Total energy never disappears; it only changes form or moves between systems.

\displaystyle KE_i + PE_i + W_{nc} + OE_i = KE_f + PE_f + OE_f

\displaystyle \text{Efficiency} = \frac{W_{out}}{E_{in}}

Law of conservation of energy — total energy is constant in any process.
W_nc — work by nonconservative forces like friction (usually negative).
OE (other energy) — chemical, thermal, electrical, nuclear, radiant (light), and so on.
Thermal energy — the random motion of atoms and molecules; friction usually turns mechanical energy into thermal energy.
Efficiency — the fraction of input energy that comes out as useful work. Always less than 100%; the rest mostly becomes thermal energy.

Energy chains

Process	Conversion
Eating and moving	Chemical → kinetic + potential + thermal
Photosynthesis	Light → chemical
Coal power plant	Chemical → thermal → mechanical (turbine) → electrical
Solar-powered motor	Radiant → electrical → mechanical

Typical efficiencies (Table 7.2)

Device or activity	Efficiency
Electric motor	98%
Gas heater	90%
Coal power plant	42%
Diesel engine	35%
Gasoline engine	30%
Cycling and climbing	20%
Solar cell	10%
Weightlifting	9%
Shoveling	3%
Surface swimming	2%

Energy problem-solving steps

Define the system, knowns, and unknown. Sketch it.
List the forces. Do you know a potential energy for each?
All conservative → KE_i + PE_i = KE_f + PE_f.
Friction or other energy involved → use the full equation with W_nc and OE.
Zero out terms: set h = 0 at the start or end; cross out KE when something is at rest.
Check: friction work should be negative, PE lower at the bottom, speeds reasonable.

Common mistakes: saying energy is "lost" (it's converted, usually to thermal); efficiency over 100%; calculating work by gravity separately and also counting PE (that double-counts it).

Section 7.5 (Nonconservative Forces) wasn't included in this batch. 7.6 uses W_nc from it, so it's worth adding if it's assigned.