall depends on mass. It does not (if air resistance is ignored); mass cancels in $m g \Delta h = \tfrac{1}{2} m v^2$.