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 · chemical · elastic (strain) · nuclear · electrostatic · internal (thermal)

Energy is transferred between stores — by forces (mechanical work), by electrical currents (electrical work), by heating, and by electromagnetic, sound and other waves. 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 the internal (thermal) store of the ball and the ground, with some energy transferred by sound waves (a transfer, not a store) to the internal store of the surroundings; 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 = 9.8 m/s², no air resistance).
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 × 9.8 × 5) = √98 ≈ 9.9 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.