Work, Energy and Power

• Work done = force × displacement in the direction of the force.
• Principle of conservation of energy: energy cannot be created or destroyed, only transferred.
• Efficiency = useful energy output ÷ total energy input.
• Power = work done per unit time; P = W/t and P = Fv.
• ΔE_P = mgΔh in a uniform field, derived from W = Fs.
• E_K = ½mv², derived from the equations of motion.

Work, efficiency and power

Work done by a force is the force multiplied by the displacement in the direction of the force. If the force is at angle θ to the displacement, only F cos θ does work. 1 J = 1 N m.

Conservation of energy: energy cannot be created or destroyed; it can only be transferred from one form to another. The total energy of a closed system is constant.

Efficiency is the ratio of useful energy output to total energy input (equivalently useful power out ÷ total power in). It is never greater than 1.

Power is work done per unit time. For a force F moving its point of application at constant speed v: P = W/t = F(s/t) = Fv.

Two energy stores you derive

Gravitational potential energy: to lift a mass m at constant speed through Δh you apply force mg over distance Δh, so the work done is W = Fs = mgΔh. This is the gain in GPE (valid where g is uniform, near the Earth's surface).

Kinetic energy: a constant force F accelerates mass m from rest over distance s. Using v² = 0 + 2as and F = ma, the work done is Fs = ma × v²/(2a) = ½mv². This is the kinetic energy.