Energy, Work and Power: Revision Notes

Condensed for the final weeks. For the full explanation, use the Energy, Work and Power study guide.

Energy stores

Kinetic · gravitational potential · elastic potential · chemical · thermal (internal) · nuclear · electrostatic

Energy is transferred between stores — mechanically, electrically, by heating, or by radiation. It is never “used up” or “created”.

A falling ball transfers energy from its gravitational potential store to its kinetic store, and eventually, on landing, to internal/thermal and sound stores; a battery-powered motor transfers energy from a chemical store to a kinetic store via electrical work. The principle of conservation of energy underlies every such transfer: the total amount of energy stays constant throughout, however many stores it passes through.

Where this fits in 5054

Work is what a force does when it moves something, and it is the mechanism by which energy is transferred from one store to another; power then measures how quickly that transfer happens. Together, energy, work and power form the calculation core of Topic 1’s final section, so fluency with all four equations — kinetic energy, gravitational PE, work done and power — pays off across every question type this sub-topic contains.

Equations

kinetic energy        Ek = 1/2 m v^2
gravitational PE      ΔEp = m g Δh    (Δh = CHANGE IN HEIGHT)
work done             W  = F x d       (force x distance MOVED IN THE
                                        DIRECTION OF THE FORCE)
power                 P  = W / t  =  ΔE / t
efficiency            = (useful energy out / total energy in) x 100%

Units: energy and work in joules (J), power in watts (W) = J/s.

Worked examples for each equation

Kinetic energy of a 1500 kg car at 20 m/s:

Ek = 1/2 m v^2 = 1/2 x 1500 x 20^2 = 1/2 x 1500 x 400 = 300000 J

Change in gravitational PE when a 5 kg object is lifted 3 m (g = 9.8 N/kg):

ΔEp = m g Δh = 5 x 9.8 x 3 = 147 J

Work done when a 40 N force pushes a crate 6 m:

W = F x d = 40 x 6 = 240 J

Power of a motor doing 6000 J of work in 15 s:

P = W / t = 6000 / 15 = 400 W

Work done and energy transferred are the same quantity measured the same way — doing work on an object is precisely how energy is transferred into or out of it by a force, which is why both are measured in joules.

Conservation of energy

Total energy is always conserved. In a falling object, Ep converts to Ek:

m g h  =  1/2 m v^2      ->      v = sqrt(2 g h)

Mass cancels — which is why, ignoring air resistance, heavy and light objects reach the same speed after the same drop.

Efficiency and dissipation

No device is 100% efficient. Energy is dissipated, usually as thermal energy to the surroundings, where it becomes spread out and less useful — not destroyed.

Reduce dissipation by lubrication (friction), streamlining (drag) and insulation (thermal transfer).

A motor that uses 500 J of energy but does only 350 J of useful work has an efficiency of (350/500) × 100 = 70%, with the remaining 150 J dissipated, typically as thermal energy to the surroundings — always express the “useful energy out” and “total energy in” in the same units before dividing, since a units mismatch is a common source of an efficiency figure that looks plausible but is actually wrong.

Common mistakes worth avoiding specifically

Forgetting to square the velocity in Ek = ½mv² is one of the most common errors — a frequent slip is calculating ½mv instead, so always square v before multiplying by the mass and the one-half. Using the wrong height in ΔEp = mgΔh is another: it is the change in height that matters, not the absolute height above some fixed reference, unless a question specifically defines a reference level. Mixing up power’s two equivalent formulas, P = W/t and P = ΔE/t, is not actually an error since they give the same result — but knowing that they are the same formula expressed two ways, rather than two separate things to remember, avoids unnecessary confusion under exam pressure.

Exam traps

• In W = F × d, the distance must be along the direction of the force. Carrying a box horizontally does no work against gravity.
• KE depends on v², so doubling speed quadruples kinetic energy — the standard braking-distance question.
• Efficiency can never exceed 100%; if it does, recheck which value is “useful out”.
• Say energy is “dissipated” or “transferred to the surroundings”, never “lost” or “used up”.
• Power is the rate of transfer, not an amount of energy.
• Check h is a vertical height, not a distance along a slope.

Self-test

1. A 2 kg ball is dropped 5 m. Find its speed on landing (g = 10 m/s²).
2. Why does doubling a car’s speed quadruple its braking distance?
3. A motor uses 500 J and does 350 J of useful work. Find its efficiency.
4. Does a waiter carrying a tray horizontally at constant speed do work against gravity?
5. State the difference between energy and power.

Answers: 1. v = √(2 × 10 × 5) = 10 m/s. 2. Ek ∝ v², so four times the kinetic energy must be removed by the braking force over four times the distance. 3. (350/500) × 100 = 70%. 4. No — the force (upward) is perpendicular to the motion (horizontal), so no work is done against gravity. 5. Energy is the capacity to do work, measured in joules; power is the rate of energy transfer, measured in watts.