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IGCSE Physics 0625 · Chapter 4 notes · ~11 min read

Energy, work & power

Where energy is stored, how it moves, how fast, and how much is wasted — plus every energy resource you may be asked to compare.

Energy stores & transfersConservation of energyKinetic & gravitational energyWork donePowerEfficiency & Sankey diagramsEnergy resources
RSby Riyaz Sir
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No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • Energy is never created or destroyed. It is transferred between stores, and some always ends up as wasted thermal energy.
  • Work done = force × distance (in joules). Work done = energy transferred.
  • Power = work ÷ time (in watts) — how fast energy is transferred.
  • EXT Ek = ½mv², ΔEp = mgΔh and efficiency = useful ÷ total × 100%.

By the end you can

  • Name the energy stores and the four ways energy is transferred.
  • Use W = Fd and P = W ÷ t.
  • Calculate kinetic energy and changes in gravitational energy. EXT
  • Read a Sankey diagram and calculate efficiency. EXT
  • Compare the energy resources, renewable and non-renewable.

1Energy stores and transfers

The energy stores

StoreExample
kinetica moving car, a falling ball
gravitational potentiala book on a shelf, water behind a dam
chemicalfood, fuel, a battery
elastic (strain)a stretched spring or elastic band
nuclearuranium, the core of the Sun
electrostaticseparated charges, a charged balloon
internal (thermal)the moving particles in a hot object

Four ways energy is transferred

TransferWhat happens
by a force (work done)a force moves something
electricallya current flows round a circuit
by heatingthermal energy moves from hot to cold (conduction, convection, radiation)
by waveslight and sound carry energy away from a source

Conservation of energy — energy is never created or destroyed — the total energy before always equals the total energy after.

  • Example flow: phone battery → chemical → electrical → light + sound + thermal (wasted).
  • Dissipated energy spreads out into the surroundings as thermal energy. It still exists, but it is too spread out to use again.
Picture itA lamp warms the room by a tiny amount. All that energy is still there, but you cannot gather it back into the lamp.
Common mistake"The energy is used up." Energy is never used up — it ends up in stores that are not useful.

Kinetic and gravitational energyEXTENDED

Ek = ½ m v²
kinetic energy (J) = ½ × mass (kg) × speed² (m/s)²
ΔEp = m g Δh
change in gravitational potential energy (J) = mass × g × change in height (m)
GPE 50KE 0GPE 25KE 25GPE 0KE 50energy converted — the total stays 50
A ball falls: gravitational energy turns into kinetic energy. At every height the two add up to the same total (50 units).
Worked example

EXT A 2.0 kg ball is dropped from 5.0 m. Find its speed just before it lands. (g = 9.8 N/kg, ignore air resistance)

  1. Loss in GPE = mgΔh = 2.0 × 9.8 × 5.0 = 98 J
  2. All of it becomes kinetic energy: ½ × 2.0 × v² = 98
  3. v² = 98, so v = 9.9 m/s
Worked example

EXT Find the kinetic energy of a 1200 kg car travelling at 15 m/s.

  1. Ek = ½mv² = ½ × 1200 × 15²
  2. = ½ × 1200 × 225
  3. = 135 000 J (135 kJ)
Exam tipDoubling the speed makes the kinetic energy four times bigger, because v is squared. That is why fast crashes are so much more damaging.
Common mistakeForgetting to square the speed.

2Work and power

Work done

Work done — the energy transferred when a force moves an object.

W = F d
work done (J) = force (N) × distance moved in the direction of the force (m)
  • 1 joule (J) is the work done when a force of 1 N moves an object 1 m.
  • Work done always equals energy transferred: W = ΔE.
Worked example

A person pushes a crate with a force of 50 N for 4.0 m. Find the work done. Where does the energy go?

  1. W = Fd = 50 × 4.0
  2. = 200 J
  3. The energy becomes kinetic energy of the crate and, because of friction, thermal energy of the floor and crate
Worked example

A crane lifts a 20 kg box through 3.0 m. Find the work done. (g = 10 N/kg)

  1. To lift at steady speed, force = weight = mg = 20 × 10 = 200 N
  2. W = Fd = 200 × 3.0
  3. = 600 J
  4. This is stored as gravitational potential energy

Power

Power — how fast work is done, or energy is transferred.

P = Wt = ΔEt
power (W) = work done (J) ÷ time (s) = energy transferred (J) ÷ time (s)
  • 1 watt (W) = 1 joule per second. 1 kW = 1000 W; 1 MW = 1 000 000 W.
Picture itTwo people carry the same box up the same stairs. The work done is the same, but the one who does it faster has more power.
Worked example

A 60 kg student runs up stairs 3.0 m high in 5.0 s. Find the power. (g = 10 N/kg)

  1. Work done = mgΔh = 60 × 10 × 3.0 = 1800 J
  2. P = W ÷ t = 1800 ÷ 5.0
  3. = 360 W
Common mistakeMixing up joules and watts. A 100 W lamp transfers 100 J every second.

3Efficiency and Sankey diagrams

Wasted energy

  • In nearly every device some energy is wasted, mostly as thermal energy (and sometimes as sound).
  • More efficient means more of the input energy is turned into the useful output.
  • Improve efficiency by reducing friction (lubricants), insulating (to stop heat loss), and streamlining (to cut air resistance).
EXT efficiency = useful energy outputtotal energy input × 100%
always less than 100%
EXT efficiency = useful power outputtotal power input × 100%
the same idea with power
100 Jelectricaluseful light 5 Jwasted as heat 95 Jefficiency = 5 ÷ 100 × 100% = 5%band width = amount of energy
A Sankey diagram. The width of each band shows the amount of energy. A filament lamp turns only 5 J of every 100 J into light and wastes 95 J as heat.
Worked example

EXT A motor takes in 500 J of electrical energy and lifts a load, gaining 350 J of gravitational energy. Find the efficiency.

  1. efficiency = useful output ÷ total input × 100%
  2. = 350 ÷ 500 × 100%
  3. = 70%
  4. The other 150 J is wasted as thermal energy and sound
Worked example

EXT A power station takes in 100 MJ of chemical energy from fuel and delivers 40 MJ of electrical energy. Find the efficiency and the wasted energy.

  1. efficiency = 40 ÷ 100 × 100% = 40%
  2. wasted = 100 − 40 = 60 MJ
  • EXT In a multi-stage process (fuel → boiler → turbine → generator) energy is wasted at every stage. Total in = total useful out + all the wasted energy.
Common mistakeEfficiency above 100%. That would mean creating energy, which is impossible.

4Energy resources

Renewable and non-renewable

Renewable — replaced as fast as we use it, so it will not run out.

Non-renewable — a finite supply that cannot be replaced in a human lifetime.

ResourceTypeAdvantageDisadvantage
coal, oil, gasnon-renewablecheap, reliable, easy to switch onreleases CO₂, causes acid rain, will run out
nuclear fissionnon-renewableno CO₂, a lot of energy from a little fuelradioactive waste, accident risk, costly to build and close
windrenewableno fuel cost, no pollutionnot always windy, noisy, spoils views
hydroelectricrenewablereliable, no fuel, can store waterfloods land and destroys habitats, costly to build
waves and tidesrenewableno fuel cost, tides are predictablecostly, can harm marine life, hard to build
geothermalrenewablereliable, low CO₂only practical in volcanic regions
solar cells and panelsrenewableno pollution, good for remote placesonly works in daylight, depends on weather
biofuelsrenewablecan be regrown, plants absorb the CO₂ releasedneeds farmland, still releases CO₂ when burned
  • Solar cells make electricity directly. Solar panels heat water.
FuelchemicalBoilerthermalTurbinekineticGeneratorelectricalfossil fuels · biofuels · nuclear · geothermal: heat makes steamwind · waves · tides · hydroturbine → generatorsolar cells skip the turbine: light → electrical
Most power stations share one chain. A fuel makes steam, the steam turns a turbine, and the turbine spins a generator. Wind, waves, tides and hydro skip the boiler. Solar cells skip the turbine too.
  • Compare resources on: renewable or not, how available, how reliable, the scale of power, and the environmental impact.
Exam tipIn a "discuss" question give one advantage AND one disadvantage, and compare reliability. Wind and solar depend on the weather. Fossil fuels and hydro can be switched on when needed.

The Sun's roleEXTENDED

  • The Sun is the main source of energy for almost every resource: fossil fuels (ancient plants stored sunlight), wind (the Sun heats the air), waves, hydroelectric (the Sun evaporates water), biofuels and solar. Exceptions: geothermal, nuclear and tidal.
  • The Sun releases energy by nuclear fusion — hydrogen nuclei join to make helium. See the stars and Universe chapter.
  • Researchers are working on fusion power stations on Earth. Fusion has not yet been used for large-scale electricity.

5Test yourself

Test yourself — cover the answers first

Quick check

  1. Name the four ways energy can be transferred.
  2. How much work does a force of 30 N do moving a box 5.0 m?
  3. A motor does 4800 J of work in 60 s. What is its power?
  4. Which are renewable: coal, wind, uranium, solar?
  5. Find the kinetic energy of a 0.50 kg ball at 4.0 m/s.
  6. Why can no device be 100% efficient?

Exam-style

  1. A 0.50 kg ball is thrown straight up at 12 m/s. Find the maximum height. (g = 10 N/kg, ignore air resistance)
  2. A lift motor does 24 000 J of useful work in 8.0 s. Its input power is 4.0 kW. Find the efficiency.
  3. A 1000 kg car slows from 20 m/s to rest. How much kinetic energy is transferred, and to what store?
  4. Give one advantage and one disadvantage of generating electricity from nuclear fission. [2]
Show answers
  1. by a force (work), electrically, by heating, by waves
  2. 30 × 5.0 = 150 J
  3. 4800 ÷ 60 = 80 W
  4. wind and solar
  5. ½ × 0.50 × 4.0² = 4.0 J EXT
  6. Some energy is always wasted, usually as thermal energy spreading into the surroundings.
  7. Ek at launch = ½ × 0.50 × 12² = 36 J
    all of it becomes GPE: mgh = 0.50 × 10 × h = 36
    h = 36 ÷ 5.0 = 7.2 m
  8. useful power = 24 000 ÷ 8.0 = 3000 W
    efficiency = 3000 ÷ 4000 × 100% = 75%
  9. Ek = ½ × 1000 × 20² = 200 000 J
    transferred to thermal (internal) energy in the brakes, tyres and surroundings
  10. Advantage: no carbon dioxide is produced / a lot of energy from a little fuel
    Disadvantage: radioactive waste stays dangerous for a long time / risk of an accident
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Energy, work & powerEnergy resources
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