Work done by a force, kinetic and gravitational potential energy, the principle of conservation of energy, power as the rate of doing work, and efficiency.

What this dot point is asking

Edexcel wants you to calculate the work done by a force (including at an angle), use kinetic energy and gravitational potential energy, apply the principle of conservation of energy, define power as the rate of doing work, and calculate efficiency.

The answer

Work done

When the force is along the motion ($\theta = 0$), $W = Fs$. A force at right angles to the motion ($\theta = 90$) does no work, which is why the centripetal force in circular motion and the magnetic force on a moving charge do no work. Work done is the area under a force-displacement graph.

Kinetic and potential energy

These two stores convert into each other freely under gravity: a falling object loses $mgh$ of potential energy and gains $\frac{1}{2}mv^2$ of kinetic energy, so for a frictionless fall $v = \sqrt{2gh}$ regardless of mass.

Conservation of energy

This principle lets you solve problems without tracking forces: equate the total energy at the start and end, accounting for any work done against resistive forces.

Power and efficiency

No real machine is $100\%$ efficient because some input energy is always dissipated, usually as heat through friction or resistance. The wasted energy is not destroyed; it simply ends up in a less useful store.

Examples in context

Pumped-storage hydroelectric stations convert electrical energy to gravitational potential energy by pumping water uphill, then recover most of it as electricity at peak demand, with an overall efficiency around $75\%$. A car engine is only about $30\%$ efficient, most of the fuel energy leaving as heat in the exhaust and coolant. Regenerative braking in electric vehicles recovers kinetic energy that would otherwise become heat in the brakes. The $P = Fv$ relation explains why a car needs far more power to maintain high speed against drag.

Try this

Q1. State the principle of conservation of energy. [1 mark]

• Cue. Energy cannot be created or destroyed, only transferred between stores; the total in a closed system is constant.

Q2. A $2.0$ kg object moves at $5.0$ m per second. Find its kinetic energy. [2 marks]

• Cue. $E_k = \frac{1}{2}mv^2 = \frac{1}{2} \times 2.0 \times 5.0^2 = 25$ J.

Q3. A motor takes in $500$ W and delivers $400$ W of useful power. Find its efficiency. [2 marks]

• Cue. Efficiency $= \frac{400}{500} = 0.80 = 80\%$.