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Energy and Its Conservation

Energy and Its Conservation — American System Physics Revision Notes & Topical Questions

5 min read 6 parts Lesson 1 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Energy: Work, Stores, Conservation, Power and Efficiency — AMERICAN SYSTEM PHYSICS notes: Calculate work, kinetic energy, power and efficiency and apply energy conservation using stores and transfers.Energy is the capacity of a system to do work (to cause a change); it is a scalar in joules (J).

  • Gravitational field strength
  • Mechanical energy
  • Nuclear fission
  • Worked example 1
  • Worked example 2
  • Worked example 3

Part 1 of 4Work and energy

Energy is the capacity of a system to do work (to cause a change); it is a scalar in joules (J). Work done is the energy transferred when a force moves an object through a distance in the direction of the force: W = Fd (W in J, F in N, d in m), or in general W = Fd cos θ.

Work and energy
Only the component of force along the motion does work: holding a heavy box still does no work on it,
  • and a waiter carrying a tray horizontally does no work with the upward force.
    • (the distance moved along the force is 0)
Negative work removes energy (friction).

Energy is never used up; it is transferred from one store to another. "Using" energy means moving it into less useful stores, usually the internal store of the surroundings. Each store is linked to a measurable quantity, such as speed for kinetic or height for gravitational potential.

StoreWhere foundExample change
Kineticany moving objecta car braking (store empties)
Gravitational potentialobject raised in a fielda book lifted onto a shelf (store fills)
Chemicalfuels, food, batteriespetrol burning in an engine
Elastic (strain)stretched or compressed springs, rubber bands, drawn bowa catapult being released
Nuclearnuclei (uranium, hydrogen in stars)fission in a power station
Electrostaticseparated chargesa lightning strike
Internal (thermal)all matter; greater when hottera cup of tea cooling

Light and sound are not stores; they are ways of transferring energy by waves.

Transfer pathwayDriven byExample
Mechanical workinga force moving through a distancepushing a trolley
Electrical workingan electric currentkettle element heated by current
Heatinga temperature differencehot plate warming a pan
Waves (radiation, sound)oscillations carrying energysunlight warming the Earth

Part 2 of 4Kinetic energy, gravitational field strength and conservation

Kinetic energy is Ek = ½mv2 (J), always zero or positive.

Kinetic energy, gravitational field strength and conservation
Gravitational field strength
To find speed, v = √(2Ek/m), taking the square root as the final step. Gravitational field strength g = W/m is the gravitational force per unit mass; near Earth's surface g = 9.8 N/kg (equal to the free-fall acceleration 9.8 m/s2). Mechanical energy is the sum of kinetic and gravitational (and elastic) potential energies.
Energy is conserved; real machines are always less than 100% efficient, and compound machines combine simple machines (a bicycle).
At every stage the total stays the same, which lets you check a calculation by adding all the stores before and after.

Part 3 of 4Power and efficiency

Power is work done divided by time, P = W/t (watts; 1 W = 1 J/s).

Power is also force times velocity, P = Fv.
Efficiency
Horsepower is about 746 W. Efficiency is useful energy (or power) output divided by total input, often as a percentage; it has no unit and is always less than 100% for real devices.
Nuclear fission
A device's useful output follows from its power rating: useful energy = efficiency × power input × time. Nuclear fission is the splitting of a large nucleus (for example uranium-235) into smaller nuclei, releasing energy from the nuclear store,
  • as used in nuclear power stations.

Part 4 of 4Worked examples

  1. A student pushes a box with a horizontal force of 45 N across 3.2 m. How much work is done? [2]2 marks

  2. A crane does 2.4 × 105 J of work lifting a beam through 30 m at constant speed. What upward force does it exert? [2]2 marks

  3. A waiter carries a 12 N tray horizontally for 8.0 m. How much work does the upward force do? [2]2 marks

  4. A 0.15 kg ball has 30 J of kinetic energy. Find its speed. [2]2 marks

Key terms

TermMeaning
EnergyThe capacity of a system to do work; a scalar measured in joules.
Work doneEnergy transferred when a force moves an object a distance in the direction of the force, W = Fd.
Elastic (strain) energy storeEnergy in an object that is stretched, squashed or twisted.
Kinetic energyEnergy due to motion, Ek = ½mv2.
Gravitational field strength (g)Gravitational force per unit mass, g = W/m; 9.8 N/kg near Earth.
Mechanical energyThe sum of kinetic and potential (gravitational and elastic) energies.
EfficiencyUseful output divided by total input; no unit and below 100% for real devices.
Watt (W)A rate of energy transfer of one joule per second.
Nuclear fissionSplitting of a large nucleus into smaller ones, releasing energy.

Avoid these mistakes

1
Saying energy is used up — it is transferred to other stores, often internal.
2
Calculating work with force perpendicular to motion — it does no work.
3
Treating light and sound as energy stores — they are transfers by waves.
4
Stating efficiency can reach 100% for real machines — it is always less.
5
Taking the square root too early when finding speed from Ek.

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