The ramp, worked
50 kg, 6 m up: Ep = m g h = 50 × 9.8 × 6 = 2940 J
At the bottom, no friction: ½ × 50 × v² = 2940
v² = 117.6, so v = 10.8 m/s
Energy stores and transfers If energy is never used up, why does a rolling ball stop?
Foundation and Higher · AQA · 45 minutes
Students vote on how high a ball rolls up the far side of a smooth half-pipe, then follow its energy between stores on a virtual ramp, with friction off and on. Kinetic and gravitational energy, why mass cancels for a falling object, wasted energy and efficiency follow. Slides to present, a vote that shows who's stuck, practice and homework.
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A trolley of mass m kg: across is its speed in m/s, up its kinetic energy in joules. Move m. Then read the energy at 2 m/s and at 4 m/s: what does doubling the speed do to the energy? And doubling the mass?
y = 4x²/2
The idea in one minute
Energy is kept in stores: kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, magnetic and electrostatic. It moves between them in four ways: mechanically (a force moving something), electrically (a current), by heating and by radiation (waves such as light). It is never made or destroyed: in a closed system the total stays the same. Two stores can be worked out: kinetic energy Ek = ½ m v² and gravitational potential energy Ep = m g h (g = 9.8 N/kg). A falling or rolling object with no friction swaps one for the other, so ½ m v² = m g h and its speed is v = √(2 g h), whatever its mass. Energy that ends up spread out in the surroundings, usually heating them, is wasted: efficiency = useful output ÷ total input.
The lesson starts with a prediction before anyone explains: how high does a ball rise up the far side of a smooth half-pipe? A virtual ramp (a model, not a practical) then shows the stores as bars that always add up to the same total, first with no friction, then with friction taking energy into the thermal store. It is for Foundation and Higher; the stretch, a ball thrown upwards with air resistance, and ways of wasting less lean towards Higher.
By the end, students can
- name the energy stores and the four ways energy is transferred between them
- say where the energy goes in a change, using conservation of energy, never "used up"
- work out kinetic energy with Ek = ½ m v² and gravitational potential energy with Ep = m g h, and rearrange them
- find the speed of a falling or rolling object from ½ m v² = m g h, and explain why its mass cancels
- work out efficiency as a decimal and a percentage, and describe wasted energy in words
Key words
- energy store
- kinetic energy
- gravitational potential energy
- thermal store
- conservation of energy
- closed system
- wasted energy
- dissipated
- efficiency
- joule (J)
Before this lesson
Students should know weight = m g (g = 9.8 N/kg), square and square-root on a calculator, and rearrange a formula such as W = m g.
Next: Specific heat capacity.
The lesson, step by step
45 minutes in total. The stretch is optional.
5 min 1 · Hook · students think
How high will it go?
A ball let go on a smooth half-pipe: students vote on how high it rises on the far side before anyone explains.
Say“A ball is let go 2 m up a smooth half-pipe: no friction, no air resistance. How high does it get up the other side? Higher than 2 m, exactly 2 m, lower, or does it depend on its mass?”
Ask- At the top, where is its energy? At the bottom?
- And on a rough half-pipe: what would change?
Watch forSaying it goes higher because it speeds up on the way down, or that a heavier ball rises higher: keep both answers for the explain step.
For the teacher
Give a minute of silent thinking, then vote. Many choose C, because real things always slow down, or D, because heavier things seem to carry on further.
Don't explain yet. On a perfectly smooth track nothing takes energy out of the ball's stores, so it rises back to exactly 2 m, whatever its mass (B). On a real, rough track it rises less each time and stops: that is the lesson's question.
Take a vote with Ask the class: A, B, C or D. Keep the votes on the board for the explain step.
Shorter: Vote once, no discussion (−2 min).
14 min 2 · Explain · you explain
Stores, transfers and efficiency
The stores and the four ways energy moves; conservation answers the hook; Ek and Ep, a fall where the mass cancels; a virtual ramp; then wasted energy and efficiency.
Say“Energy is never used up. It sits in stores, and it moves between them mechanically, electrically, by heating or by radiation. The total stays the same.”
Ask- The ball at the top of the half-pipe: which store? At the bottom?
- A car brakes to a stop. Where did its kinetic energy go?
- A motor is 80% efficient. Where is the other 20%?
Watch forWriting ½ m v² as (½ m v)², or forgetting to square v: work out v² first, every time.
Efficiency
A motor: 500 J in, 400 J lifts the load
Efficiency = 400 ÷ 500 = 0.8, or 80%
The other 100 J heats the motor and the air
For the teacher
Stores: kinetic (anything moving), gravitational potential (anything raised), elastic potential (stretched, squashed or bent), thermal (anything warm), chemical (food, fuels, batteries), nuclear, magnetic and electrostatic. Ask students to name the store, not just the object: the energy is in the kinetic store of the car.
Four ways it moves: mechanically (a force moves something through a distance: work done), electrically (a current flows), by heating (from hotter to colder) and by radiation (waves such as light and sound). A torch: the battery's chemical store, electrically to the bulb, away as light and by heating, ending in the thermal store of the surroundings.
Conservation: energy is never made or destroyed, only moved between stores; in a closed system the total stays the same. Back to the hook: smooth, so the ball rises back to 2 m. Rough: friction heats the ball, the track and the air, the energy spreads out and is no use to us any more (wasted, or dissipated), so the ball rises less each time and stops.
Ek = ½ m v² (m in kg, v in m/s) and Ep = m g h (h in m, g = 9.8 N/kg), both in joules. Square the speed only, then multiply by the mass, then halve. 50 kg at 6 m: 2940 J; 50 kg at 4 m/s: 400 J.
Falling or rolling with no friction: all of m g h becomes ½ m v². The mass is on both sides and cancels: v² = 2 g h, v = √(2 g h). From 6 m, about 10.8 m/s, for any mass.
Try it: the ramp starts at 6 m with 50 kg and friction 0. It reads 2940 J in all, and the Total bar never changes: the ball rises back to its start height and the speed at the bottom reads 10.8 m/s. Set friction to 0.1: the thermal bar grows, each swing is lower, and in the end it stops. Change the mass: the total changes, the speed at the bottom doesn't.
Efficiency = useful output ÷ total input, as a decimal, or × 100 for a percentage; never more than 1. A Sankey diagram in words: 500 J in, 400 J useful to the load's gravitational store, 100 J wasted heating the motor and the air. (Higher) Waste less: lubricate moving parts, insulate, streamline.
Before the Try it slide, ask: with no friction, how high will the ball go up the far side, and how fast will it be at the bottom? Then let the class watch the bars.
Shorter: Name the stores in a line and skip the falling-speed slide (−5 min).
10 min 3 · Your turn · students write
Worked, then yours
Each worked example beside a twin that students solve themselves: Ep, Ek, a fall, a height from Ep, an efficiency.
Say“Units first: kilograms, metres, metres per second. Then the formula, then the numbers.”
Ask- Which store is that? Which formula goes with it?
- Did you square the speed?
Watch forForgetting the ½, or squaring before multiplying by the mass in the wrong order: ½ × m × v², the square on v alone.
A gravitational store
A 2.0 kg box is lifted 1.5 m
Ep = m g h = 2.0 × 9.8 × 1.5 = 29.4 J
Then theirs
A 0.50 kg ball is lifted 12 m. Its gain in Ep?
A kinetic store
A 0.40 kg ball moves at 5.0 m/s
Ek = ½ m v² = ½ × 0.40 × 5.0² = 5.0 J
Then theirs
A 1200 kg car moves at 10 m/s. Its Ek?
A fall: Ep becomes Ek
A stone falls 10 m from rest, no air resistance
½ m v² = m g h, so v = √(2 g h)
v = √(2 × 9.8 × 10) = √196 = 14 m/s
Then theirs
A stone falls 2.5 m from rest. Its speed?
Rearranging: a height
1176 J lifts a 20 kg sack. How high?
h = Ep ÷ (m g) = 1176 ÷ (20 × 9.8) = 6.0 m
Then theirs
2205 J lifts a 45 kg load. How high?
An efficiency
A motor: 800 J in, 600 J useful
Efficiency = 600 ÷ 800 = 0.75, or 75%
Then theirs
A kettle: 2000 J in, 1700 J heats the water. Its efficiency?
For the teacher
Work the first example aloud, saying the store each time: the gravitational store of the box. The second pair catches ½ × 1200 × 10 (v not squared) and 1200 × 10² (no ½).
The fall: ask who used the stone's mass. It isn't given, and it isn't needed. The rearranging pair catches 2205 ÷ 45 with g left out; the kettle, 2000 ÷ 1700, more than 1.
Open the answers slide once most have finished their twins.
Shorter: Do the first two pairs and the efficiency pair only (−3 min).
Longer: Each student writes a twin for a partner, its answer on the back (+3 min).
12 min 4 · Who's stuck? · students vote
Vote, then practise
One question shows who still thinks energy is used up; then practice in levels, and a ball thrown upwards as the stretch.
Say“Choose an answer on your own. Nobody talks until everyone has chosen.”
Ask- The pendulum has stopped. Where is the energy now? Could you get it back?
Watch forChoosing "used up" or "turned into air resistance": ask which store the energy is in now, and what got a little warmer.
Show your working on paper. Use g = 9.8 N/kg. Give energies in joules (J); turn grams into kilograms first. The stretch is optional.
The question that shows who's stuck
- A pendulum is let go 10 cm above its lowest point. Each swing is a little lower, and a few minutes later it hangs still. What has happened to the energy it started with?
In your Classroom, as they answer (an example) - A9
- B11
- C4
- D3
Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.
- A spring is stretched and held. Which store holds the energy you put in?
- A torch is switched on. Energy moves from the ___ store of its battery, is transferred ___ to the bulb, then away by ___ and by heating, ending in the ___ store of the surroundings.
- A 3.0 kg bag is lifted 2.0 m onto a shelf. How much energy goes into its gravitational store, in joules?
- A 60 kg runner moves at 5.0 m/s. How much energy is in her kinetic store, in joules?
- A 900 g ball rolls at 4.0 m/s. How much energy is in its kinetic store, in joules?
- A 0.50 kg ball has 49 J in its gravitational store, measured from the ground. How high is it, in metres?
- A stone is dropped from rest and falls 2.5 m. Ignoring air resistance, how fast is it going when it has fallen that far, in m/s?
- A 1 kg ball and a 4 kg ball roll from rest down the same smooth slope, 5 m high. Which is faster at the bottom?
- An electric motor is given 1200 J. It lifts a 15 kg load through 6.0 m. What is its efficiency, as a percentage?
- A light bulb is given 60 J each second. Of that, 51 J heats the bulb and the room around it. What is its efficiency, as a decimal?
- Stretch: a 0.20 kg ball is thrown straight up at 14 m/s. With no air resistance it would rise 10 m; with air resistance it rises only 9.0 m. How much energy, in joules, went to the thermal store of the air and the ball on the way up?
Support · For each question, write three things before any numbers: the store at the start, the way it moves, the store at the end. Then the formula, then the numbers in kilograms, metres and metres per second.
For the teacher
Everyone chooses before anyone explains. Then ask in turn: where is the energy at the start? Where is it at the end? How did it get there?
Questions 1–2 name stores and ways; 3–5 build fluency with Ep and Ek (5 is in grams); 6–8 rearrange and reason (8: the mass cancels); 9–10 are exam-style efficiencies. The stretch throws a ball upwards with air resistance.
Students show their working on paper or the board; the quiz keeps their final answers.
If many chose A or D, rub your hands together fast: they get warm. Ask which store the energy moved into, then what the air around a swinging pendulum does to it.
Shorter: After the vote, questions 1–5 only (−5 min).
Longer: The stretch: a ball thrown upwards, with air resistance (+8 min).
4 min 5 · Exit · students show
A child on a slide
A gravitational store at the top and a kinetic store at the bottom show who can follow energy, and say where the rest went.
Say“Ep at the top, Ek at the bottom. The difference went somewhere: where?”
Watch forGiving her kinetic store as the energy wasted.
Use g = 9.8 N/kg. Write the store at the top and the store at the bottom first.
- A 40 kg child sits at the top of a slide 3.0 m high. How much energy is in her gravitational store, measured from the bottom of the slide, in joules?
- She starts from rest and reaches the bottom at 6.0 m/s. How much energy, in joules, was wasted on the way down?
For the teacher
A 40 kg child at the top of a slide 3.0 m high, starting from rest. At the bottom she moves at 6.0 m/s.
Find her gravitational store at the top, then how much was wasted on the way down, and where it went.
Those who said the energy was used up need the half-pipe again next lesson; set the homework.
Longer: What fraction of her energy reached her kinetic store? Give it as an efficiency. (+4 min).
One to one: for every change, ask the student to say the store at the start, the way the energy moves and the store at the end, before any numbers; let them drive the virtual ramp while you only ask what they predict before each change.
Homework: Energy stores and transfers
Use g = 9.8 N/kg. For each change, write the store at the start and the store at the end before any numbers.
- Name the store that holds the energy: a stretched catapult, a hot cup of tea, a moving bike, a battery.
- A 1.2 kg book is lifted onto a shelf 1.5 m high. How much energy goes into its gravitational store?
- A 1000 kg car has 50 000 J in its kinetic store. How fast is it going?
- A diver drops from rest from a board 10 m above the water. Ignoring air resistance, how fast is she going as she reaches the water? Would a heavier diver be faster?
- A kettle is given 220 000 J, and 187 000 J of it heats the water. Find its efficiency as a decimal and a percentage, then describe where all the energy goes, in words.
- A ball is dropped and bounces lower each time. Explain why, using energy stores. Has any energy been destroyed?
Print the worksheet with working space and homework. Teacher answers come with your Library copy.
Teaching energy stores and transfers: common questions
Is this on Foundation and Higher, and in combined science?
Yes. In AQA GCSE Physics (8463) energy stores, Ek = ½ m v², Ep = m g h, conservation and efficiency are for both tiers, and the same content is in AQA's combined science. Describing ways to make a transfer more efficient is Higher only, and the stretch, a ball thrown upwards with air resistance, leans towards Higher.
Do students have to learn all eight stores?
They should recognise them and name the right one for a situation: kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, magnetic and electrostatic. The habit that matters most is naming the store, not the object: the energy is in the kinetic store of the car, not in the car.
Why does the mass cancel when something falls?
A heavier object has more energy in its gravitational store, m g h, but needs just as much more to speed up, ½ m v². Setting them equal, the m on each side cancels, leaving v = √(2 g h). This is only true while friction and air resistance can be ignored; the virtual ramp shows it by changing the mass and reading the speed at the bottom.
What is the virtual ramp, and is it a practical?
It is a simulation, a model of a ball on a curved ramp whose energy bars always add up to the same total. It is not a practical. With friction at 0 the ball rises back to its start height; with friction on, the thermal bar grows until the ball stops. Its friction setting is a number from 0 to 0.2 that says how rough the ramp is.
Where are Sankey diagrams and the elastic potential energy equation?
This lesson describes a Sankey diagram in words (energy in, useful out, wasted out, all adding up) so students see that the total is conserved before they draw one. The elastic potential energy equation, Ee = ½ k e², comes in the next lesson, on kinetic, gravitational and elastic energy.
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Yes. Read the lesson, print the worksheet and open its slides, with the virtual ramp, without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the quizzes, the answers and the answer slides.
Curriculum reference: AQA GCSE Physics 8463: 4.1.1.1 (energy stores and systems), 4.1.1.2 (changes in energy: kinetic and gravitational potential energy), 4.1.2.1 (energy transfers in a system: conservation and wasted energy) and 4.1.2.2 (efficiency).
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