Why energy is never lost, only transformed: forms of energy, kinetic and potential energy, efficiency, power stations and energy resources, with diagrams and worked examples.
A pendulum swings, a kettle boils, a phone charges, a plant grows. In every case something is happening, and in every case energy is being transferred or transformed. Energy is one of the most important ideas in science because it follows a strict rule: it is never created or destroyed. It can only move from one place to another or change from one form into another. This single rule lets us predict how fast a roller coaster will go, how much fuel a power station needs, and why no machine can ever be 100% efficient. This article explains the forms of energy, how to calculate them, where our energy comes from, and how to use it wisely.
Energy is the ability to make things happen: to lift a load, heat a room, light a lamp or make a sound. It is not a substance you can hold. It is a quantity, measured in joules (J). One joule is a small amount: roughly the energy needed to lift a small apple (about 100 g) up by 1 metre. Bigger units are the kilojoule (1 kJ = 1000 J) and the megajoule (1 MJ = 1 000 000 J).
When a force moves an object, work is done and energy is transferred: work done = force × distance moved in the direction of the force. Energy transferred and work done are both measured in joules. The article on work, power and simple machines explores this in more detail.
| Form | What it is | Example |
|---|---|---|
| Kinetic | Energy of movement | A moving car, flowing water, wind |
| Gravitational potential | Energy stored by an object's height in a gravitational field | Water behind a dam, a book on a shelf |
| Elastic (strain) potential | Energy stored in a stretched or squashed object | A drawn bow, a compressed spring |
| Chemical | Energy stored in the bonds of substances | Food, fuels, batteries |
| Thermal (internal) | Energy of the random motion and interactions of particles | A hot cup of tea |
| Electrical | Energy carried by moving charges | Current in a wire |
| Light (radiant) | Energy carried by electromagnetic waves | Sunlight, a torch beam |
| Sound | Energy carried by vibrations in a medium | Music, thunder |
| Nuclear | Energy stored in the nucleus of atoms | Uranium fuel, the Sun's core (see Atomic and Nuclear Physics) |
Some courses describe energy in stores (kinetic store, chemical store, and so on) and pathways (heating, electrical work, mechanical work, radiation). The ideas are the same: energy is transferred from one store to another, and the total stays constant.
Anything that moves has kinetic energy. It depends on the mass and, even more strongly, on the speed.
KE = ½ × m × v²
KE in joules, m in kilograms, v in metres per second. Because speed is squared, doubling the speed makes the kinetic energy four times bigger.
Find the kinetic energy of a 1200 kg car travelling at 20 m/s (72 km/h). What is it at 40 m/s?
At 20 m/s: KE = ½ × 1200 × 20² = ½ × 1200 × 400 = 240 000 J (240 kJ).
At 40 m/s: KE = ½ × 1200 × 40² = 960 000 J, four times as much.
This is why high-speed crashes are so much more destructive and why braking distance rises with the square of speed.
Gravitational potential energy (GPE) is the energy an object has because of its height above a chosen reference level, such as the ground. Lifting an object requires work against its weight, and that work is stored.
GPE = m × g × h
m = mass (kg), g = gravitational field strength (9.8 N/kg on Earth), h = height above the reference level (m).
A 60 kg student climbs a staircase 3.0 m high. How much GPE does she gain?
GPE = mgh = 60 × 9.8 × 3.0 = 1764 J ≈ 1.8 kJ.
Elastic potential energy is stored when something springy is stretched or compressed. For many springs, Hooke's law applies: the force is proportional to the extension, F = kx, where k is the spring constant (N/m) and x the extension (m). The stored energy is the area under the force–extension graph:
Eelastic = ½ × k × x²
A spring with k = 200 N/m is stretched by 0.10 m. Find the force and the stored energy.
F = kx = 200 × 0.10 = 20 N. E = ½kx² = ½ × 200 × 0.10² = 1.0 J.
Energy cannot be created or destroyed. It can only be transferred from one place to another or transformed from one form into another. The total energy of an isolated system stays constant.
A swinging pendulum shows this beautifully. At the highest point it stops momentarily: all its energy is gravitational potential. As it swings down, GPE becomes kinetic energy, which is largest at the lowest point. Then it rises again, turning kinetic energy back into GPE. If there were no air resistance and no friction at the pivot, the swing would continue forever. In reality, a little energy is transferred to the air and the pivot as thermal energy at each swing, so the pendulum gradually slows.
A 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 m/s²)
Step 1. Loss of GPE = gain in KE: mgh = ½mv². The mass cancels.
Step 2. v² = 2gh = 2 × 9.8 × 5.0 = 98.
Step 3. v = √98 ≈ 9.9 m/s.
The same speed results for a heavy ball or a light one, and it agrees with the equations of motion (v² = u² + 2as).
In every energy transformation, some of the energy ends up in forms we did not want, usually as thermal energy spread out into the surroundings. We call this wasted energy (or dissipated energy). It has not disappeared, but it is spread so widely that it is no longer useful. A light bulb warms the room; a car engine warms the air; friction warms moving parts. The efficiency of a device tells us how much of the energy input becomes useful output.
efficiency = (useful energy output ÷ total energy input) × 100%
Efficiency can never be 100% or more for real devices.
A Sankey diagram shows energy flow with bands whose width is proportional to the amount of energy.
An electric motor takes in 500 J of electrical energy and lifts a load, gaining 400 J of useful energy. Find its efficiency and the wasted energy.
Efficiency = 400 ÷ 500 × 100% = 80%.
Wasted energy = 500 − 400 = 100 J (mostly as heat and sound).
To increase efficiency we reduce friction with lubricants and bearings, add insulation to cut heat loss, and use better designs and materials.
Power is the rate of transferring energy: P = E ÷ t. The unit is the watt (W), where 1 W = 1 J/s. A 60 W lamp transfers 60 J of energy every second. Electricity bills use the kilowatt-hour (1 kWh = 3.6 × 10⁶ J), as explained in the article on electricity and magnetism.
The student in Worked example 2 climbs the stairs in 4.0 s. What is her power?
P = E ÷ t = 1764 ÷ 4.0 ≈ 440 W (for a short burst).
Nearly all the energy we use comes, directly or indirectly, from the Sun. The Sun is powered by nuclear fusion, in which hydrogen nuclei join to form helium and release energy. Its total power output is about 3.8 × 10²⁶ W. At the Earth, sunlight arriving above the atmosphere delivers about 1361 W on each square metre facing the Sun, a quantity called the solar constant. Fossil fuels are the stored remains of ancient plants and animals that captured sunlight millions of years ago.
Non-renewable resources will run out or take millions of years to replace: coal, oil, natural gas and nuclear fuel (uranium). Renewable resources are replenished naturally on a human timescale: solar, wind, hydroelectric, geothermal, tidal and wave energy, and biomass.
| Resource | Advantages | Drawbacks |
|---|---|---|
| Coal | Plentiful, reliable, easy to store | Releases the most CO₂ per unit of energy plus air pollutants; non-renewable |
| Oil | Energy-dense, ideal for transport | Releases CO₂; spills harm wildlife; non-renewable |
| Natural gas | Releases less CO₂ than coal per unit of energy; flexible | Still releases CO₂; methane leaks are a strong greenhouse gas; non-renewable |
| Nuclear fission | Very low CO₂ in operation; large energy from a small mass of fuel | Radioactive waste needing long-term storage; high construction cost; accident risk is low but serious |
| Solar | No fuel and no emissions in use; works at any scale | Depends on sunshine, so needs storage or backup; manufacturing has an environmental cost |
| Wind | No fuel or emissions in use | Depends on wind; visual and noise impact; can affect birds and bats |
| Hydroelectric | Reliable, can store energy in reservoirs, quick to respond | Dams flood land, displace people and change river ecosystems |
| Geothermal | Steady day and night | Only suitable in certain regions |
| Tidal and wave | Predictable (tides) | Expensive, limited sites, effects on marine life |
| Biomass | Can be renewable if replanted; uses waste | Needs land; burning releases CO₂ and particles |
No resource is perfect. "Renewable" does not mean "no impact", and "non-renewable" does not mean "unusable"; real energy systems combine several sources and add storage, such as batteries and pumped storage hydro, to balance supply and demand.
A solar panel of area 2.0 m² receives sunlight of intensity 1000 W/m² (a typical test value for bright sun) and has an efficiency of 20%. Find its electrical power, and the energy collected in 5.0 hours of such sunlight.
Step 1. Input power = 1000 × 2.0 = 2000 W.
Step 2. Output power = 20% of 2000 = 400 W.
Step 3. Energy = 0.40 kW × 5.0 h = 2.0 kWh. Real output varies with weather, angle and temperature.
Water of mass 1000 kg falls through a height of 20 m every second. What is the maximum power available, and the output if the plant is 80% efficient?
Step 1. Energy per second = mgh = 1000 × 9.8 × 20 = 196 000 J/s = 196 kW.
Step 2. Output = 0.80 × 196 kW ≈ 157 kW.
Most electricity is made by a generator turned by a turbine, using the electromagnetic induction described in the article on electricity and magnetism. In a thermal power station (coal, gas, nuclear or biomass), the fuel's energy heats water into high-pressure steam, which spins the turbine. In hydroelectric, wind and tidal plants, moving water or air turns the turbine directly. Solar photovoltaic panels are different: they convert light directly into electricity with no moving parts.
A hydroelectric plant skips the boiler and its heat losses: gravitational potential energy of water stored high in a reservoir turns into kinetic energy as it falls through a pipe, spins the turbine, and the generator produces electricity.
Burning fossil fuels releases carbon dioxide, a greenhouse gas. The Intergovernmental Panel on Climate Change (IPCC) has concluded that human activities, mainly burning fossil fuels, have caused the observed global warming. Meanwhile, billions of people still need more energy for lighting, cooking, health care and education. Energy planning therefore balances supply, cost, reliability and environmental impact. Fossil fuels still provide most (roughly four-fifths) of the world's primary energy, but the share of renewables is growing quickly; consult the International Energy Agency (IEA) or the Energy Institute for the latest figures.
Energy in food. Our bodies run on chemical energy from food. Carbohydrates and proteins provide about 17 kJ per gram, and fat about 37 kJ per gram. Food energy is also quoted in Calories (kcal); 1 kcal = 4.184 kJ. Daily needs vary widely with age, sex and activity; adults typically need roughly 8000–11 000 kJ per day.
Try each question before opening the answer.
KE = ½mv² = ½ × 0.50 × 6.0² = 9.0 J.
GPE = mgh = 2.0 × 9.8 × 1.5 = 29.4 J.
KE ∝ v², so it increases by 3² = 9 times.
200 ÷ 800 × 100% = 25%.
E = Pt = 100 × (5 × 60) = 30 000 J.
Chemical energy in the battery → electrical energy → light energy (and some thermal energy).
Advantage: no fuel and no emissions while operating. Disadvantage: output depends on the wind, so backup or storage is needed.
Air resistance and friction at the pivot transfer some of its energy to the surroundings as heat, so its swing gradually decreases.
Hands-on ideas: release a pendulum or a trolley on a ramp from different heights and measure the speed with a phone video to test conservation of energy; measure the energy supplied to heat a known mass of water with a joulemeter; compare an LED lamp, a CFL and a filament lamp using a lux meter and a power meter; build a small wind turbine or solar-powered motor; discuss the energy sources used in your own country, using official statistics. Please handle hot water with care and supervise any use of mains-powered meters. Numerical values are rounded; check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions, constants and statistics were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: energy statistics change each year; the "four-fifths" figure for fossil fuels is approximate and should be checked against the latest IEA or Energy Institute release. Please check all values against your own syllabus or exam board specification before relying on them.
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