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10.3Energy and Its Conservation

Conservation of Energy, Efficiency, Power and Energy Resources — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 5 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

State and apply the principle of conservation of energy.Conservation (no losses)mgΔh = ½mv2, so a falling object reaches v = √(2gΔh), independent of mass.Efficiency = useful energy output ÷ total energy input (× 100%): η = Euseful / Ein.Efficiency = useful power output ÷ total po…

  • Power = work done ÷ time taken
  • Power = energy transferred ÷ time taken
  • Supplement idea
  • Closed (isolated) system
  • Wasted energy
  • Dissipation

Section 1 of 7Conservation of Energy, Efficiency, Power and Energy Resources

1
10.3 Conservation of Energy, Efficiency,… concept map: Conservation (no losses), Power = work done ÷ time taken, Power = energy transferred ÷, Supplement idea, Principle of conservation of
Visual guide to the key ideas explained in this lesson.
2
The principle of conservation of energy says the total energy is constant. In a falling ball, the loss of GPE equals the gain in KE plus any energy transferred to the surroundings by air resistance.
3
If air resistance is negligible, mgΔh = ½mv2, so v = √(2gΔh). Mass cancels, which is why (without air resistance) heavy and light objects dropped from the same height land at the same speed.
4
A swinging pendulum continually transfers energy between gravitational potential and kinetic stores: maximum GPE at the ends of the swing (momentarily at rest), maximum KE at the lowest point. The swing gradually dies away because energy is dissipated by air resistance and friction at the pivot.
5
No real machine is 100% efficient; some energy is always dissipated, usually by heating due to friction or electrical resistance. Efficiency can be improved by lubrication, streamlining and thermal insulation.
6
Efficiency has no unit. It can be given as a decimal (0.25) or a percentage (25%). An answer above 100% means a calculation error.
7
Power tells us how quickly energy is transferred. Two cranes lifting the same load to the same height do the same work, but the one that does it in less time has the greater power.
8
Electricity is usually generated by spinning a turbine connected to a generator.
  • In fossil fuel, nuclear, geothermal and biofuel power stations, thermal energy boils water to make high-pressure steam that turns the turbine;
    • in wind, hydroelectric and tidal schemes moving air or water turns the turbine directly.
9
Solar cells transfer energy from light directly to electrical energy with no moving parts. Solar panels (thermal collectors) use sunlight to heat water.
10
The Sun's energy comes from nuclear fusion of hydrogen nuclei into helium. Sunlight drives the water cycle (hydroelectric), winds and plant growth (biofuels and, long ago, fossil fuels).
11
Choosing a resource involves cost, reliability, power output, environmental impact (CO2 and global warming, habitat loss, radioactive waste) and whether it is renewable.
12Supplement idea
Supplement idea a device's useful output can be calculated from its power rating: useful energy = efficiency × power input × time.

Section 2 of 7Process & sequence

1
Pendulum practical: set up a pendulum with a heavy bob and measure the release height above the lowest point with a metre rule.
2What the symbols mean:
Calculate the GPE lost from release to lowest point: ΔEp = mgΔh.
What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
3
Measure the bob's speed at the lowest point with a light gate (bob width ÷ time to pass the gate).
4What the symbols mean:
Calculate the kinetic energy at the lowest point: Ek = ½mv2.
What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
5
Compare: KE gained should be slightly less than GPE lost; the difference was transferred by air resistance to the internal store of the air.
6
Calculate efficiency of the transfer = useful energy out ÷ total energy in × 100% and repeat for different heights.

Energy through one swing of a pendulumwrite these steps in this order; each step is a marking point.

1
Bob held at highest point: maximum gravitational potential energy, zero kinetic energy.
2
Bob released and falls: GPE decreases as KE increases.
3
Lowest point: minimum GPE, maximum KE and maximum speed.
4
Bob rises on the other side: KE decreases as GPE increases.
5
Each swing is slightly lower because some energy is dissipated to the internal store of the air and pivot.

Section 3 of 7Compare

Energy resources for generating electricity
ResourceRenewable?Reliable?Main advantageMain disadvantage
Fossil fuelsNoYesHigh power output on demandCO2 (global warming), acid rain
Nuclear fissionNoYesNo CO2 while running; much energy from little fuelRadioactive waste; high build/decommission cost
WindYesNo (needs wind)No fuel cost or emissionsNoisy, visual impact, low output per turbine
Solar cellsYesNo (daytime, cloud)No emissions; good for remote placesLow efficiency, large area needed
HydroelectricYesYesQuick response to demandFloods valleys, destroys habitats
TidalYesYes (predictable)Predictable, no emissionsFew suitable sites, affects estuaries
GeothermalYesYesConstant supplyOnly in volcanic areas
BiofuelsYesYesCarbon-neutral in principleUses farmland

Most resources ultimately get energy from the Sun; the exceptions are geothermal, nuclear and tidal (tidal comes mainly from the Moon's gravity).

Section 4 of 7Worked examples

9.9 m/s
A 0.50 kg ball is dropped from a height of 5.0 m. Ignoring air resistance, find its speed just before it hits the ground (g = 9.8 N/kg).
  • GPE lost = mgΔh = 0.50 × 9.8 × 5.0 = 24.5 J.
    • This all becomes KE: ½mv2 = 24.5 J, so v2 = 2 × 24.5 ÷ 0.50 = 98, v = √98 = 9.9 m/s.
70%
An electric motor takes in 800 J of electrical energy and lifts a load, giving it 560 J of GPE. Calculate the efficiency.
  • Efficiency = useful output ÷ total input × 100% = 560 J ÷ 800 J × 100% = 70% (0.70).
    • The remaining 240 J is dissipated, mainly by heating.
A 60 kg climber gains 4.0 m of height every 10 s. Calculate her useful power output (g = 9.8 N/kg).
  • Work done = mgΔh = 60 × 9.8 × 4.0 = 2352 J. P = W ÷ t = 2352 J ÷ 10 s = 235.2 W ≈ 2.4 × 102 W.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Principle of conservation of energy · Closed (isolated) system · Efficiency · Useful energy output · Wasted energy · Dissipation · Power (P) · Watt (W) · Renewable energy resource · Non-renewable energy resource · Fossil fuel · Nuclear fission · Nuclear fusion
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
energy is produced by the power stationenergy is transferred from the fuel's chemical (or nuclear) store to electrical working.
2
efficiency = input ÷ outputefficiency = useful output ÷ total input.
3
power is energypower is energy transferred per unit time (rate of energy transfer).
4
renewable means it causes no pollutionrenewable means it is replenished naturally and will not run out.
5
efficiency = 70 Jefficiency = 0.70 or 70% (no unit).
6
solar cells use heatsolar cells transfer energy from light directly to electrical energy.

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