Unit 4: Energy

Executive Summary

Energy is physics' most powerful bookkeeping tool: track kinetic, potential, and work instead of forces when the path is complicated.

Work and kinetic energy

Work $W = Fd\cos\theta$ transfers energy. The work-energy theorem says $W_{net} = \Delta K$ with $K = \frac{1}{2}mv^2$. Friction does negative work; a force perpendicular to motion does zero work.

Potential energy and conservation

$U_g = mgh$ (near Earth), $U_s = \frac{1}{2}kx^2$ (springs). When only conservative forces act, $K_i + U_i = K_f + U_f$. With friction, the lost mechanical energy equals the work friction does.

Power

$P = \frac{W}{t} = Fv$ — the rate of energy transfer.

Exam traps

Work can be negative (energy removed). Conservation of energy applies only in closed systems (no external work). A roller coaster's speed at the bottom depends only on height, not the path shape. Spring energy uses x², so compressing twice as far stores four times the energy.