$$\text{Work } W = F\times d \qquad \text{Power } P = \frac{W}{t} = Fv \qquad \text{Energy is measured in joules (J)}$$ $$\text{Kinetic energy } E_k = \tfrac{1}{2}mv^2 \qquad \text{Gravitational potential energy } E_p = mgh$$

• Conservation of energy: $mgh = \tfrac{1}{2}mv^2$ (falling object, no friction).
• Work done by a force at an angle: $W = Fd\cos\theta$.
• 1 kilowatt-hour $= 3\,600\,000$ J.

Efficiency

$$\text{Efficiency} = \frac{\text{useful output energy (or power)}}{\text{total input energy (or power)}}\times 100\%$$

Machines

$$\text{MA} = \frac{\text{load}}{\text{effort}} \qquad \text{VR} = \frac{\text{distance moved by effort}}{\text{distance moved by load}} \qquad \text{Efficiency} = \frac{\text{MA}}{\text{VR}}\times 100\%$$

• Inclined plane: $\text{VR} = \dfrac{l}{h}$. Pulley system: $\text{VR} =$ number of rope sections supporting the load.
• Screw jack: $\text{VR} = \dfrac{2\pi r}{p}$ ($r$ = handle length, $p$ = pitch). Gear wheels: $\text{VR} = \dfrac{\text{teeth on driven wheel}}{\text{teeth on driving wheel}}$.