Work, Energy and Power

$\text{Work done}$ is the energy transferred when a force moves its point of application. It equals the force multiplied by the distance moved $\text{in the direction of the force}$. The unit is the joule (J): one joule is transferred when a force of one newton moves through one metre.

If the force acts at an angle $\theta$ to the direction of motion, only the component along the motion does work, so $W=Fs\cos \theta$. A force at right angles to the motion (like the tension holding a conker in a circle) does no work at all.

$\text{Kinetic energy}$ is the energy an object has because of its motion. Doing work to accelerate a mass from rest transfers energy into its kinetic store, giving $E_k=\frac{1}{2}m{v}^2$.

Because the speed is squared, doubling the speed quadruples the kinetic energy — which is exactly why stopping distances grow so sharply with speed.

Lifting an object against gravity transfers energy to its $\text{gravitational potential}$ store. Near the Earth’s surface, where $g$ is effectively constant, the change is $\Delta E_p=mg\Delta h$.

Only the change in $\text{height}$ matters, not the path taken — carrying a bag up a ramp or straight up a ladder to the same height needs the same gain in gravitational potential energy.

$\text{Power}$ is the rate of transferring energy, or equivalently the rate of doing work, measured in watts (1 W = 1 J s⁻¹). For a force pushing an object along at a steady speed, power can also be written as force × velocity.

$\text{Efficiency}$ compares the useful energy (or power) output with the total input. It is always less than 1 (or 100%) because some energy is dissipated, usually as heat through friction and resistance.