Physics · 1 Motion, forces and energy

1.7.1 Energy

Before you start

Mass is measured in kg and speed in m/s. Convert grams to kilograms (divide by $1000$ ) before you put a mass into any equation.
Weight is the gravitational force on a mass, $W = m g$ , where $g = 9.8$ N/kg near the Earth's surface.
Friction and air resistance are forces that act against motion.
Using the square and square-root keys on your calculator, and rearranging an equation to make a different quantity the subject.

Syllabus objectives covered (6)

State that energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal)
Describe how energy is transferred between stores during events and processes, including examples of transfer by forces (mechanical work done), electrical currents (electrical work done), heating, and by electromagnetic, sound and other waves
Know the principle of the conservation of energy and apply this principle to simple examples including the interpretation of simple flow diagrams
Recall and use the equation for kinetic energy Ek = ½mv²
Recall and use the equation for the change in gravitational potential energy ΔEp = mgΔh
Know the principle of the conservation of energy and apply this principle to complex examples involving multiple stages, including the interpretation of Sankey diagrams

Part 1 of 7

Energy sits in stores

Physics describes energy with two separate ideas: where the energy is, called a store, and how it gets from one store to another, called a transfer. Keep the two apart from the start. This section is about stores only.
The syllabus names seven stores. Learn them by exactly these names, because the names are what a 'State' question credits.
Kinetic: the energy an object has because it is moving. A rolling ball, a moving car and flowing water all have energy in their kinetic store.
Gravitational potential: the energy an object has because of its position in a gravitational field. Lift an object higher and its gravitational potential store increases.
Chemical: energy stored in fuels, food and batteries. Chemical reactions, such as burning a fuel, release it.
Elastic (strain): energy stored in an object that has been stretched, squashed or bent and will spring back. A stretched spring, a drawn bow and a squashed ball all have energy in an elastic store.
Nuclear: energy stored in the nuclei of atoms. Nuclear reactions release it, for example fission in a nuclear power station and fusion in the Sun.
Electrostatic: energy stored by electric charges that attract or repel each other. Two oppositely charged objects held apart have energy in an electrostatic store.
Internal (thermal): energy stored in the particles of a substance. Raising the temperature of an object increases its internal store.
Notice what is not on the list: light, sound and 'electrical energy'. None of these is a store. Each is a way of moving energy from one store to another, which is the next section. If you write 'light store' or 'electrical store', you have named a store that is not in the syllabus.

Part 2 of 7

Four ways energy moves between stores

Energy moves from one store to another in four ways: by forces, by electrical currents, by heating, and by waves. These are the transfers. They are not stores, because energy does not stay in them.
By forces (mechanical work done). When a force makes an object move in the direction of the force, it transfers energy. Your hand pushing a trolley, the weight of a falling ball and the friction force in a car's brakes all transfer energy this way. The energy transferred by a force is called the work done; the equation for it is the next subtopic.
By electrical currents (electrical work done). A current transfers energy from a battery, a solar cell or the mains supply to a component such as a lamp, a motor or a heater.
By heating. Energy transfers from a hotter object to a colder one because of the difference in temperature. A hot drink cools because energy transfers by heating from the drink to the cooler mug and air.
By waves. Electromagnetic waves (light, infrared, microwaves and the others), sound waves and other waves such as water waves all carry energy from one place to another. A lamp transfers energy by light. A loudspeaker transfers energy by sound.
To describe any event, use the same three pieces in order: the store that decreases, the way the energy is transferred, and the store or stores that increase. If one of the three pieces is missing, the description is incomplete.
Example: a car brakes to a stop. The kinetic store of the car decreases. The friction force between the brake pads and the discs transfers the energy (mechanical work done). The internal store of the brakes increases, and the hot brakes then transfer energy by heating to the air, so the internal store of the surroundings increases.
Example: an electric kettle boils water. The current transfers energy electrically from the mains to the heating element. The element transfers energy by heating to the water, so the internal store of the water increases. Some energy also heats the kettle itself and the air around it.

Part 3 of 7

Conservation of energy and simple flow diagrams

The principle of the conservation of energy: energy cannot be created or destroyed. It can only be transferred from one store to another, so the total amount of energy stays the same.
Use it as a counting rule. Add up the energy in every store before an event, and again after it. The two totals are equal, provided you include every store involved, including the surroundings.
So energy is never 'used up'. When a device 'wastes' energy, the energy has gone to a store you did not want, usually the internal store of the surroundings. It warms the surroundings by a very small amount.
Energy that has spread out into the surroundings like this is called dissipated energy. The energy is all still there, but it is spread so thinly that it is much less useful.
A simple flow diagram shows the energy going through a device. Boxes show the device or the stores, and arrows show the transfers, each labelled with the type of transfer and the amount of energy. This one is for a torch:
$chemical store of battery \overset{\overset{}{electrically}}{\to} lamp \overset{\overset{}{by light and by heating}}{\to} internal store of surroundings$
To use a flow diagram with numbers, apply the counting rule: total energy in equals total energy out. If a lamp receives $100$ J electrically and transfers $15$ J by light, the other $85$ J must transfer by heating. You need no information about the lamp, only that the total stays the same.
$100 J = 15 J + 85 J$
A swinging pendulum shows conservation all the time. At the top of each swing the bob stops for an instant: its kinetic store is zero and its gravitational potential store is at its largest. At the lowest point its gravitational potential store is at its smallest and its kinetic store is at its largest. The energy moves between these two stores by the work done by the bob's weight.
apparatus diagram — not drawn yet
A pendulum hanging from a fixed pivot, with the bob drawn at three positions along a dashed arc: at the left end of the swing labelled 'highest: kinetic store zero, gravitational potential store largest', at the bottom labelled 'lowest: kinetic store largest, gravitational potential store smallest', and at the right end labelled the same as the left.
Energy moves between the kinetic store and the gravitational potential store twice in every swing; the total stays the same.
Each swing is a little lower than the one before. The energy does not disappear. Air resistance and friction at the pivot transfer a little energy on every swing to the internal store of the air and the pivot.

Part 4 of 7

Kinetic energy: Ek = ½mv²

On the Extended papers you calculate the energy in an object's kinetic store. Paper 4 has no formula sheet, so you must recall this equation.
$E_{k} = \frac{1}{2} m v^{2}$
$E_{k}$ is the kinetic energy in joules (J), $m$ is the mass in kilograms (kg) and $v$ is the speed in metres per second (m/s). With those units, the answer is in joules.
Only the speed is squared. Square $v$ first, then multiply by $m$ , then halve. If you key $0.5 \times m \times v^{2}$ into your calculator in that order, nothing else gets squared.
Because speed is squared, it has a larger effect than mass. Double the mass and the kinetic energy doubles. Double the speed and the kinetic energy becomes four times as large. Triple the speed and it becomes nine times as large.
Kinetic energy uses speed, not velocity. $v^{2}$ is positive in whichever direction the object moves, so kinetic energy is never negative and has no direction.
To find a speed from a kinetic energy, rearrange: multiply both sides by $2$ , divide by $m$ , then take the square root. If you forget the square root, your answer is $v^{2}$ , not $v$ .
$v = \sqrt{\frac{2 E_{k}}{m}}$
Check the mass unit before you start. A $60$ g ball has a mass of $0.060$ kg. If you use $60$ , your answer is a thousand times too large.

Part 5 of 7

Change in gravitational potential energy: ΔEp = mgΔh

When an object moves up or down, its gravitational potential store changes. This equation gives the change, so you never need to decide where the store is zero.
$Δ E_{p} = m g Δ h$
$m$ is the mass in kg, $g$ is the gravitational field strength in N/kg, and $Δ h$ is the change in height in m. The answer is in J.
You do not have to memorise the value of $g$ . The front page of Paper 4 tells you to take the weight of $1.0$ kg as $9.8$ N, so $g = 9.8$ N/kg. This is the same number as the acceleration of free fall, $9.8$ m/s². Use $9.8$ , not $10$ .
$m g$ is the object's weight. So $Δ E_{p}$ is weight × change in height. It is the work done to lift the object against its weight.
$Δ h$ is the vertical change in height only. If you push a trolley $5.0$ m along a ramp that rises $1.2$ m, its gravitational potential store increases for a height of $1.2$ m. The distance along the slope is not in this equation.
When the object goes up, its store increases. When it comes down the same height, its store decreases by the same amount. The equation gives the size of the change; the situation tells you whether it is an increase or a decrease.

Part 6 of 7

Multi-stage problems: follow the energy through the chain

A complex example is several transfers linked together. Treat it as a chain. Write down every store at the start and every store at the end, then use conservation of energy to link them.
The simplest chain is a falling object with no air resistance. All the energy that leaves the gravitational potential store goes into the kinetic store.
$m g Δ h = \frac{1}{2} m v^{2}$
The mass is on both sides, so it cancels. With no air resistance, a heavy ball and a light ball dropped from the same height reach the ground at the same speed.
$v = \sqrt{2 g Δ h}$
Real objects are slowed by air resistance or friction. Then the kinetic store gains less energy than the gravitational potential store loses. The difference is the energy transferred to the internal store of the surroundings.
$energy to surroundings = decrease in E_{p} - increase in E_{k}$
The trap here is an object that is already moving at the start. Its starting kinetic energy is part of the starting total. Write the full balance every time.
$E_{k, start} + Δ E_{p} = E_{k, end} + energy to surroundings$
A bouncing ball is a longer chain. As it falls, energy goes from the gravitational potential store to the kinetic store. When it hits the floor and squashes, energy goes to its elastic store. As it springs back, energy returns to the kinetic store, and as it rises, to the gravitational potential store.
Each bounce is lower than the last. At every impact some energy transfers by sound and by heating, and air resistance transfers a little more during each flight. So less energy returns to the gravitational potential store each time.

Part 7 of 7

Sankey diagrams

A Sankey diagram is an energy flow diagram drawn to scale. The width of each arrow shows how much energy it carries.
The input arrow enters from the left and splits into output arrows. By convention the useful output continues straight on and each wasted output curves away from it.
graph diagram — not drawn yet
A Sankey diagram for an electric motor lifting a crate, drawn to the scale 1 mm represents 5 J: an input arrow 70 mm wide labelled '350 J electrically' enters from the left; it splits into a useful arrow 49 mm wide continuing straight to the right labelled '245 J to gravitational potential store of crate', and a wasted arrow 21 mm wide curving downwards labelled '105 J by heating and sound'.
The two output widths add up to the input width, 49 mm + 21 mm = 70 mm, because energy is conserved.
Because energy is conserved, the width of the input arrow equals the total width of all the output arrows. That one fact lets you find any missing arrow.
To read a Sankey diagram, find the scale (for example, $1$ mm represents $5$ J, or one grid square represents $50$ J). Measure or count the width of the arrow, then multiply by the scale.
To draw one, choose a scale that gives the input arrow a sensible width. Divide each energy by the scale to get each width, and check that the output widths add up to the input width before you draw. Label every arrow with what it is and how much energy it carries.
A Sankey diagram can also show a process with several stages. The useful arrow from one stage becomes the input to the next, and each stage has its own wasted arrow.
In the subtopic on energy resources you use the same diagram to calculate efficiency. Here you need only the energy balance: input = useful output + wasted output.

Worked examples

Example 1. A torch runs on a battery. While it is switched on, $1800$ J is transferred electrically from the battery to the lamp, and the lamp transfers $270$ J by light. Describe the energy transfers, and calculate the energy that the lamp transfers by heating.

Show the working

Start with the store that decreases. The energy comes from the chemical store of the battery.
Say how it moves. The current in the circuit transfers it electrically (electrical work done) to the lamp.
Say how it leaves the lamp. The lamp transfers energy by light, which is an electromagnetic wave, and by heating.
Say where it ends up. The light is absorbed by the surfaces it hits and the heating warms the air, so both end in the internal (thermal) store of the surroundings.
Now the number. Conservation of energy says the energy out of the lamp equals the energy into it. The lamp has two outputs, so the heating output is what is left after the light.
$E_{heating} = 1800 - 270 = 1530 J$
Check: $270 + 1530 = 1800$ J, which is the same as the input.

Answer: Chemical store of the battery → electrically to the lamp → by light and by heating → internal store of the surroundings. Energy transferred by heating $= 1530$ J.

Example 2. A cyclist and her bicycle have a total mass of $75$ kg. Calculate their kinetic energy at $8.0$ m/s, and the increase in their kinetic energy when they speed up to $12$ m/s.

Show the working

Recall the equation and check the units: mass in kg and speed in m/s, so the answer is in J.
$E_{k} = \frac{1}{2} m v^{2}$
At $8.0$ m/s, square the speed first, then multiply by the mass and halve.
$E_{k} = \frac{1}{2} \times 75 \times {8.0}^{2} = \frac{1}{2} \times 75 \times 64 = 2400 J$
At $12$ m/s, do the same.
$E_{k} = \frac{1}{2} \times 75 \times 12^{2} = \frac{1}{2} \times 75 \times 144 = 5400 J$
The increase is the final value minus the initial value.
$Δ E_{k} = 5400 - 2400 = 3000 J$
The trap: if you square the change in speed, $\frac{1}{2} \times 75 \times {4.0}^{2}$ , you get $600$ J, which is five times too small. Kinetic energy depends on the square of the speed, so find each kinetic energy and then subtract.

Answer: $2400$ J at $8.0$ m/s; the increase in kinetic energy is $3000$ J.

Example 3. A ball of mass $0.25$ kg is dropped from rest from a height of $3.2$ m. (a) Calculate the decrease in its gravitational potential energy as it falls to the ground. (b) Ignoring air resistance, calculate its speed just before it hits the ground. (c) Its speed just before it hits the ground is actually $7.5$ m/s. Calculate the energy transferred to the surroundings by air resistance.

Show the working

(a) The change in height is the whole $3.2$ m drop.
$Δ E_{p} = m g Δ h = 0.25 \times 9.8 \times 3.2 = 7.84 J$
(b) With no air resistance, all the energy that leaves the gravitational potential store goes into the kinetic store. So $E_{k} = 7.84$ J just before the ball hits the ground.
Rearrange $E_{k} = \frac{1}{2} m v^{2}$ for $v$ : multiply by $2$ , divide by $m$ , then take the square root.
$v = \sqrt{\frac{2 E_{k}}{m}} = \sqrt{\frac{2 \times 7.84}{0.25}} = \sqrt{62.72} = 7.9 m/s$
Check with $v = \sqrt{2 g Δ h} = \sqrt{2 \times 9.8 \times 3.2}$ . It gives the same $7.9$ m/s, because the mass cancels.
(c) Calculate the kinetic energy that the ball actually has.
$E_{k} = \frac{1}{2} \times 0.25 \times {7.5}^{2} = 7.03 J$
The gravitational potential store decreased by $7.84$ J, but only $7.03$ J went to the kinetic store. Conservation of energy says the difference went somewhere: air resistance did work on the ball and transferred it to the internal store of the air and the ball.
$7.84 - 7.03 = 0.81 J$

Answer: (a) $7.84$ J (about $7.8$ J); (b) $7.9$ m/s; (c) $0.81$ J.

Example 4. An electric motor lifts a crate of mass $10$ kg from rest through a vertical height of $2.5$ m, and the crate stops at the top. The motor is supplied with $350$ J electrically. Calculate the energy wasted, and work out the arrow widths for a Sankey diagram drawn with $1$ mm representing $5$ J.

Show the working

Trace the chain first. Energy is transferred electrically to the motor, and the motor's force on the rope does work on the crate. Energy is wasted by heating in the motor and by sound.
The crate starts and finishes at rest, so its kinetic store is the same at the end as at the start. The useful energy is the increase in its gravitational potential store.
$Δ E_{p} = m g Δ h = 10 \times 9.8 \times 2.5 = 245 J$
Conservation of energy: the energy that is not useful is wasted.
$E_{wasted} = 350 - 245 = 105 J$
For the Sankey widths, divide each energy by $5$ J per mm.
$350 \div 5 = 70 mm, 245 \div 5 = 49 mm, 105 \div 5 = 21 mm$
Check before you draw: $49 + 21 = 70$ mm, so the output widths add up to the input width. Draw the useful arrow straight on and the wasted arrow curving away, and label each one with its energy.

Answer: Energy wasted $= 105$ J. Arrow widths: input $70$ mm; useful (gravitational potential store of the crate) $49$ mm; wasted (heating and sound) $21$ mm.

Where people go wrong

Mistake: Working out $\frac{1}{2} m v^{2}$ as ${(\frac{1}{2} m v)}^{2}$ , or squaring the mass as well as the speed.

Instead: Square only $v$ , then multiply by $m$ and halve.

The equation squares the speed alone. For a $75$ kg cyclist at $8.0$ m/s, squaring the whole bracket gives $90 000$ J instead of the correct $2400$ J.

Mistake: Finding an increase in kinetic energy as $\frac{1}{2} m {(v_{2} - v_{1})}^{2}$ .

Instead: Calculate the kinetic energy at each speed, then subtract: $\frac{1}{2} m v_{2}^{2} - \frac{1}{2} m v_{1}^{2}$ .

Kinetic energy depends on the square of the speed. For a $75$ kg cyclist, going from $8.0$ m/s to $12$ m/s adds $3000$ J, but going from $0$ to $4.0$ m/s adds only $600$ J, although both are increases of $4.0$ m/s.

Mistake: Using the distance along a slope as $Δ h$ .

Instead: Use the vertical change in height only.

The gravitational potential store changes only when the object moves up or down, along the line of its weight, and weight acts vertically.

Mistake: Naming light, sound or 'electrical energy' as energy stores.

Instead: Call them transfers: energy is transferred by light (electromagnetic waves), by sound waves or by an electric current. The stores are the seven in the syllabus list.

A store is where energy is kept. Light, sound and current only carry energy from one store to another.

Mistake: Saying that wasted energy is 'lost', 'used up' or 'destroyed'.

Instead: Say where it went: 'transferred to the internal (thermal) store of the surroundings', or 'dissipated'.

Energy cannot be destroyed. A statement that it disappeared contradicts the principle of the conservation of energy.

Check yourself

An archer draws a bow and holds it still, ready to fire. Which store holds the energy? Which store increases when she releases the arrow, and how does the energy get there?
Answer
The elastic (strain) store of the bent bow. When she releases the arrow, the force of the string does work on the arrow (mechanical work done), so the kinetic store of the arrow increases.
A friend says that a lamp 'changes electrical energy into light energy'. Rewrite this in terms of stores and transfers.
Answer
A current transfers energy electrically to the lamp. The lamp transfers the energy by light (electromagnetic waves) and by heating to the surroundings, where it ends in the internal store. 'Electrical' and 'light' are ways of transferring energy, not stores.
Describe the energy transfers when a moving car brakes to a stop.
Answer
The kinetic store of the car decreases. The friction force at the brakes transfers the energy (mechanical work done) to the internal store of the brakes. The hot brakes transfer energy by heating to the air, so the internal store of the surroundings increases. Some energy may also be transferred by sound.
A pendulum is pulled to one side and released. Where in the swing is its kinetic store largest? Why is each swing a little lower than the one before?
Answer
At the lowest point of the swing, where its gravitational potential store is smallest. Each swing is lower because air resistance and friction at the pivot transfer some energy to the internal store of the surroundings. The energy is not destroyed.
Calculate the kinetic energy of a $0.50$ kg ball moving at $6.0$ m/s. What is its kinetic energy at $18$ m/s?
Answer
$E_{k} = \frac{1}{2} \times 0.50 \times {6.0}^{2} = 9.0$ J. At $18$ m/s the speed is three times as large, so the kinetic energy is $3^{2} = 9$ times as large: $81$ J.
A $50$ kg student climbs stairs that rise through a vertical height of $3.0$ m. Calculate the increase in her gravitational potential store.
Answer
$Δ E_{p} = m g Δ h = 50 \times 9.8 \times 3.0 = 1470$ J (about $1.5 \times 10^{3}$ J).
A ball of mass $0.20$ kg falls from rest through $5.0$ m and reaches the ground at $9.0$ m/s. Calculate the energy transferred to the surroundings by air resistance.
Answer
Decrease in gravitational potential energy $= 0.20 \times 9.8 \times 5.0 = 9.8$ J. Kinetic energy at the ground $= \frac{1}{2} \times 0.20 \times {9.0}^{2} = 8.1$ J. Energy transferred to the surroundings $= 9.8 - 8.1 = 1.7$ J.
A Sankey diagram is drawn with $1$ cm representing $40$ J. The input arrow is $5.0$ cm wide and the useful output arrow is $1.5$ cm wide. Determine the energy input, the useful energy output and the wasted energy.
Answer
Input $= 5.0 \times 40 = 200$ J. Useful output $= 1.5 \times 40 = 60$ J. Wasted $= 200 - 60 = 140$ J, which is drawn $3.5$ cm wide.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. A garden light has a solar cell, a rechargeable battery and an LED. During the day, light from the Sun falls on the solar cell and the battery charges. At night, the battery lights the LED.

(a) State the energy store of the battery that increases during the day. 1 mark No calculator

Mark scheme

B1 chemical (store)

(b) Describe the energy transfers at night, from the battery to the surroundings. 3 marks No calculator

Mark scheme

B1 energy from the chemical store of the battery
B1 transferred electrically / by an electric current to the LED
B1 transferred by light (electromagnetic waves) and by heating, ending in the internal (thermal) store of the surroundings; do not credit 'light store' or 'electrical store'

(c) During one night, $2700$ J is transferred electrically to the LED. The LED transfers $1080$ J by light. The rest is transferred by heating. Calculate the energy transferred by heating. 2 marks

Mark scheme

C1 2700 − 1080 seen, or energy in = energy out used
A1 1620 J; unit required

Question 2. A roller-coaster car of mass $500$ kg passes over the top of a hill at a speed of $4.0$ m/s. It then descends through a vertical height of $30$ m to the bottom of the track, where its speed is $23$ m/s. Take $g = 9.8$ N/kg.

(a) Calculate the kinetic energy of the car at the top of the hill. 2 marks

Mark scheme

C1 Ek = ½mv² or 0.5 × 500 × 4.0² seen
A1 4000 J (accept 4.0 × 10³ J); unit required

(b) Calculate the decrease in the gravitational potential energy of the car as it descends to the bottom of the track. 2 marks

Mark scheme

C1 ΔEp = mgΔh or 500 × 9.8 × 30 seen
A1 147 000 J (accept 1.47 × 10⁵ J or 1.5 × 10⁵ J); unit required

(c) Determine the energy transferred to the surroundings by friction and air resistance as the car moves from the top of the hill to the bottom of the track. 4 marks

Mark scheme

C1 kinetic energy at the bottom = 0.5 × 500 × 23² = 132 250 J (accept 1.32 × 10⁵ J)
C1 total energy at the top = 4000 + 147 000 = 151 000 J, ecf from (a) and (b); or increase in kinetic energy = 132 250 − 4000 = 128 250 J
C1 energy to surroundings = total energy at the top − kinetic energy at the bottom, or = decrease in gravitational potential energy − increase in kinetic energy, owtte
A1 18 750 J (accept 18 800 J, 1.88 × 10⁴ J or 1.9 × 10⁴ J); unit required

Question 3. An electric fan is supplied with $300$ J of energy electrically. $180$ J is transferred to the kinetic store of the air. The rest is transferred by heating and by sound.

(a) Calculate the total energy transferred by heating and by sound. 1 mark

Mark scheme

A1 120 J; unit required

(b) Sketch a Sankey diagram for the fan. Label each arrow with the energy it represents. 3 marks No calculator

Mark scheme

B1 one input arrow labelled 300 J (electrical) that splits into two output arrows
B1 output arrows labelled 180 J (kinetic store of the air, useful) and 120 J (heating and sound, wasted), ecf from (a)
B1 widths in proportion: the 180 J arrow is clearly wider than the 120 J arrow, and the two outputs together are as wide as the input

(c) Explain, using the principle of the conservation of energy, why the two output arrows together must be as wide as the input arrow. 2 marks No calculator

Mark scheme

B1 energy cannot be created or destroyed / the total energy stays the same
B1 the width of an arrow represents the amount of energy, so the total energy out equals the energy in and the total width out equals the width in, owtte

How this is examined

Following energy through a moving object that is slowed by friction or air resistance, to find the energy transferred to the surroundings: a structured question about a falling, sliding or rolling object: Calculate $E_{k}$ , Calculate $Δ E_{p}$ , then Determine the energy transferred to the surroundings from the two Each calculation scores separately: the equation or the substituted numbers earns a C mark, and the value with J earns the A mark. In the last part, the energy balance 'starting kinetic energy + decrease in gravitational potential energy = final kinetic energy + energy to surroundings' is the step that connects the parts. Include any starting kinetic energy.
Calculating kinetic energy or a change in gravitational potential energy from equations you recall: a 2-mark Calculate that substitutes into $E_{k} = \frac{1}{2} m v^{2}$ or $Δ E_{p} = m g Δ h$ , or a 3-mark one that also needs a rearrangement to find $v$ or $Δ h$ C1 for the equation or the substituted numbers, A1 for the correct value with the unit J (or m/s for a speed). Square only $v$ , use the vertical height, use $g = 9.8$ N/kg and mass in kg.
Describing an event as stores and transfers: a 2- or 3-mark Describe about a device or an everyday event, such as a battery-powered lamp or a braking car One marking point for each link: the named store that decreases (e.g. 'chemical store of the battery'), the named way the energy moves (electrically, by heating, by a force, by light or by sound), and the named store that increases (e.g. 'internal store of the surroundings'). Use the seven syllabus store names; 'light' and 'electrical' are not stores.
Reading or sketching a Sankey diagram so that it balances: a Sketch of a Sankey diagram from given energies, or a Determine that reads arrow widths against a scale A sketch scores for one input arrow that splits into labelled useful and wasted arrows, with widths in proportion so that the outputs together are as wide as the input. A reading scores for width × scale, then input − useful = wasted.
Stating conservation of energy and using it to say where 'wasted' energy went: a 1- or 2-mark State or Explain, or a Calculate that finds a missing output in a flow diagram 'Energy cannot be created or destroyed; it is only transferred from one store to another.' Then name the destination of the wasted energy: 'the internal (thermal) store of the surroundings'. For a flow diagram, energy in = total energy out.

Words to know

Energy store: A place where energy is kept: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic or internal (thermal).
Kinetic store: The energy an object has because it is moving: $E_{k} = \frac{1}{2} m v^{2}$ .
Gravitational potential store: The energy an object has because of its position in a gravitational field. Its change is $Δ E_{p} = m g Δ h$ .
Elastic (strain) store: The energy in an object that has been stretched, squashed or bent and will spring back.
Internal (thermal) store: The energy of the particles of a substance. Raising an object's temperature increases it.
Energy transfer: The movement of energy from one store to another: by forces (mechanical work done), by electrical currents (electrical work done), by heating, or by waves.
Work done: The energy transferred by a force, or by an electric current.
Conservation of energy: Energy cannot be created or destroyed; it can only be transferred from one store to another, so the total stays the same.
Dissipated energy: Energy that has spread out into the surroundings, usually into their internal store, where it is much less useful.
Sankey diagram: An energy flow diagram drawn to scale, in which the width of each arrow represents the amount of energy it carries.

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