How energy is stored and moved, how to calculate gravitational, kinetic and elastic energy, power and efficiency, and how the main energy resources compare.
Objectives
Name the main energy stores, describe how a system changes and how energy is transferred between stores.
Explain that energy is conserved, that wasted energy is dissipated, and how lubrication and insulation cut the waste.
Calculate gravitational potential energy, kinetic energy and elastic potential energy using the equations.
Calculate power and efficiency, with correct units.
Describe the main energy resources and compare them for reliability, environmental effects, cost and use over time.
Link the gravitational potential energy lost by a falling object to its kinetic energy, and describe ways to raise efficiency (Higher tier).
work done = force × distance (along the line of action of the force)
W=Fs
W work done (J)
F force (N)
s distance moved along the line of action (m)
change in thermal energy = mass × specific heat capacity × temperature change
ΔE=mcΔθ
ΔE change in thermal energy (J)
m mass (kg)
c specific heat capacity (J/kg°C)
Δθ temperature change (°C)
energy transferred = charge flow × potential difference
E=QV
E energy transferred (J)
Q charge flow (C)
V potential difference (V)
power = energy transferred ÷ time
P=tE
P power (W)
E energy transferred (J)
t time (s)
power = work done ÷ time
P=tW
P power (W)
W work done (J)
t time (s)
energy transferred = power × time
E=Pt
E energy transferred (J)
P power (W)
t time (s)
Energy stores and transfers explained
Start here
Think about your phone. It starts the day with a full battery and ends the day nearly empty, so where did that energy go? Some made the screen light up, some made the speaker work, and some made the back of the phone feel warm.
Energy is what makes things happen. Nothing moves, heats up, lights up or makes a sound unless energy is moved from one place to another, like a football flying through the air or a toaster glowing orange. We measure energy in joules, written J, and one joule is about the energy needed to lift an apple up by one metre.
Here is a way to picture it. Imagine your money kept in different places, such as a bank account, your pocket and a piggy bank. You can move money between them, but the total does not just disappear.
Energy works the same way. The places where it is kept are called stores, and moving energy from one store to another is called a transfer. Physicists keep a careful account of every joule.
By the end of this lesson you will be able to do four things. First, name the energy stores and say how energy moves between them. Second, use equations to work out gravitational, kinetic and elastic energy, power and efficiency. Third, explain why some energy is always wasted as heat and how to cut the waste. Fourth, compare the energy resources we use, such as coal, wind and solar.
Energy stores
A store is a place where energy is kept. Energy sitting in a store is not doing anything yet, and it only becomes useful when it moves to another store. Think of a water tank on a roof, where the water is ready to flow but nothing happens until you turn on a tap.
We often look at a system, which is an object or a group of objects. When a system changes, the way energy is stored in it changes. A ball thrown upwards, a kettle heating water and a car slowing down are all systems that change.
You already know some stores. A moving bike has energy in its kinetic store, and a mug of hot tea has energy in its thermal store. A battery, a bar of chocolate and a tank of petrol all have energy in a chemical store, and your body uses the chemical store in your breakfast to move your muscles.
A book on a high shelf has energy in its gravitational potential store, because it could fall. A stretched elastic band or a squashed spring has energy in its elastic potential store. The centre of an atom, called the nucleus, holds energy in the nuclear store, which is the store a nuclear power station uses.
The table shows one everyday example of each store. Learn the names, because exam questions often ask you to pick the right store and the name has to be exact.
A good habit is to ask what an object is doing. Is it moving, hot, lifted up, stretched or full of fuel? Each answer points to one store, and one object can have energy in several stores at once.
Energy transfers and conservation
Energy does not stay in one place. It moves from one store to another, and this is called an energy transfer. A kettle moves energy from the mains, along a wire, into the thermal store of the water.
There are four ways to transfer energy. Mechanically means a force moves something, and electrically means a current flows. By heating means energy moves from a hot thing to a cooler thing, and by waves means light or sound carries energy away.
Think of a child on a swing. At the top of the swing the energy is in the gravitational potential store, and as the swing goes down it is transferred to the kinetic store. Each swing goes a little lower than the last one, because some energy goes into the thermal store of the air and the chains through friction.
Here are some common situations. A ball thrown upwards: energy moves from your chemical store to the ball's kinetic store, then to its gravitational potential store as it rises. A moving object hits an obstacle: its kinetic store falls and the thermal store of the object, the obstacle and the air rises. A constant force accelerates an object: work done by the force fills its kinetic store. A vehicle slows down: kinetic energy moves to the thermal store of the brakes. A kettle boils water: electrical energy from the mains fills the thermal store of the water.
There are three main ways to change the energy stored in a system. A force can do work, with W = F × s. Heating can change the thermal store, with ΔE = m × c × Δθ. A current can do work, with E = Q × V. You meet these three in the forces, particle model and electricity lessons.
The key rule is conservation of energy. Energy can be stored, transferred or dissipated, but it cannot be created or destroyed. In a closed system, energy only moves between stores, so there is no net change in the total. Dissipated means spread out into the surroundings, usually as heat, where it is no longer useful.
A flow chart for a toy car. Energy starts in the chemical store of the battery, is transferred electrically along the wires, ends up in the kinetic store of the car, and some is dissipated to the thermal store of the surroundings.
Gravitational, kinetic and elastic energy
Lift a heavy bag onto a shelf and you can feel gravity pulling it down. You are working against gravity, so the higher you lift the bag and the heavier it is, the more energy goes into its gravitational potential store. Climbing a flight of stairs with a rucksack is the same idea.
In words: gravitational potential energy = mass × gravitational field strength × height. In symbols: gpe = m × g × h. The answer is in joules (J) when the mass is in kg, g is in N/kg and the height is in m. Take g = 10 N/kg in this lesson.
Check the units first. If the mass is in grams, divide by 1000 to get kilograms. If the height is in centimetres, divide by 100 to get metres. A 2 kg bag lifted 1 m gains 2 × 10 × 1 = 20 J. Lifted 2 m it gains 40 J, so twice the height means twice the energy.
Anything that moves has energy in its kinetic store. A rolling football has a little, and a speeding car has a huge amount. The more mass something has and the faster it goes, the more kinetic energy it has, so a lorry and a bicycle at the same speed are very different.
In words: kinetic energy = 0.5 × mass × speed². In symbols: ke = 0.5 × m × v². Mass is in kg, speed is in m/s and the answer is in joules. Always do the square first, because that is where most marks are lost. A 4 kg trolley at 3 m/s has 3² = 9, then 0.5 × 4 × 9 = 18 J.
If the speed is given in km/h, change it to m/s before you start. Speed is squared, so it matters more than mass. Double the speed and the kinetic energy goes up four times, which is why a car crash at 60 mph is far worse than one at 30 mph.
A stretched or squashed spring has energy in its elastic potential store. In words: elastic potential energy = 0.5 × spring constant × extension². In symbols: Ee = 0.5 × k × e². The spring constant is in N/m and the extension is in m. A spring with k = 40 N/m stretched by 0.10 m stores 0.5 × 40 × 0.10² = 0.2 J. This only works if the spring has not passed its limit of proportionality.
Higher tier: if there is no friction, all the gravitational potential energy lost by a falling object becomes kinetic energy. So m × g × h = 0.5 × m × v². The mass cancels, so v² = 2 × g × h.
Power
Two people carry the same box up the same stairs. One walks and one runs, so both transfer the same amount of energy, but the runner does it faster. The runner has the higher power.
Power is the rate of transferring energy, which means how much energy is moved each second. It is measured in watts (W), and one watt is one joule per second. A watt is a tiny amount, so many devices are rated in kilowatts.
In words: power = energy transferred ÷ time. In symbols: P = E ÷ t. Power is also the rate at which work is done, so power = work done ÷ time, P = W ÷ t, because work done is energy transferred. Energy is in joules (J), time is in seconds (s) and power is in watts (W).
A 2000 W kettle transfers 2000 J every second, and a 60 W bulb transfers 60 J every second. One kilowatt (kW) is 1000 W. A hoist that transfers 900 J in 15 s has a power of 900 ÷ 15 = 60 W.
Use the equation when you are given an amount of energy and a time. If you are given power and time, rearrange it to find the energy, E = P × t. Watch the time, which must be in seconds, so two minutes is 120 s and not 2 s.
A formula triangle for power. Energy E is at the top, and power P and time t are along the bottom. Cover the one you want to find.
Efficiency and reducing wasted energy
A phone charger gets warm while it works. The warmth is not what you wanted, because you wanted the energy to go into the battery. Only some of the energy does the job you want, and the rest leaks away as heat.
Useful energy is the energy transferred to where we want it. Wasted energy is the rest, and it is usually dissipated to the thermal store of the surroundings. A lamp is meant to give light but it also gets hot, and a motor is meant to turn but it also makes noise and warmth.
Efficiency tells us what share of the input energy is useful. In words: efficiency = useful output energy ÷ total input energy. In symbols: efficiency = E useful ÷ E total, and you multiply by 100 to make a percentage.
A toy motor takes in 100 J and gives out 40 J of useful energy, so the efficiency is 40 ÷ 100 = 0.4, which is 40%. The other 60 J is wasted as heat and sound. The Sankey diagram shows this as a wide arrow that splits in two, and the thicker the arrow, the more energy it carries.
Efficiency can never be more than 100%, because that would mean making energy from nothing. If you get an answer above 100%, you have divided the wrong way round. You can also use power: efficiency = useful power output ÷ total power input. Efficiency can be given as a decimal or a percentage.
You can cut unwanted energy transfers. Oil on moving parts is lubrication, and it reduces friction, so less energy is dissipated as heat. Thermal insulation, such as loft insulation, slows the flow of energy out of a house.
Different materials conduct heat at different rates. The higher the thermal conductivity of a material, the faster energy is transferred through it by conduction. A house cools more slowly if its walls are thicker, and if they are made of a material with a low thermal conductivity.
Higher tier: to increase the efficiency of a transfer, reduce the waste. Lubricate moving parts, insulate hot parts, make vehicles streamlined to cut air resistance, and use devices designed to waste less, such as an LED lamp instead of a filament lamp.
A Sankey diagram for a toy motor. 100 joules go in, 40 joules are useful and 60 joules are wasted to the surroundings, so the efficiency is 40 divided by 100 which is 0.4.
Energy resources
We use energy resources for transport, for making electricity and for heating. The main ones are the fossil fuels (coal, oil and gas), nuclear fuel, biofuel, wind, hydroelectricity, geothermal energy, the tides, the Sun and water waves.
A renewable resource is being replaced as it is used, or can be replaced. Wind, solar, hydroelectric, tides, waves, geothermal and biofuel are renewable. Fossil fuels and nuclear fuel are non-renewable. Once they are used up, they cannot be replaced in a human lifetime.
Petrol and diesel come from oil and power most vehicles. Biofuels can replace some of them. Electricity comes from power stations that burn gas or coal or use nuclear fuel, and also from wind turbines, falling water, tides, waves, geothermal heat and solar cells. Homes are heated mostly by gas boilers and electric heaters, and some use biofuels, solar panels or geothermal heat.
A reliable resource gives energy whenever we need it. Fossil fuels, nuclear fuel, biofuel and geothermal can run day and night. Wind and waves depend on the weather, and solar only works well in daylight. Tides are predictable, because they come at known times, but their size changes. Hydroelectricity is fairly reliable if a reservoir stores the water.
Burning fossil fuels releases carbon dioxide, which adds to global warming, and coal and oil can also cause acid rain. Nuclear power gives out no carbon dioxide, but it makes radioactive waste that stays dangerous for a very long time. Wind farms spoil views and can harm birds. Hydroelectric dams and tidal barrages flood land and change habitats. Growing biofuel crops uses land, but the crops take in carbon dioxide as they grow.
Cost matters too. Wind, solar and tidal power need no fuel, but they are expensive to build. Nuclear power stations cost a great deal to build and to close down. Fossil fuel costs rise and fall with the price of the fuel. Over recent years the UK has used less coal and much more wind and solar power. The reasons include climate targets, government choices and falling costs for renewables. Gas and nuclear still fill the gaps when the wind is weak.
Science can show what happens when we use an energy resource, but it cannot decide what we do. Those choices also depend on politics, money, society and ethics. A wind farm cuts carbon dioxide, but some neighbours dislike the view. A country with plenty of coal may keep using it because it is cheap and local jobs depend on it.
You may be asked about patterns and trends in energy use. Over time the use of renewable resources such as wind and solar has grown, while the use of coal has fallen in many countries. The reasons include the aim of reducing carbon dioxide emissions, falling costs of renewables and government policy. Fossil fuels are still used because they are reliable and the supply can be controlled.
When you describe a trend, quote figures from the graph or table, say whether the values rise or fall, and give a reason that fits the data. When you give a reason, make it a comparison: wind is renewable but is not available when the wind is not blowing, whereas a gas power station can be switched on when needed.
Recap
Energy is kept in stores and moved by transfers, and it is never created or destroyed. A system is an object or a group of objects. Wasted energy is dissipated to the thermal store of the surroundings, where it is not useful any more. A good answer always names the store.
The equations are gpe = m × g × h with g = 10 N/kg, ke = 0.5 × m × v², Ee = 0.5 × k × e², P = E ÷ t, and efficiency = useful output ÷ total input. Multiply the efficiency by 100 for a percentage. Lubrication and insulation raise the efficiency by cutting the waste.
Fossil fuels and nuclear fuel are non-renewable. Wind, solar, hydroelectric, tides, waves, geothermal and biofuel are renewable. Reliable resources work whenever we need them, and each resource has its own environmental effects and costs.
The units are joules (J) for energy, watts (W) for power, kilograms (kg) for mass, metres (m) for height, metres per second (m/s) for speed and seconds (s) for time.
How this is asked in an exam: a "name the store" question is usually one mark, and the exact store name earns it. A "calculate" question is usually two or three marks, so write the equation, substitute the numbers and give the answer with its unit. An "explain why the efficiency is below 100%" question wants the idea that some energy is dissipated to the thermal store of the surroundings. A resources question wants one fact and one reason, such as wind is renewable but not reliable because it depends on the weather.
Key points
Energy is kept in stores and moved by transfers. It is never created or destroyed.
gpe = m × g × h, with g = 10 N/kg. ke = 0.5 × m × v², and square the speed first. Ee = 0.5 × k × e² for a spring.
Power = energy transferred ÷ time, measured in watts. 1 W is 1 J/s.
Efficiency = useful output ÷ total input. Multiply by 100 for a percentage.
Wasted energy is dissipated to the thermal store of the surroundings. Lubrication and insulation cut the waste.
Fossil fuels and nuclear fuel are non-renewable. The others are renewable.
Compare resources by reliability, environmental effects, cost and how their use is changing.
Check units before you start: kg, m, m/s, s and J.
Worked examples
Example 1
A 3 kg box is lifted 4 m onto a shelf. Take g = 10 N/kg. Calculate the gravitational potential energy gained.
Write the equation: gpe = m × g × h
Substitute the numbers: gpe = 3 × 10 × 4
Work it out: 3 × 10 = 30, then 30 × 4 = 120 J
Answer: 120 J
Common slips
Slip: gpe = m × h The equation has three parts. g must be in it as well.
Slip: 3 × 4 = 12 This leaves out g. Multiply by 10 N/kg as well.
Slip: 12 J The sum 3 × 10 × 4 is 120, not 12. The 10 is easy to drop.
Example 2
A 4 kg trolley moves at 3 m/s. Calculate its kinetic energy.
Write the equation: ke = 0.5 × m × v²
Square the speed first: 3² = 3 × 3 = 9
Substitute and work out: 0.5 × 4 × 9 = 18 J
Answer: 18 J
Common slips
Slip: ke = m × v Kinetic energy needs the half, and the speed must be squared.
Slip: 0.5 × 4 × 3 = 6 The speed was not squared. 3² is 9, not 3.
Slip: 6 J This comes from using 3 instead of 3². Using 9 gives 0.5 × 4 × 9 = 18.
Example 3
A heater takes in 800 J of energy and transfers 200 J to the room as useful heat. Calculate the efficiency as a percentage and say where the rest of the energy goes.
Write the equation: efficiency = useful ÷ total × 100
Substitute the numbers: 200 ÷ 800 × 100
Work out 200 ÷ 800 = 0.25, then × 100 = 25%. The other 600 J is dissipated to the thermal store of the surroundings.
Answer: 25%
Common slips
Slip: efficiency = total ÷ useful The useful energy goes on top. Efficiency cannot be above 100%.
Slip: 800 ÷ 200 = 4 This divides the wrong way round. Divide 200 by 800, then convert to a percentage.
Slip: 4% Dividing the wrong way gives 4. The correct sum is 200 ÷ 800 × 100 = 25%.
Questions and answers
Energy stores and transfers practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
A 7 kg bag of sand is raised 5 m. Work out the energy gained in the gravitational store. Take g = 10 N/kg.
Show answer
Answer: 350 J
gpe = m × g × h
7 × 10 × 5 = 350 J
Question 2 Easy
A 2 kg bag of sand is raised 5 m. Work out the energy gained in the gravitational store. Take g = 10 N/kg.
Show answer
Answer: 100 J
gpe = m × g × h
2 × 10 × 5 = 100 J
Question 3 Easy
Chris lifts a 6 kg crate by 6 m at a warehouse. Calculate the gravitational potential energy gained. Take g = 10 N/kg.
Show answer
Answer: 360 J
gpe = m × g × h
6 × 10 × 6 = 360 J
Question 4 Easy
A 6 kg crate is raised 4 m. Work out the energy gained in the gravitational store. Take g = 10 N/kg.
Show answer
Answer: 240 J
gpe = m × g × h
6 × 10 × 4 = 240 J
Question 5 Medium
Work out the kinetic energy of a 10 kg cart moving at 7 m/s.
Show answer
Answer: 245 J
ke = 0.5 × m × v²
0.5 × 10 × 7² = 245 J
Question 6 Medium
Leila finds an 8 kg trolley moving at 6 m/s. Calculate its kinetic energy.
Show answer
Answer: 144 J
ke = 0.5 × m × v²
0.5 × 8 × 6² = 144 J
Question 7 Medium
Leila's winch transfers 1600 J in 50 s. Calculate the power.
Show answer
Answer: 32 W
power = energy ÷ time
1600 ÷ 50 = 32 W
Question 8 Medium
A motor transfers 1600 J in 20 s. Work out the power.
Show answer
Answer: 80 W
power = energy ÷ time
1600 ÷ 20 = 80 W
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A kettle transfers 600 J to the water from 1500 J taken from the mains.
(a) Calculate the efficiency. [2 marks]
(b) Explain why the efficiency is below 100%. [2 marks]
Show answer and marking points
Answer: (a) 40% (b) Some energy is dissipated to the thermal store of the surroundings.
(a) 600 ÷ 1500 × 100 (1)
(a) 40% (1)
(b) energy is dissipated or wasted (1)
(b) to the thermal store of the surroundings (1)
Exam-style question 24 marks
A 4 kg bag is lifted 5 m. Take g = 10 N/kg.
(a) Calculate the gravitational potential energy gained. [2 marks]
(b) State the unit of energy. [1 mark]
(c) The bag is dropped. State the energy store that increases as it falls. [1 mark]
Show answer and marking points
Answer: (a) 200 J (b) joule (c) kinetic store
(a) 4 × 10 × 5 (1)
(a) 200 J (1)
(b) joule or J (1)
(c) kinetic store (1)
Common mistakes
Leaving g out of gpe = m × g × h
Multiply the mass, g and the height. Take g = 10 N/kg unless you are told otherwise.
Forgetting to square the speed, or forgetting the half, in kinetic energy
Square the speed first. Then multiply by the mass and by 0.5.
Saying friction destroys energy
Friction transfers energy to the thermal store of the surroundings. The total stays the same.
Dividing total energy by useful energy to find efficiency
Divide the useful output by the total input, then multiply by 100 for a percentage. It cannot be above 100%.
Using grams or minutes in an equation without changing them
Change grams to kilograms by dividing by 1000. Change minutes to seconds by multiplying by 60.
Questions students ask
Is Energy stores and transfers on the Foundation or Higher tier?
Energy stores and transfers is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 5.
What is a common mistake on Energy stores and transfers?
Leaving g out of gpe = m × g × h. Multiply the mass, g and the height. Take g = 10 N/kg unless you are told otherwise.
Where are the answers to the Energy stores and transfers questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.