Middle School Physical Science

The paper towel that refuses to get wet

Push a crumpled paper towel into the bottom of a drinking glass so it will not fall out. Turn the glass upside down and push it straight down into a bowl of water until the glass is completely under. Hold it there. Pull it back out and unwrap the towel.

It is dry. Not damp. Dry.

Something was already inside that glass, and it would not move over to make room for the water. You could not see it, taste it, or feel it in the way you feel a chair, but it took up the whole space and held the water at bay. That something was air, and it is matter, exactly as much as the glass is.

Key idea: Matter is anything that has mass and takes up space, whether or not you can see it.

Mass and volume, which are not the same thing

Two words do most of the work in this course, so get them apart now.

• Mass is how much stuff there is. It is measured in grams and kilograms, and a kitchen scale reads it.
• Volume is how much space that stuff takes up. It is measured in cubic centimetres, millilitres and litres, and a measuring jug reads it.

A kilogram of feathers and a kilogram of lead have the same mass and wildly different volumes. The feathers fill a sack; the lead fits in your hand. That relationship between the two has a name, density, which is mass divided by volume. Water comes out at about 1 gram for every cubic centimetre, which is a handy number to carry: anything denser than that sinks in water and anything less dense floats.

Some things you deal with every day are not matter at all, because they have no mass and take up no space. Light is not matter. Sound is not matter. Heat is not matter. They are all forms of energy, which is a different sort of thing entirely and gets its own module later. A useful test: if you cannot put it on a scale, it is probably not matter.

The particle model, in three sentences

Nobody has ever seen an individual particle of air with their own eyes. What scientists have is a model, which is a simplified picture that explains what you can observe and lets you predict what you have not seen yet. The particle model of matter says three things.

1. All matter is made of extremely small particles. Far too small to see, even with a school microscope.
2. Those particles are always moving. Never still, not even in a block of ice. Warmer means faster.
3. There is space between the particles. How much space depends on the state, and that is the whole of the next lesson.

Three sentences, and they explain an enormous amount. Watch them work.

Four everyday things the model explains

You can smell toast from another room. Particles from the toast leave it, move about randomly, and spread through the air until some reach your nose. This spreading is called diffusion. It takes time, which is why the smell arrives a while after the toast pops, and it is faster in a warm room because warm particles move faster.

Sugar disappears into tea. The sugar has not vanished, it has broken apart into individual particles that fit into the gaps between the water particles. The tea gets slightly heavier and tastes sweet, which are exactly the two things the model predicts.

A bicycle pump can be squashed with your thumb over the end. Gas particles have big gaps between them, so pushing the plunger just moves them closer together. Nothing is destroyed and nothing leaks; the same particles now occupy less space.

A syringe full of water cannot be squashed at all. Same syringe, different contents, completely different result. In a liquid the particles are already touching. There is almost no gap left to close, so the plunger will not move however hard you press. This is why the brakes on a car use liquid in the pipes rather than air: pressing the pedal has to move the brake instantly, not first squash a gas.

Why this matters: A gas is squashable and a liquid is not, and that single difference comes straight from how much empty space sits between the particles.

Experiment: prove air is really there

This one is completely safe and needs nothing sharp, hot or unusual. Do it over a sink.

1. Crumple a paper towel or a tissue and push it firmly into the bottom of a clear drinking glass. Turn the glass upside down and shake it once; the paper must stay put.
2. Fill a mixing bowl or a sink about two thirds with cold water.
3. Hold the glass perfectly upside down, straight up and down, not tilted.
4. Push it straight down into the water until the whole glass is under the surface. Hold it there for ten seconds.
5. Lift it straight back out, still upside down. Dry the rim, then pull the paper out and feel it.
6. Now repeat the whole thing, but this time tilt the glass slightly once it is under the water.

What to expect: The first time, the paper comes out dry. The second time, you will see bubbles escape as you tilt, and the paper comes out wet.

Why it happens: The glass was full of air before you started, and air is matter, so it occupies the space. Water cannot get in because there is nowhere for the air to go. Tilting opens an escape route at the rim, the air bubbles out, water floods in to replace it, and the paper soaks. The bubbles you see are the proof: that is the air you could not see, made visible for a second as it leaves.

A second experiment: watching diffusion happen

1. Fill two identical clear glasses with water, one with cold water from the tap and one with warm water from the tap. Do not use hot water; warm from the tap is enough and keeps this safe to do alone.
2. Let both stand still for two minutes so the water stops swirling.
3. Gently add one drop of food colouring to each, right in the centre, without stirring.
4. Watch for five minutes without touching either glass.

What to expect: The colour spreads through both glasses, and it spreads noticeably faster in the warm one.

Why it happens: Nobody stirred, so the spreading was done by the particles themselves, moving randomly and mixing. That is diffusion, and it is direct evidence for part two of the model. The warm water spreads faster because its particles are moving faster, which is what temperature measures. If particles were still, the drop would sit there as a dot forever.

Common misconceptions

"Air is nothing, or empty space." Air is matter. It has mass, which is why a football feels heavier when pumped up, and it takes up space, which is why the paper towel stayed dry.

"The particles in a solid are not moving." They are, all the time. In a solid they vibrate in place rather than travelling, but they never stop while the material is above absolute zero, which nothing on Earth is.

"When sugar dissolves it disappears." It spreads out into individual particles too small to see. Put the glass on a scale before and after and the mass is unchanged, which is what tells you the sugar is still there.

"Heat and light are kinds of matter." Neither has mass and neither takes up space. They are energy. This distinction becomes important in the energy module, so it is worth fixing early.

What to carry forward

• Matter is anything with mass that takes up space. Light, heat and sound are not matter.
• Mass is how much stuff; volume is how much space; density is mass divided by volume.
• The particle model: matter is made of tiny particles, they are always moving, and there is space between them.
• Diffusion, dissolving and the squashability of gases are all explained by that one model.
• A gas squashes because of the gaps between its particles; a liquid barely squashes because there are almost none.

The next lesson changes just one thing, the amount of space between particles, and gets solids, liquids, gases and every change between them.

Sources

1. National Geographic Society. (n.d.). Matter. National Geographic Education. education.nationalgeographic.org
2. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Phases and classification of matter. Chemistry 2e. OpenStax, Rice University. openstax.org
3. Khan Academy. (n.d.). Middle school chemistry. khanacademy.org
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). States of matter: basics. phet.colorado.edu

Ice at zero degrees, water at zero degrees

Put a thermometer into a glass of crushed ice and stir. It reads 0 degrees Celsius. Leave it on the counter for twenty minutes so half the ice melts, and stir again. It still reads 0 degrees Celsius.

The room has been pouring heat into that glass for twenty minutes and the temperature has not moved a single degree. That is strange enough to need an explanation, and the explanation is the whole point of this lesson.

Key idea: Heat added during a change of state goes into pulling particles apart, not into making them move faster, so the temperature stays flat until the change is finished.

Three states, one difference

Solid, liquid and gas are not three different substances. They are the same particles at three different spacings and speeds.

	Solid	Liquid	Gas
Arrangement	Packed in a regular pattern, touching	Close together, touching, but disordered	Far apart, mostly empty space
Movement	Vibrate on the spot	Slide past one another	Fly about freely and fast
Shape	Keeps its own	Takes the shape of the container	Fills the whole container
Volume	Fixed	Fixed	Not fixed, expands to fill
Squashable?	Almost not at all	Almost not at all	Yes, easily

Read the shape row carefully, because it is where the difference between a solid and a liquid actually lives. A litre of milk poured from a bottle into a bowl becomes bowl-shaped without changing volume. A litre of ice will not do that. In the liquid the particles can slide past each other, so the material flows; in the solid they are locked into position and can only vibrate.

The six changes, and which way energy goes

Each change of state has a name, and each one either takes energy in or gives it out.

Change	From	To	Energy	Everyday example
Melting	Solid	Liquid	Taken in	An ice cube on a warm plate
Freezing	Liquid	Solid	Given out	Water in an ice tray
Evaporating or boiling	Liquid	Gas	Taken in	A puddle drying in the sun
Condensing	Gas	Liquid	Given out	Mist on a cold window
Subliming	Solid	Gas	Taken in	Solid carbon dioxide turning straight to gas
Depositing	Gas	Solid	Given out	Frost forming on grass overnight

The pattern is simple once you see it: any change that spreads particles further apart needs energy put in, and any change that brings them closer together releases energy. Melting, evaporating and subliming all take energy. Freezing, condensing and depositing all give it back.

That is why sweating cools you. The sweat evaporating from your skin needs energy to do it, and it takes that energy from your skin, which is exactly what feeling cooler means.

Melting and boiling points belong to the substance

Every pure substance changes state at its own temperatures, and those temperatures are as much a property of it as its colour.

Substance	Melting point	Boiling point
Water	0 degrees Celsius	100 degrees Celsius
Iron	about 1538 degrees Celsius	about 2862 degrees Celsius
Oxygen	about −219 degrees Celsius	about −183 degrees Celsius

Look at the oxygen row and something clicks. Oxygen is a gas in your room not because it is a gas by nature, but because your room is more than 180 degrees above its boiling point. Cool it enough and it becomes a liquid, then a solid, with the same particles the whole way. There is nothing special about being a gas; it depends entirely on the temperature you happen to be at. By exactly the same reasoning, iron is a solid in your kitchen only because your kitchen is nowhere near 1538 degrees.

The two water numbers hold at sea level. Up a mountain, where the air pushes down less hard, water boils at a lower temperature, which is why cooking instructions at altitude tell you to allow longer.

Remember: There is no such thing as a substance that is a solid, full stop. There are only substances that are solid at the temperature you are asking about.

Back to the flat thermometer

Now the opening puzzle can be answered properly. Heat a beaker of ice steadily and plot temperature against time. The graph does something surprising: it climbs, goes flat, climbs, goes flat, climbs.

1. Below 0 degrees, the added energy makes the ice particles vibrate harder, so the temperature rises.
2. At 0 degrees the graph goes flat. All the energy arriving is being used to break the particles out of their fixed positions so they can slide. Temperature does not move until every last piece of ice has melted.
3. Between 0 and 100 degrees, energy makes the liquid particles move faster again, so the temperature climbs.
4. At 100 degrees it goes flat again, while energy is used to tear the particles fully apart into a gas.
5. Above that, the steam heats up.

Temperature measures how fast particles are moving. During a change of state, the incoming energy is not speeding them up, it is separating them, so the thermometer has nothing to report. That is why a drink with ice in it stays at about the same temperature until the last cube has gone, and then starts to warm quickly.

Evaporating is not the same as boiling

Both turn a liquid into a gas, and they are different processes.

• Boiling happens at one particular temperature, throughout the whole liquid, with bubbles forming inside it.
• Evaporation happens at any temperature, only at the surface, with no bubbles.

A puddle dries up on a cold day even though it is nowhere near 100 degrees. Particles at the surface that happen to be moving fastest can escape into the air, and the puddle slowly empties one escaping particle at a time. Wind speeds it up by carrying escaped particles away, and a larger surface area speeds it up by giving more particles a place to leave from, which is why wet washing is hung out spread wide rather than in a bundle.

The odd thing water does

Almost every substance takes up less space as a solid than as a liquid, because cooling packs the particles closer. Water breaks that rule: it expands by roughly 9 percent when it freezes.

Two consequences you have seen. Ice floats, because the same mass now fills more space and is therefore less dense than the water beneath it, which is why ponds freeze from the top down and fish survive the winter underneath. And a full bottle of water left in a freezer bulges or splits, because the ice needs more room than the bottle has. The same effect cracks water pipes in cold weather and, over centuries, breaks rock apart.

Experiment: catch condensation in the act

Safe to do alone. Nothing here is hot or sharp.

1. Put a clean, dry drinking glass in the fridge for fifteen minutes. Dry the outside carefully when you take it out.
2. Look closely at the outside surface and confirm it is dry.
3. Set it on the counter in a warm room and leave it for five minutes.
4. Touch the outside. Then, using a paper towel, dry it completely and watch what happens over the next few minutes.
5. As a second test, breathe out slowly onto a cold window or a mirror.

What to expect: The outside of the glass becomes wet, and it becomes wet again after you dry it. Your breath leaves a patch of mist on the window that fades away.

Why it happens: The water did not leak through the glass, and it did not come out of the drink. Air always carries some water as an invisible gas. When that air touches the cold surface, it loses energy, its water particles slow down and pull together into a liquid, and droplets form. That is condensation, and it gives energy out, which is why the glass warms slightly. Your breath does the same thing on the window, and the mist fades because the warmer room evaporates it again.

Experiment: race two puddles

1. Measure exactly two tablespoons of water into a wide dinner plate and the same amount into a narrow cup or glass.
2. Stand both in the same warm spot, well away from anything that might spill them.
3. Check both after two hours, then again after a day.

What to expect: The plate empties far sooner. The cup can still have water in it a day later.

Why it happens: Evaporation only happens at the surface, and the plate offers a much larger surface for the same amount of water. More particles are near the top where they can escape, so more escape per minute. Same liquid, same temperature, different surface area, different speed.

Common misconceptions

"The water on the outside of a cold glass leaked through it." Glass does not leak. The water condensed out of the air, which always carries some water as an invisible gas. Try it with a sealed empty glass and it still gets wet.

"Steam is the white cloud you see above a kettle." True steam is an invisible gas. The white cloud is tiny droplets of liquid water that have already condensed in the cooler air. Look just above the spout and you will see a clear gap: that gap is the actual steam.

"Adding heat always raises the temperature." Not during a change of state. At 0 degrees the energy goes into melting rather than warming, and the thermometer stays put until the last ice has gone.

"Ice floats because it is lighter." A block of ice can weigh a great deal. It floats because it is less dense: freezing makes water expand by about 9 percent, so the same mass takes up more space than the liquid beneath it.

The short version

• Solids, liquids and gases differ in particle spacing, arrangement and speed, not in what the particles are.
• Changes that spread particles apart take energy in; changes that bring them together give energy out.
• Melting and boiling points are properties of the substance, so whether something is solid or gas depends on the temperature you ask at.
• Temperature stays flat during a change of state, because the energy is separating particles rather than speeding them up.
• Evaporation happens at the surface at any temperature; boiling happens throughout at one temperature.
• Water is unusual: it expands on freezing, which is why ice floats and pipes burst.

Next: what happens when two different substances are in the same container, and how to get them apart again.

Sources

1. Khan Academy. (n.d.). States of matter. Middle school chemistry. khanacademy.org
2. NASA Glenn Research Center. (n.d.). States of matter. Beginner's Guide to Aeronautics. grc.nasa.gov
3. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). States of matter: basics. phet.colorado.edu
4. Wikipedia contributors. (n.d.). State of matter. Wikipedia. en.wikipedia.org

Thirty-five grams of salt in every kilogram of sea

Seawater is about 3.5 percent salt by mass, which is roughly 35 grams of dissolved salts in every kilogram. Scoop some up and it looks like ordinary water. Nothing floats in it, nothing settles out of it, and you cannot filter the salt back out with any paper on Earth.

And yet the salt is unquestionably in there. Leave a shallow dish of seawater in the sun for a week and you will find a white crust in the bottom, and the water will be gone.

Seawater is a mixture, and the interesting question is not whether the salt is present but what property of it lets you get it out again. That question is what this lesson is really about.

Key idea: Every separation method works by exploiting one property in which the components differ. Choose the property first, and the method chooses itself.

Pure substances and mixtures

A pure substance contains only one kind of particle throughout. Distilled water is a pure substance. So is table salt, and so is copper.

A mixture contains two or more substances that are physically jumbled together but not chemically joined. Air is a mixture. Seawater is a mixture. Milk, sand, muddy water, brass and a bowl of cereal are all mixtures.

Two features of mixtures matter for everything that follows.

1. The proportions can vary. Seawater can be saltier or less salty and still be seawater. A pure substance has no such flexibility; water is always exactly water.
2. The parts keep their own properties. Salt in seawater still tastes salty. Iron filings mixed into sand are still attracted to a magnet. Nothing has been chemically changed, so nothing has lost what it was.

That second point is why mixtures can always be separated by physical means. Nothing needs to be undone chemically, because nothing was chemically done.

Solutions and suspensions

Not all mixtures look alike, and the difference is about particle size.

	Solution	Suspension
Example	Salt in water, sugar in tea	Sand in water, flour in water
Appearance	Clear, though it may be coloured	Cloudy
Does it settle if left?	No, never	Yes, given time
Can filter paper catch it?	No, the particles are far too small	Yes
Particle size	Individual particles, spread evenly	Clumps big enough to see or to trap

The vocabulary for a solution is worth getting right, because it comes up constantly.

• The solute is what dissolves. In salt water it is the salt.
• The solvent is what does the dissolving. In salt water it is the water.
• The solution is the result: the two together, evenly mixed.

Water is called the universal solvent because it dissolves more substances than any other common liquid, but it does not dissolve everything. Oil, sand and wax all refuse.

What matters here: Dissolving is not melting. Melting needs heat and turns one substance from solid to liquid. Dissolving needs a solvent and spreads one substance through another. Salt melts at about 800 degrees Celsius, and none of that happens in your glass of cold water.

What makes something dissolve faster

Three things speed up dissolving, and all three come straight from the particle model.

1. Stirring. This moves solvent that has already got its share of solute out of the way and brings fresh solvent to the surface.
2. Heating. Warmer particles move faster and hit the solid harder and more often, knocking particles off its surface more quickly.
3. Grinding it smaller. Dissolving happens at the surface, so breaking a lump into powder exposes far more surface for the same amount of solid. It is the same reasoning as the puddle on the plate in the last lesson.

None of those three changes how much can eventually dissolve. They change how long it takes. Only temperature changes the limit, and it is a real limit: keep adding sugar to a cup of tea and eventually it stops disappearing and sits on the bottom. At that point the solution is saturated, meaning it is holding all the solute it can at that temperature. Warm it and it will take more; cool it again and some comes back out as crystals, which is exactly how rock candy is made.

Choosing a separation method

Here is the table this lesson exists for. Read the third column first, because it is the one that decides.

Method	What it does	The property it exploits	Use it for
Picking out by hand	Separates visible pieces	Size and appearance	Sweets by colour, stones from lentils
Sieving	Holds back the larger pieces	Particle size	Pasta from cooking water, gravel from sand
Using a magnet	Pulls out magnetic material	Magnetism	Iron filings from sand
Filtration	Traps undissolved solids, lets liquid through	Whether the solid is dissolved	Sand from water, tea leaves from tea
Evaporation	Removes the solvent, leaves the solute	Boiling point, when you want the solid	Salt from seawater
Distillation	Evaporates then condenses, keeping both	Boiling point, when you want the liquid	Pure water from seawater
Chromatography	Spreads dissolved substances different distances	How strongly each sticks to the paper	Separating the dyes in an ink

Notice that filtration is useless on salt water. Filter paper catches lumps, and dissolved salt is not in lumps; the individual particles slip through with the water. That is not a flaw in the method, it is a mismatch between the method and the property that differs. Salt and water differ in boiling point, so a boiling-point method is what you need.

Notice too the difference between the evaporation row and the distillation row. Both split salt water. Evaporation throws the water away and keeps the salt. Distillation catches the water vapour and cools it back to liquid, keeping both. Which you choose depends entirely on which half you actually want.

Experiment: pull an ink apart with chromatography

Completely safe, and it is the most surprising result in this lesson. Use washable felt-tip pens, not permanent markers.

1. Cut a strip of white coffee filter paper or kitchen towel about 3 cm wide and 12 cm long.
2. About 2 cm up from one end, draw a fat dot with a black washable felt-tip pen. Add a second dot from a different colour further along if you want to compare.
3. Pour water into a glass to a depth of about 1 cm. That must be less than 2 cm, or you will wash the dot straight off.
4. Hang the strip so the bottom edge sits in the water but the dot stays above the surface. Tape the top to a pencil laid across the rim.
5. Leave it alone for ten to twenty minutes and watch the water creep upwards past the dot.

What to expect: The black dot separates into a smear of colours, often blue, pink and yellow, spread out at different heights up the strip.

Why it happens: Black ink is a mixture of several coloured dyes. As the water climbs through the paper it carries the dyes with it, but each dye sticks to the paper by a different amount. The ones that cling hardest are dragged only a short way; the ones that cling least are carried furthest. After twenty minutes each dye has found its own height, and a mixture you would have sworn was one colour is visibly several. That difference in stickiness is the property being exploited, and it is why chromatography can separate substances that are all dissolved in the same liquid.

Experiment: get salt back out of salt water

Safe and needs no heat source, only patience and a sunny windowsill.

1. Stir half a teaspoon of table salt into half a cup of warm tap water until it disappears completely.
2. Hold the glass up to the light. It should be clear, with nothing floating and nothing on the bottom. Taste a drop on a clean fingertip to confirm the salt is still there.
3. Pour a thin layer, no more than half a centimetre deep, into a wide saucer or plate.
4. Put the plate on a warm, sunny windowsill and leave it undisturbed for two or three days.
5. When it is completely dry, tip the plate towards the light and look closely.

What to expect: A white crust of salt crystals, some large enough to see as cubes if you look closely.

Why it happens: The salt never left. Evaporation removes only the water, because water has by far the lower boiling point and its particles can escape from the surface while the salt particles cannot. What is left behind has to be everything else, which is the salt. Note that this method destroys the water: if you wanted the water instead, you would have to catch and cool the vapour, which is distillation.

Common misconceptions

"Dissolving and melting are the same thing." They are not. Melting is a change of state caused by heat, and salt melts at about 800 degrees Celsius. Dissolving is one substance spreading through a solvent, and it happens in cold water without any state change in the salt at all.

"When something dissolves, it is gone." The mass is still there. Weigh the water, weigh the sugar, dissolve, and weigh again: the total is unchanged. This is the conservation of mass, which gets its own lesson shortly.

"You can filter salt out of salt water." Filter paper catches lumps. Dissolved salt is spread out as individual particles, far smaller than any hole in the paper, so it goes straight through with the water.

"A clear liquid is pure." Salt water is perfectly clear and is a mixture. Clear only tells you there is nothing suspended in it big enough to scatter light.

Pulling it together

• A pure substance has one kind of particle; a mixture has several, jumbled but not chemically joined.
• Mixture components keep their own properties, which is why physical methods can always separate them.
• In a solution the solute spreads through the solvent and never settles; a suspension is cloudy and settles.
• Stirring, heating and grinding speed up dissolving; only temperature changes how much can dissolve.
• Pick a separation method by asking which property differs: size, magnetism, solubility, boiling point, or stickiness to paper.
• Evaporation keeps the solid, distillation keeps the liquid, and both split the same mixture.

So far nothing has changed chemically. The next module is about substances that genuinely become other substances.

Sources

1. National Oceanic and Atmospheric Administration. (n.d.). Why is the ocean salty? NOAA National Ocean Service. oceanservice.noaa.gov
2. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Phases and classification of matter. Chemistry 2e. OpenStax, Rice University. openstax.org
3. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Sugar and salt solutions. phet.colorado.edu
4. Wikipedia contributors. (n.d.). Chromatography. Wikipedia. en.wikipedia.org

The chemist who left holes in his own table

In 1869 Dmitri Mendeleev arranged the sixty-odd elements known at the time into rows and columns, sorting them so that ones with similar behaviour lined up. To make the pattern work he had to leave empty squares, and rather than fudge the arrangement he claimed those squares belonged to elements nobody had yet found. He went further and predicted what they would be like.

Gallium was discovered in 1875 and germanium in 1886. Both slotted into his empty squares, and both behaved close to how he had said they would. A chart that can predict the properties of a substance nobody has ever seen is not a filing system. It is a statement about how matter is put together.

Key idea: The periodic table is arranged so that position predicts behaviour, which is why it is a tool and not just a list.

Atoms and elements

An atom is the smallest particle of an element that still counts as that element. An element is a substance made of just one kind of atom, and it cannot be broken down into simpler substances by any chemical means.

Around 118 elements have been confirmed. Roughly 90 occur naturally and the rest have been made in laboratories, often only a handful of atoms at a time. Every material object you have ever touched is built from that one list.

Each element has a one or two letter symbol, written with the first letter capital and any second letter lower case. That rule is not decoration: Co is cobalt, an element, while CO is carbon plus oxygen, a compound.

Element	Symbol	Where the symbol comes from
Hydrogen	H	The English name
Carbon	C	The English name
Oxygen	O	The English name
Sodium	Na	Latin natrium
Iron	Fe	Latin ferrum
Gold	Au	Latin aurum

The Latin ones catch people out, and they are worth learning simply because iron, sodium, potassium, copper, silver, gold, lead and tin are all common and all have symbols that look nothing like their English names.

Compounds: elements chemically joined

A compound forms when atoms of different elements join chemically in a fixed ratio. The formula records the ratio.

• Water, H₂O. Two hydrogen atoms joined to one oxygen atom. Always two to one, in every drop of water in the universe.
• Table salt, NaCl. One sodium to one chlorine.
• Carbon dioxide, CO₂. One carbon to two oxygen.

Now the fact that makes compounds genuinely strange, and it is the best thing in this lesson.

Sodium on its own is a soft, silvery metal so reactive that it fizzes and catches fire on contact with water. Chlorine on its own is a choking, poisonous, greenish gas that was used as a weapon in the First World War. Join them and you get sodium chloride, which you sprinkle on chips.

Nothing about salt could be guessed from its ingredients. The compound is not a blend of a metal and a gas, and it is not somewhere in between them. It is a new substance with its own properties, and the properties of what went in have simply gone.

The point: A compound's properties are unrelated to the properties of its elements. That is the sharpest difference between a compound and a mixture.

Mixture or compound?

	Mixture	Compound
How the parts are held	Physically jumbled	Chemically joined
Proportions	Can vary freely	Fixed, always the same ratio
Properties	Each part keeps its own	Entirely new properties
Separating it	Physical methods work	Needs a chemical reaction
Example	Iron filings stirred into sulfur powder	Iron sulfide, made by reacting them

Take that last row seriously, because it is the cleanest test there is. Stir iron filings into yellow sulfur powder and you can pull the iron straight back out with a magnet, because the iron is still iron. React them and the result is a grey solid that a magnet ignores, because there is no iron left in the mixture sense; there is only iron sulfide, and getting the iron back now requires chemistry, not a magnet.

How the table is laid out

Elements are listed in order of atomic number, which counts the protons in one atom of that element. Hydrogen is 1, helium is 2, carbon is 6, oxygen is 8, iron is 26, gold is 79. The atomic number is what makes an element that element; change it and you have a different element entirely.

The layout has two directions and they mean different things.

• Rows are called periods. Reading across a period, properties change gradually from metal on the left to nonmetal on the right.
• Columns are called groups. Elements in the same group behave alike, and that is the whole point of the arrangement. Mendeleev's gaps worked because he trusted the columns.

Three groups are worth knowing by name.

Group	Members include	How they behave
Group 1, the alkali metals	Lithium, sodium, potassium	Soft metals, extremely reactive, react vigorously with water
Group 17, the halogens	Fluorine, chlorine, bromine, iodine	Very reactive nonmetals, form salts with metals
Group 18, the noble gases	Helium, neon, argon	Almost completely unreactive, which is why argon fills light bulbs

The broad split across the whole table is metals on the left and in the middle, nonmetals on the upper right, with a staircase of in-between elements separating them. Metals share a family resemblance: shiny when clean, good conductors of heat and electricity, and bendable rather than brittle. Nonmetals are usually dull, poor conductors, and either brittle solids or gases.

Experiment: sort your kitchen into metals and nonmetals

Completely safe. Use warm tap water, not hot, so this can be done alone.

1. Collect five or six objects made of different materials: a metal spoon, a plastic spoon, a wooden spoon, a coin, a ceramic mug, a rubber band.
2. For each one, note whether it is shiny when clean and whether it bends or snaps when gently flexed.
3. Hold a fridge magnet against each one and record which are attracted.
4. Stand the metal spoon and the plastic spoon in a mug of warm tap water, handles sticking out, and wait one minute.
5. Touch the two handles. Record which feels warmer.

What to expect: The metal objects are shiny and bend rather than snap. The magnet picks out only some of the metals. The metal spoon handle warms up noticeably and the plastic one barely changes.

Why it happens: Metals conduct heat well because their particles pass energy along easily, so warmth travels up the spoon to the handle in under a minute. Plastic and wood are poor conductors, which is why saucepan handles are made from them. The magnet test is the interesting one: it separates the metals from each other rather than from the nonmetals, because only iron, nickel, cobalt and a few alloys are magnetic. Aluminium and copper are unmistakably metals and a magnet ignores both, which is a useful reminder that magnetic and metallic are not the same word.

Experiment: count the elements in a fizzy drink

No equipment at all, and it tests whether the vocabulary has landed.

1. Find a bottle of fizzy water or a soft drink and read the ingredients list.
2. Write down each ingredient and label it element, compound or mixture.
3. Open the bottle and watch the bubbles. Write down which substance you think they are.

What to expect: Almost nothing on the list is an element. Water is a compound, sugar is a compound, citric acid is a compound, and the drink as a whole is a mixture. The bubbles are carbon dioxide, a compound of one carbon and two oxygen atoms.

Why it happens: Free elements are rare in everyday life because most of them react with something and end up locked into compounds. The oxygen and nitrogen in the air above the liquid are among the few elements you meet uncombined, and the gold in a ring is another.

Common misconceptions

"A compound is just a mixture of its elements." Sodium is a metal that catches fire in water and chlorine is a poisonous gas, yet sodium chloride is table salt. The properties of the elements do not survive into the compound.

"All metals are magnetic." Only iron, nickel, cobalt and some of their alloys are. Aluminium, copper, gold and silver are all metals and all ignored by a magnet.

"The atomic number is the element's position by accident." It counts the protons in one atom, which is what defines the element. The ordering follows from the counting, not the other way round.

"CO and Co mean the same thing." Co is cobalt, one element. CO is carbon monoxide, a compound of two. Capital letters carry real information in chemical symbols.

What you now know

• An element is made of one kind of atom and cannot be broken down chemically; there are around 118, with about 90 occurring naturally.
• Symbols use a capital first letter and a lower case second, and several come from Latin names.
• A compound is elements chemically joined in a fixed ratio, with completely new properties.
• Mixtures can be separated physically; compounds cannot.
• The periodic table orders elements by atomic number, which counts protons; rows are periods and columns are groups.
• Elements in the same group behave alike, which is what let Mendeleev predict elements nobody had found.

Next: how to tell, by looking, whether a new substance has actually been made.

Sources

1. Los Alamos National Laboratory. (n.d.). Periodic table of elements. periodic.lanl.gov
2. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Phases and classification of matter. Chemistry 2e. OpenStax, Rice University. openstax.org
3. Wikipedia contributors. (n.d.). Periodic table. Wikipedia. en.wikipedia.org
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Build an atom. phet.colorado.edu

Two things you can do to a steel nail

Bend a steel nail in a vice and it comes out crooked. It is still a nail, still steel, still shiny, still magnetic, and if you were strong enough you could bend it straight again.

Leave the same nail in a saucer of water on a windowsill for a week and something else happens. An orange-brown crust grows on it. That crust is not steel. It is softer, it flakes, it is a different colour, and no amount of bending will turn it back. The nail has lost mass to it and, oddly, the nail plus crust together now weigh more than the nail did at the start, because something from the air has joined in.

Both are changes. Only one of them made a new substance.

Key idea: A physical change alters the form of a substance. A chemical change produces a different substance, with different properties.

Physical change: the substance survives

In a physical change, the particles are rearranged, moved apart, or broken into smaller pieces, but they are the same particles doing the same chemistry as before. Every change of state is a physical change. So is dissolving, tearing, crushing, mixing and melting.

• Ice melting is still water. Freeze it and you have the ice back.
• Sugar dissolving in tea is still sugar. Evaporate the water and it crystallises out.
• Paper torn in half is still paper.
• Copper drawn into a wire is still copper.

Physical changes are usually reversible, and that is a useful clue, but it is not the definition and it is not always true. Scrambling an egg is a chemical change; smashing a plate is a physical one, and nobody is putting the plate back together. Reversibility is evidence, not proof.

Chemical change: something new appears

In a chemical change, also called a chemical reaction, the atoms are rearranged into different combinations, so the substances present at the end are not the substances present at the start. The starting materials are the reactants and the new ones are the products.

Rusting is the classic. Iron plus oxygen plus water becomes iron oxide, which is a genuinely different material: different colour, different hardness, not magnetic in the way the iron was, and it will not go back to iron by any physical means.

You cannot see atoms rearranging, so chemists look for evidence instead. Five signs are worth memorising.

1. A gas is produced when nothing is boiling. Bubbles appearing in a cold liquid mean a new gas is being made.
2. A colour change that is not simply mixing two colours together.
3. A temperature change with no heater involved. Some reactions release energy and get hot; others absorb it and get genuinely cold.
4. A solid appears in a clear liquid, called a precipitate.
5. Light or a new smell is produced.

Add a sixth, softer one: the change is difficult or impossible to reverse.

What matters here: No single sign proves a chemical change on its own. Bubbles could be boiling and a temperature change could be a hot plate. Two or three signs together, with no ordinary explanation, is strong evidence.

Sorting the awkward cases

Change	Which kind	Why
Water boiling	Physical	Steam is still water, just spread out. Condense it and it is water again.
Salt dissolving	Physical	The salt is still salt, spread through the water, and evaporation brings it back.
Wood burning	Chemical	Ash, smoke and gases are new substances. The wood is gone.
An egg cooking	Chemical	The proteins are permanently rearranged. No amount of cooling un-cooks it.
Iron rusting	Chemical	Iron oxide is a new substance with different properties.
Bread going stale	Physical	Mostly water moving out of the bread; no new substance.
Milk going sour	Chemical	Bacteria make acid, which is a new substance, hence the smell and taste.
A firework exploding	Chemical	Light, heat, gas and new solids, all at once.
Chopping vegetables	Physical	Smaller pieces of the same substance.
Digesting food	Chemical	Large molecules are broken into different, smaller ones.

The bread row surprises people. Stale bread tastes different and feels different, so it seems as though something must have been created. What actually happened is mostly water leaving and starch rearranging its structure, which is a physical process. The test that decides it: sourness in milk comes with a new acid you can taste and smell, while staleness comes with no new substance at all.

Experiment: make a gas and a temperature drop at once

Safe with ordinary kitchen vinegar and baking soda. Do it over a sink, keep it away from your eyes, and wash your hands afterwards. Nothing here is hot and nothing needs an adult.

1. Pour about 60 millilitres of white vinegar into a tall glass or a jug.
2. If you have a thermometer, stand it in the vinegar, wait a minute, and write down the temperature.
3. Add one heaped teaspoon of baking soda, or bicarbonate of soda, all at once. Stand back a little.
4. Watch what happens for thirty seconds, then read the thermometer again while the fizzing continues.
5. Light a match only if an adult is present. Without one, instead hold the glass beside your face and pour the invisible gas gently towards a lit birthday candle held by an adult, or skip this step; the experiment works fine without it.

What to expect: Vigorous fizzing that climbs up the glass, and a thermometer reading that drops by several degrees. The liquid feels cold through the glass.

Why it happens: Two of the five signs are showing at once. Bubbles are appearing in a cold liquid with nothing boiling, so a new gas is being made; it is carbon dioxide, which is why the froth smothers a small flame rather than feeding it. And the temperature falls, which is the second sign. This reaction absorbs energy from its surroundings rather than releasing it, and your thermometer is watching that happen. Neither the vinegar nor the baking soda is still there afterwards in its original form, which is exactly what a chemical change means.

Experiment: a change that goes all the way back

Run this straight after the last one so the contrast is fresh.

1. Stir a teaspoon of salt into half a cup of warm tap water until the liquid is completely clear.
2. Note that there were no bubbles, no colour change and no noticeable temperature change.
3. Pour a thin layer onto a saucer and leave it on a warm windowsill for two days.
4. Look at what is left.

What to expect: White salt crystals, and no sign at all of the water.

Why it happens: None of the five signs appeared, and the change reversed completely. The salt was never chemically altered; it was only spread out among the water particles. Compare that with the vinegar and baking soda, where no amount of waiting will give you your vinegar back. Same word, change, two entirely different things happening to the particles.

Common misconceptions

"If it looks different, it is a chemical change." Ice, water and steam look completely different and are all the same substance. Appearance alone decides nothing.

"Bubbles always mean a chemical reaction." Boiling water bubbles furiously and is purely physical. What counts is bubbles appearing when nothing is being boiled, which means a new gas has been made.

"Chemical changes always give out heat." Many do, but plenty absorb it. Vinegar and baking soda get colder, and that temperature drop is itself a sign of reaction.

"Reversible means physical, every time." It is a strong clue, not a rule. A smashed plate is a physical change nobody can reverse, and some chemical reactions can be driven backwards under the right conditions.

Looking back

• A physical change alters form; the substance survives and its particles are unchanged.
• A chemical change rearranges atoms into new substances, called products, from starting materials called reactants.
• Five signs point to a chemical change: unexpected gas, colour change, temperature change without a heater, a precipitate, and light or a new smell.
• No single sign is proof; look for two or three with no ordinary explanation.
• Dissolving, melting, boiling, tearing and crushing are physical. Burning, rusting, cooking, souring and digesting are chemical.
• Reversibility is evidence rather than a definition.

Something in the rusting nail was strange: the nail plus its rust weighs more than the nail did. The next lesson explains where the extra mass came from, and why it was never really extra.

Sources

1. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Physical and chemical properties. Chemistry 2e. OpenStax, Rice University. openstax.org
2. Khan Academy. (n.d.). Middle school chemistry. khanacademy.org
3. Wikipedia contributors. (n.d.). Chemical change. Wikipedia. en.wikipedia.org
4. PBS LearningMedia. (n.d.). Science collections for grades 6 to 8. pbslearningmedia.org

Lavoisier and the sealed flask

In the 1770s Antoine Lavoisier did something that sounds unremarkable and turned out to matter enormously: he weighed things before and after a reaction, in a sealed container, on a very good balance.

Everyone before him had been weighing in open dishes, where gases could arrive from the air or drift off into it unnoticed. Seal the vessel and nothing can come or go. Lavoisier found, again and again, that the sealed flask weighed exactly the same after the reaction as before, no matter how dramatic the change inside it. He published the result in 1789, and it became one of the foundations of chemistry.

Key idea: In a chemical reaction, the total mass of the products equals the total mass of the reactants. Mass is not created and not destroyed; the atoms are only rearranged.

Why it must be true

Once you accept the particle model, the law is almost obvious. A chemical reaction takes the atoms that were there and joins them up differently. It does not build new atoms and it does not delete any.

Think of a bag of building bricks. Take apart a model house and build a boat from the same bricks. The boat looks nothing like the house, it does a different job, and it has different properties. Weigh the bricks and the number on the scale has not moved by a gram, because every brick that was in the house is now in the boat.

Chemistry works the same way, with atoms as the bricks. That is exactly why the numbers in a chemical formula have to balance, and why chemists count atoms on both sides of a reaction and insist the counts match.

Working with the numbers

A worked example. 12 grams of carbon reacts completely with 32 grams of oxygen to form carbon dioxide. What is the mass of the carbon dioxide?

Step 1. Add the masses of everything that went in: 12 + 32 = 44 grams.

Step 2. Nothing else entered and nothing escaped, so the products must total the same.

Step 3. Only one product is formed, so all 44 grams of it is carbon dioxide.

A second one, running backwards. A sealed flask contains 10 grams of substance A and an unknown mass of substance B. After the reaction, the flask contains 27 grams of product. How much B was there?

Step 1. Total in must equal total out, so 10 + B = 27.

Step 2. Subtract 10 from both sides: B = 17 grams.

Step 3. Check: 10 + 17 = 27. Correct.

That second problem is a one-step equation of exactly the kind in the mathematics course, and the physics is what supplies the equals sign.

The two cases that look like exceptions

Case one: a log burns down to a handful of ash. Two kilograms of wood becomes perhaps fifty grams of ash. Where did the rest go?

It went up the chimney. Burning wood combines with oxygen from the air and produces carbon dioxide and water vapour, both invisible, both leaving the fireplace. Weigh the fire in an open room and mass appears to vanish. Weigh the wood, plus the oxygen consumed, against the ash, plus every gas released, and the totals match exactly. Nothing was destroyed; it left without being noticed.

Case two: the rusting nail from the last lesson gets heavier. A nail plus its rust weighs more than the nail did.

Same explanation, running the other way. Rusting is iron combining with oxygen from the air and with water. The oxygen atoms that join the iron had mass, and now they are part of the crust on the nail, so the nail is carrying mass it did not start with. Nothing was created; something arrived from outside.

The upshot: Every apparent violation of the law is a gas that was not counted. Seal the container, and the exceptions disappear.

Balancing, in outline

Chemists write reactions as equations, and the equation has to have the same number of each kind of atom on both sides. Take the burning of methane, the gas in a kitchen hob:

CH₄ plus 2 O₂ gives CO₂ plus 2 H₂O

Count the atoms on the left: 1 carbon, 4 hydrogen, and 4 oxygen, since there are two O₂ units of two atoms each.

Count them on the right: 1 carbon, then 4 hydrogen across the two water molecules, then 2 oxygen in the carbon dioxide plus 2 more in the two waters, giving 4.

Carbon 1 and 1, hydrogen 4 and 4, oxygen 4 and 4. Every atom is accounted for. That balance is conservation of mass written in chemical notation, and it is why the big numbers in front of formulas cannot be chosen freely.

Experiment: weigh a reaction that cannot escape

Safe, and the most convincing demonstration in this course. You need a kitchen scale that reads to the nearest gram, and a zip-seal sandwich bag that closes properly.

1. Put two heaped teaspoons of baking soda into a zip-seal bag.
2. Pour about 30 millilitres of vinegar into a small plastic bottle cap or a tiny cup that will stand upright, and lower it carefully into the bag without spilling it.
3. Squeeze out most of the air and seal the bag completely. Press along the seal twice to be sure.
4. Put the whole sealed bag on the kitchen scale and write down the mass.
5. Without opening the bag, tip it so the vinegar spills into the baking soda. Hold the bag over a sink, because it will inflate. If it starts to strain, open a corner over the sink and stop.
6. When the fizzing has finished, put the bag back on the scale, still sealed, and write down the mass again.
7. Now open the bag, let the gas out, wait a moment, and weigh it a third time.

What to expect: The second reading matches the first, to within a gram or so. The third reading, after opening, is lower.

Why it happens: The reaction made carbon dioxide, and while the bag was sealed that gas had nowhere to go, so every atom that started inside was still inside. The scale therefore reads the same, even though the substances in the bag are now completely different. Opening the bag lets the carbon dioxide escape into the room, and the mass it carried leaves with it. That drop is not mass being destroyed; it is mass walking out of the container.

If your second reading is a gram or two low, check the seal. A bag that puffs up hard will often let a little gas past, and that leak is exactly the kind of thing that fooled chemists before Lavoisier.

Experiment: the same reaction with the lid off

1. Stand an open glass on the scale. Add two teaspoons of baking soda and write down the mass.
2. Weigh 30 millilitres of vinegar in a separate cup and write that down too.
3. Add the two masses together on paper. This is your total before.
4. Pour the vinegar into the glass with the baking soda, still on the scale, and let it fizz completely.
5. Weigh the open glass and its contents.

What to expect: The final mass is clearly less than your calculated total before, typically by a gram or more.

Why it happens: The carbon dioxide left the glass as it formed. The missing mass is exactly the mass of the gas that floated away. Run the sealed version and the open version on the same afternoon and you have, in about twenty minutes, the experiment that took Lavoisier years of careful work to get right.

Common misconceptions

"Burning destroys matter." It converts it into gases you cannot see. Collect the carbon dioxide and water vapour, add the ash, and the total matches the wood plus the oxygen that was used.

"Gases do not weigh anything." They do. A litre of air has a mass of about 1.2 grams, and the carbon dioxide leaving your open glass is what makes the scale reading fall.

"When something dissolves, some mass is lost." Weigh the water, weigh the sugar, dissolve, and weigh the solution. It is the sum of the two, every time.

"Mass and volume are conserved together." Only mass is. The sealed bag keeps exactly the same mass while ballooning to several times its original volume, because the gas takes up far more room than the reactants did.

The takeaway

• The total mass of the products of a reaction equals the total mass of the reactants.
• The reason is that atoms are rearranged, never created or destroyed.
• Every apparent exception involves a gas arriving from the air or leaving into it uncounted.
• A burning log loses mass to invisible gases; a rusting nail gains mass from oxygen in the air.
• Chemical equations balance because the atom counts on both sides must match.
• Mass is conserved; volume is not, which is why a sealed bag can inflate without getting heavier.

That closes the chemistry half of the course. The next module leaves substances behind and starts asking how things move.

Sources

1. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Writing and balancing chemical equations. Chemistry 2e. OpenStax, Rice University. openstax.org
2. Wikipedia contributors. (n.d.). Conservation of mass. Wikipedia. en.wikipedia.org
3. Khan Academy. (n.d.). Middle school chemistry. khanacademy.org
4. National Institute of Standards and Technology. (n.d.). Redefining the kilogram. nist.gov

Nine point five eight seconds

On 16 August 2009, in Berlin, Usain Bolt ran 100 metres in 9.58 seconds. It is still the fastest anyone has been officially timed over that distance.

Divide one number by the other and you get 100 ÷ 9.58 = 10.44 metres per second. That is his average speed: if he had travelled at a perfectly steady pace from gun to line, that is the pace it would have been.

He did not, of course. He was standing still when the gun went, spent the first two seconds accelerating hard, and was moving considerably faster than 10.44 metres per second through the middle of the race. The single number describes the whole journey without describing any moment of it. That gap between the average and the moment is one of the two big ideas in this lesson.

Key idea: Speed is distance divided by time. An average speed describes a whole journey; it does not tell you the speed at any particular instant.

The formula, and its two rearrangements

speed = distance ÷ time

The unit follows from the formula. Divide metres by seconds and you get metres per second, written m/s. Divide kilometres by hours and you get km/h. Both are perfectly good, and the only rule is that you must not mix them inside one calculation.

Because it is a division, the same relationship can be written two other ways, and you will need all three.

You want	Formula	Example
Speed	distance ÷ time	240 m in 30 s gives 8 m/s
Distance	speed × time	8 m/s for 15 s gives 120 m
Time	distance ÷ speed	400 m at 8 m/s takes 50 s

Worked example. A cyclist covers 4500 metres in 300 seconds. Find the speed, then find how far she goes in 45 seconds at that speed.

Step 1. Speed = distance ÷ time = 4500 ÷ 300 = 15 m/s.

Step 2. Distance = speed × time = 15 × 45 = 675 metres.

Step 3. Check the size. Forty five seconds is about a seventh of 300 seconds, and 675 is about a seventh of 4500. Good.

Converting between the units. To turn m/s into km/h, multiply by 3.6, because there are 3600 seconds in an hour and 1000 metres in a kilometre. Bolt's 10.44 m/s becomes 10.44 × 3.6 = about 37.6 km/h, which is roughly the speed limit on a residential street.

Average speed against speed right now

A car drives 120 kilometres in 2 hours. Its average speed is 60 km/h. That average is true even if the car spent twenty minutes stopped at roadworks and then ran at 100 km/h to make up time. The average smooths everything out.

The speed at one instant is what a speedometer shows, and it changes constantly. Both numbers are useful and they answer different questions. If you want to know when you will arrive, you want the average. If you want to know whether you are breaking the speed limit, you want the instant.

Worked example with a stop. Someone walks 600 metres in 300 seconds, rests for 200 seconds, then walks another 400 metres in 200 seconds. What is the average speed for the whole journey?

Step 1. Total distance: 600 + 400 = 1000 metres.

Step 2. Total time, including the rest: 300 + 200 + 200 = 700 seconds.

Step 3. Average speed = 1000 ÷ 700 = about 1.43 m/s.

The rest counts. This is the step people skip, and skipping it gives an answer that is too big. Average speed is total distance over total time, not the average of the walking speeds.

Distance-time graphs

Put time along the bottom and distance from the start up the side, and a journey becomes a line. The steepness of the line is the speed.

Four shapes cover almost everything you will meet.

• A straight sloping line means constant speed. Equal distance covered in each equal slice of time.
• A steeper line means a faster speed, because more distance is covered in the same time.
• A flat, horizontal line means the object is stopped. Time is passing and distance is not changing.
• A curve getting steeper means speeding up; a curve flattening out means slowing down.

The flat line is the one people misread, usually saying the object is moving slowly. It is not moving at all. Look at what the axes say: time keeps going and distance stays put, which is precisely what standing still means.

To read a speed off a straight section, pick the two ends of it, find how much distance was covered, find how much time passed, and divide.

Reading a graph. A line runs from the point at 0 seconds and 0 metres to the point at 20 seconds and 100 metres, then stays flat until 30 seconds, then rises to 160 metres at 50 seconds.

Step 1. First section: 100 metres in 20 seconds, so 100 ÷ 20 = 5 m/s.

Step 2. Second section: flat, so the speed is 0. The object is stopped for 10 seconds.

Step 3. Third section: 160 − 100 = 60 metres, in 50 − 30 = 20 seconds, so 60 ÷ 20 = 3 m/s. Slower than the first section, and the line is correspondingly less steep.

Step 4. Whole journey: 160 metres in 50 seconds, so the average is 160 ÷ 50 = 3.2 m/s, which sits between the two moving speeds because of the stop.

Why this matters: On a distance-time graph, steepness is speed and flat is stationary. Those two facts unlock every question of this type.

Experiment: measure your own walking speed and graph it

Completely safe. You need a tape measure or a known distance, and a phone or watch with a seconds display. Do it in a hallway, a garden or a park, not near traffic.

1. Measure out 20 metres and mark the start and the end. If you have no tape measure, count 25 normal paces and measure one pace to estimate the distance.
2. Also mark the 5, 10 and 15 metre points.
3. Ask someone to time you, or set a stopwatch running and glance at it. Walk at a steady, normal pace from the start to the end.
4. Record the time as you pass each of the four marks and at the end.
5. Calculate your average speed: 20 divided by your total time.
6. Plot your five readings with time along the bottom and distance up the side, and join them.
7. Repeat, but this time stop for a count of five in the middle before carrying on.

What to expect: A typical walking speed is somewhere between 1.2 and 1.6 m/s. Your first graph should be close to a straight line. Your second will have a visible flat section in the middle.

Why it happens: Walking at a steady pace means covering roughly equal distances in equal times, which is exactly what a straight line on this graph represents. The pause produces a flat section because time keeps running while your distance from the start does not change. Notice too that the second walk has a lower average speed than the first even though you walked at the same pace, because the stopped time counts in the total.

Common misconceptions

"A flat line on a distance-time graph means moving slowly." It means stopped. Distance from the start is not changing at all while time passes.

"Average speed is the average of the speeds." It is total distance divided by total time. A journey with a long stop has a much lower average than averaging the moving speeds would suggest.

"A speedometer shows average speed." It shows speed at that instant, and it changes constantly. Bolt's average was 10.44 m/s and he was faster than that through the middle of his race.

"Metres per second and kilometres per hour are close enough." They differ by a factor of 3.6. A person walking at 1.4 m/s is doing about 5 km/h, and mixing the units inside one calculation gives an answer that is wrong by that factor.

Recap

• Speed is distance divided by time, and the same relationship rearranges to give distance or time.
• Metres per second and kilometres per hour differ by a factor of 3.6; never mix them in one calculation.
• Average speed is total distance over total time, and any stops count in the time.
• On a distance-time graph, steepness is speed, a straight line is constant speed, and a flat line is stopped.
• Curves mean the speed is changing: steepening is speeding up, flattening is slowing down.

Describing motion is one thing. The next lesson asks what makes motion change in the first place.

Sources

1. NASA Glenn Research Center. (n.d.). Speed and velocity. Beginner's Guide to Aeronautics. grc.nasa.gov
2. Khan Academy. (n.d.). Middle school physics. khanacademy.org
3. Wikipedia contributors. (n.d.). Speed. Wikipedia. en.wikipedia.org
4. Urone, P. P., and Hinrichs, R. (2020). Physics. OpenStax, Rice University. openstax.org

Eight people pulling and a rope that does not move

Four people on each end of a rope, all pulling as hard as they can. The rope is under enormous strain. The knot in the middle does not budge a centimetre.

An enormous amount of force is being applied and the result is nothing at all. That is not a failure of the forces; it is the most important single fact about how forces work. What decides whether something moves is never how much force is applied, but how much is left over once opposing forces have cancelled each other out.

Key idea: Motion changes only when forces do not cancel. Balanced forces leave motion exactly as it was.

What a force is

A force is a push or a pull on an object. It is measured in newtons, written N, and named after Isaac Newton. A newton is not a large amount: holding a small apple against gravity takes about one newton, and a 1 kilogram bag of sugar pulls down with roughly 10 newtons on Earth.

Forces have both a size and a direction, which is why they are drawn as arrows. The length of the arrow shows the size and the way it points shows the direction. Two arrows of the same length pointing opposite ways are two forces that will cancel.

Force	What causes it	Which way it acts
Weight	Gravity pulling on mass	Straight down, towards the centre of the Earth
Support force	A surface pushing back on whatever rests on it	Away from the surface, usually upwards
Friction	Two surfaces rubbing	Opposite to the direction of sliding
Air resistance	Air pushing back on a moving object	Opposite to the motion
Tension	A rope, cable or string being pulled tight	Along the rope, away from the object
Upthrust	A liquid or gas pushing up on something in it	Upwards
Applied force	A person or machine pushing or pulling	Whichever way the push or pull points

Note the support force, because it is the one people forget. A book on a table is not floating; the table is genuinely pushing up on it, hard enough to cancel the book's weight exactly. If the table could not push that hard, the book would go through it, which is precisely what happens when you put something too heavy on a flimsy shelf.

Adding forces along a line

The net force is what is left after all the forces have been added up, taking direction into account. Pick one direction as positive, call the other negative, and add.

Example 1. A box is pushed right with 30 N while friction pushes left with 12 N.

Step 1. Take right as positive: +30 and −12.

Step 2. Add: 30 − 12 = 18.

Step 3. Net force is 18 N to the right. Unbalanced, so the box speeds up in that direction.

Example 2. A parachutist has 700 N of weight pulling down and 700 N of air resistance pushing up.

Step 1. Down positive: +700 and −700.

Step 2. Add: 0.

Step 3. Net force is zero, so the forces are balanced. She does not stop, and she does not speed up. She keeps falling at exactly the speed she already had. That steady rate is called terminal velocity, and it is what makes a parachute survivable.

Example 3. Two people push a car in the same direction, one with 250 N and one with 300 N, against 400 N of friction.

Step 1. Forwards positive: +250, +300, −400.

Step 2. Add: 250 + 300 = 550, then 550 − 400 = 150.

Step 3. Net force is 150 N forwards, so the car accelerates forwards.

What balanced and unbalanced actually predict

Situation	Net force	What happens to the motion
Book resting on a table	Zero	Stays still
Car cruising at a steady 60 km/h	Zero	Keeps going at 60 km/h
Ball dropped from a hand	Downwards	Speeds up as it falls
Cyclist braking	Backwards	Slows down
Ball on a string swung in a circle	Towards the centre	Changes direction constantly

Read the second row twice, because it is the one that overturns everyday intuition. A car cruising at a steady speed has zero net force on it. Its engine is pushing forwards and friction and air resistance are pushing back by exactly the same amount. The engine is not needed to keep it moving; it is needed to cancel the friction. If you could switch off the friction, the car would keep going with no engine at all.

Read the last row too. Changing direction counts as changing motion, even at a steady speed. A ball whirled on a string is being pulled inwards the whole time, which is why it flies off in a straight line the instant the string breaks.

Remember: Balanced forces do not mean stationary. They mean unchanging, which includes moving steadily in a straight line.

Friction: the force that hides the truth

Friction is why a rolling ball stops, why a pushed book comes to rest, and why for two thousand years people believed that keeping something moving requires a continuous push. It does not. What requires a continuous push is keeping something moving against friction.

Friction is not always a nuisance. It is what lets you walk, and what lets brakes work, and what stops a ladder sliding out from under you. Reduce it too far, as on ice, and walking becomes almost impossible.

Air resistance is friction from air, and it grows with speed. That growth is what produces terminal velocity: a falling object accelerates, the air resistance rises as it goes faster, and eventually the upward air resistance equals the downward weight. From that moment the forces are balanced and the speed stops increasing.

Experiment: measure friction with a rubber band

Safe and needs nothing unusual. A rubber band is a perfectly good force meter, because the more you stretch it, the more force it is pulling with.

1. Loop a rubber band around a book or a shoe. Hold a ruler alongside so you can read how far the band stretches.
2. Pull steadily and horizontally until the object just starts to slide, and note the length of the stretched band at that moment.
3. Repeat three times on the same surface and take the middle reading, since single readings are noisy.
4. Now repeat the whole thing on three different surfaces: a smooth table, a carpet, and a tea towel laid flat.
5. Finally, put the object on top of four round pencils and pull again.

What to expect: The band stretches least on the smooth table, more on the towel and most on the carpet. On the pencils it stretches least of all, often dramatically so.

Why it happens: Rougher surfaces grip more, so more force is needed before sliding begins. The pencils replace sliding with rolling, and rolling friction is far smaller than sliding friction, which is the entire reason wheels were invented. Note also that the object stays still until the band is stretched far enough: below that point your pull and the friction are balanced, and the moment your pull wins, the forces become unbalanced and the object moves.

Experiment: two identical sheets of paper, dropped

1. Take two identical sheets of paper. Leave one flat and crumple the other into a tight ball.
2. Hold both at the same height, at arm's length, and release them at exactly the same moment.
3. Watch which lands first. Repeat three times to be sure.
4. Now lay the flat sheet on top of a hardback book, so its edges do not overhang, and drop the book. Watch the sheet.

What to expect: The crumpled ball lands well before the flat sheet. On top of the book, the flat sheet falls exactly as fast as the book and stays pressed against it.

Why it happens: Both sheets have the same mass and the same weight pulling down. The difference is air resistance: the flat sheet presents a large area to the air and is pushed back hard, while the ball presents a small one. Putting the sheet on the book means the book pushes the air out of the way, so the sheet feels almost no air resistance and falls at the rate gravity alone would give. Same paper, same weight, three different results, all decided by the second force rather than the first.

Common misconceptions

"A moving object needs a constant force to keep moving." It needs one only to cancel friction. Remove friction and motion continues on its own, which is why a spacecraft coasts between planets with its engines off.

"Balanced forces mean the object is stationary." They mean the motion is not changing. A car at a steady 60 km/h has balanced forces on it and is not stationary at all.

"Heavier things always fall faster." Without air resistance they fall at the same rate. The crumpled and flat sheets have identical mass and land at different times, which shows that the difference is air resistance, not weight.

"Friction is always bad." It is why walking, braking and holding a pencil are possible. Ice removes most of it and immediately shows what it was doing for you.

What to remember

• A force is a push or a pull, measured in newtons, with a size and a direction.
• The net force is the sum of all forces, with direction taken into account.
• Balanced forces, net zero, leave motion unchanged: still if it was still, steady if it was moving.
• Unbalanced forces change motion: speeding up, slowing down, or changing direction.
• Friction and air resistance oppose motion and are why moving things appear to need a constant push.
• Air resistance grows with speed, which produces terminal velocity when it comes to equal weight.

These ideas were written down properly in 1687, in three laws that still run every calculation an engineer makes. That is the next lesson.

Sources

1. NASA Glenn Research Center. (n.d.). Newton's first law of motion. Beginner's Guide to Aeronautics. grc.nasa.gov
2. Khan Academy. (n.d.). Forces. Middle school physics. khanacademy.org
3. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Forces and motion: basics. phet.colorado.edu
4. Urone, P. P., and Hinrichs, R. (2020). Newton's second law of motion. Physics. OpenStax, Rice University. openstax.org

The coffee cup on the dashboard

A driver brakes hard at a junction. The loose coffee cup on the dashboard slides forward and hits the windscreen. Nobody pushed it forward. No force acted on it in that direction at all.

What happened is that the car slowed down and the cup did not. The cup was travelling at 50 kilometres per hour, and when the brakes gripped the road they slowed the car, the seats, the driver and everything bolted down. Nothing was gripping the cup, so it carried on doing exactly what it had been doing, and the windscreen came back to meet it.

In 1687 Isaac Newton published the reasoning behind that in a book usually called the Principia, in three laws that are still the working tools of every engineer alive.

Key idea: Things do not stop or start or turn on their own. Every change of motion has a force behind it, and the three laws say exactly how much change a given force produces.

The first law: things carry on

An object at rest stays at rest, and an object moving stays moving at the same speed in the same straight line, unless an unbalanced force acts on it.

The tendency to carry on is called inertia, and everything with mass has it. More mass means more inertia, which is why a shopping trolley is harder to get moving when it is full, and harder to stop once it is.

Four ordinary situations, all the first law.

• The coffee cup. The car stopped; the cup kept going.
• Seat belts. In a crash the car stops in a fraction of a second and your body would keep travelling at the old speed. The belt is the unbalanced force that stops you instead of the steering wheel doing it.
• Whipping a tablecloth from under the dishes. If you pull fast enough, the friction on the dishes acts for so short a time that it barely changes their motion, so they stay where they were.
• A spacecraft between planets. Engines off, nothing to rub against, so it coasts for years without slowing. This is the first law with nothing hiding it, and it is the reason the law was so hard to discover on a planet covered in friction.

The second law: how much change, exactly

Force equals mass times acceleration. Written as a formula: F = m × a.

Acceleration means how quickly the velocity changes, measured in metres per second, per second. The formula says two sensible things at once. Push harder and you get more acceleration. Push the same on something heavier and you get less.

Because it is a multiplication, it rearranges the same way speed did.

You want	Formula
Force	mass × acceleration
Acceleration	force ÷ mass
Mass	force ÷ acceleration

Worked example 1. A net force of 10 N acts on a 2 kg ball. What is its acceleration?

Step 1. Rearrange: acceleration = force ÷ mass.

Step 2. Substitute: 10 ÷ 2.

Step 3. Acceleration = 5 metres per second per second.

Worked example 2. The same 10 N acts on a 5 kg object instead.

Step 1. 10 ÷ 5 = 2 metres per second per second.

Step 2. Compare: two and a half times the mass gives two and a half times less acceleration. The same push does much less to a heavier thing, which is the whole content of the law.

Worked example 3. What net force is needed to accelerate a 1200 kg car at 2 metres per second per second?

Step 1. Force = mass × acceleration.

Step 2. 1200 × 2 = 2400.

Step 3. The answer is 2400 N. Note how large that is compared with the newton or two you use to lift an apple, which is why cars need engines and apples do not.

What matters here: The force in this formula is the net force, the one left over after cancelling. Putting the engine's push into the formula without subtracting friction gives an answer that is too big.

The third law: forces come in pairs

For every action there is an equal and opposite reaction. Said less cryptically: whenever object A pushes on object B, object B pushes back on A with the same size of force in the opposite direction.

The part everyone misses is the last four words of the proper statement: the two forces act on different objects. That is why they never cancel each other out.

Situation	Action	Reaction	What moves, and why
Walking	Your foot pushes backwards on the ground	The ground pushes forwards on your foot	You move forwards. The Earth is pushed back too, but its mass is so vast that the acceleration is unmeasurable.
Swimming	Your hands push water backwards	The water pushes you forwards	You move. The water is pushed the other way.
A rocket	The engine pushes gas downwards	The gas pushes the rocket upwards	The rocket rises. It does not need air to push against; it pushes on its own exhaust.
A book on a table	The book pushes down on the table	The table pushes up on the book	Nothing moves, but note these two forces act on different objects.

If the pairs cancelled, nothing could ever move, and the obvious fact that things do move is the strongest possible evidence that they do not cancel. Your foot pushes the Earth and the Earth pushes your foot. One of those forces acts on you; the other acts on the planet. To work out whether you accelerate, you only count the forces acting on you.

Experiment: the coin and the card

Safe. Do it over a table so the coin does not roll away.

1. Stand an empty glass or mug on a flat table.
2. Lay a playing card or a piece of stiff card flat across the top of the glass.
3. Balance a coin in the centre of the card, right over the mouth of the glass.
4. Flick the edge of the card sharply and horizontally with your finger, so the card shoots sideways.
5. Watch the coin. Then try again, this time pulling the card away slowly.

What to expect: With a sharp flick, the card flies off and the coin drops straight into the glass. Pulled slowly, the coin travels with the card and falls off the side.

Why it happens: This is the first law with a stopwatch attached. Friction between card and coin does push the coin sideways, but during a fast flick that force acts for only a few thousandths of a second, far too briefly to change the coin's motion noticeably. The coin stays where it was, the support disappears, and gravity takes it down. Pull slowly and the same friction has plenty of time to drag the coin along with the card.

Experiment: a balloon rocket on a string

Safe, and the clearest demonstration of the third law you can do indoors.

1. Thread a drinking straw onto a long piece of smooth string, four or five metres if you have the room.
2. Tie one end of the string to a door handle and hold or tie the other end so the string is stretched tight and roughly level.
3. Blow up a balloon and pinch the neck closed. Do not tie it.
4. Have someone tape the balloon to the straw, with the neck pointing back along the string towards you.
5. Let go of the neck.
6. Repeat with the balloon blown up half as much, and again with a heavier straw or a second balloon taped on as extra mass.

What to expect: The balloon shoots along the string away from the direction the air came out. Less air means a shorter, slower trip. Extra mass means slower acceleration.

Why it happens: The balloon pushes air backwards out of the neck, and by the third law the air pushes the balloon forwards with an equal force. Nothing is pushing against the room; the balloon is pushing against its own escaping air, which is exactly how a rocket works in the vacuum of space. The last two runs are the second law: the same balloon with less air gives a smaller force and less acceleration, and adding mass to the same force also reduces the acceleration.

Common misconceptions

"Action and reaction cancel out, so nothing should move." They act on different objects, so they can never cancel. When you push a wall, one force acts on the wall and the other acts on you. Only the forces acting on you decide whether you accelerate.

"Heavier objects need more force to move at all." Any unbalanced force at all will move any mass. What a bigger mass changes is how much acceleration you get: the same 10 N gives 5 metres per second per second to a 2 kg mass and only 2 to a 5 kg mass.

"A rocket pushes against the air." It pushes against its own exhaust. That is why rockets work in space, where there is no air at all, and why the third law rather than air pressure is the correct explanation.

"The first law only applies to objects at rest." It covers both states equally. Something moving carries on moving at the same speed in the same direction, which is the harder half to see on a planet where friction stops everything.

Putting it together

• First law: objects keep doing what they are doing unless an unbalanced force acts. The tendency is called inertia, and more mass means more of it.
• Second law: force equals mass times acceleration, which rearranges to give acceleration or mass.
• The force in that formula is the net force, after opposing forces have been cancelled.
• Third law: forces always come in equal and opposite pairs, acting on two different objects.
• Because the pair acts on different objects, action and reaction never cancel each other.
• Walking, swimming and rockets are all the third law, and seat belts and dashboard cups are all the first.

One force has been in the background of every example: the one pulling everything down. It gets the next lesson.

Sources

1. NASA Glenn Research Center. (n.d.). Newton's laws of motion. Beginner's Guide to Aeronautics. grc.nasa.gov
2. NASA Glenn Research Center. (n.d.). Newton's third law of motion. grc.nasa.gov
3. Wikipedia contributors. (n.d.). Newton's laws of motion. Wikipedia. en.wikipedia.org
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Forces and motion: basics. phet.colorado.edu

A hammer and a feather, dropped on the Moon

On 2 August 1971, standing on the surface of the Moon at the end of the Apollo 15 mission, astronaut David Scott held out a geology hammer in one hand and a falcon feather in the other. He let go of both at the same moment. They fell together and hit the dust at the same instant, on camera, in front of a live television audience.

On Earth the feather would have drifted down long after the hammer. The difference is not gravity. It is that the Moon has no air, so there was no air resistance to hold the feather back. Remove the air and everything falls at the same rate, whatever its mass, exactly as Galileo had argued nearly four centuries earlier without ever being able to prove it cleanly.

Key idea: Gravity pulls harder on more massive objects, but more massive objects are also harder to accelerate, and the two effects cancel exactly. That is why everything falls at the same rate when air is out of the way.

What gravity is

Gravity is an attraction between any two objects that have mass. Every object attracts every other one. You are attracting your chair, your phone and the Moon, right now.

Two things decide how strong the pull is.

1. Mass. More mass on either object means a stronger pull.
2. Distance. The further apart, the weaker the pull, and it drops off quickly.

The reason you never notice the pull between yourself and your chair is that gravity is an extraordinarily weak force unless one of the objects is enormous. The Earth qualifies. It is massive enough that its pull is the dominant force in your everyday life, and that pull is what holds the atmosphere down, keeps the Moon in orbit, and makes dropped things fall.

Near the Earth's surface, gravity pulls with about 9.8 newtons on every kilogram of mass. That number is usually rounded to 10 for mental arithmetic and it is called the gravitational field strength.

Mass and weight are different quantities

In ordinary speech the two words are used interchangeably. In physics they are not, and keeping them apart clears up a whole family of confusions.

	Mass	Weight
What it measures	How much matter there is	The force of gravity pulling on that matter
Unit	Kilograms	Newtons
Does it change with location?	No, it is the same everywhere	Yes, it depends on the gravity where you are
What measures it	A balance, comparing against known masses	A spring scale, measuring a pull
Is it a force?	No	Yes

The formula is weight = mass × gravitational field strength.

Worked example. A student has a mass of 60 kg. Find her weight on Earth, on the Moon, and on Mars.

Step 1. Earth, where the field strength is about 9.8 N per kg: 60 × 9.8 = 588 N. Round to about 590 N.

Step 2. The Moon, where it is about 1.6 N per kg, roughly one sixth of Earth's: 60 × 1.6 = 96 N.

Step 3. Mars, where it is about 3.7 N per kg: 60 × 3.7 = 222 N.

Step 4. Her mass in all three places: 60 kg. It never changed. She is made of exactly the same amount of matter on Mars as in her kitchen.

So an astronaut on the Moon weighs about a sixth of what she weighs at home, which is why the Apollo crews bounced. Their muscles were pushing against a sixth of the usual downward pull while their bodies still had all their usual inertia, which is a genuinely strange combination to walk in.

The point: Mass is how much of you there is. Weight is how hard the nearest large object is pulling on you. Travel and one changes; the other does not.

Why astronauts float, and what it is not

Video from the International Space Station shows people and water droplets drifting about, and the usual explanation is that there is no gravity up there. That explanation is wrong.

The station orbits roughly 400 kilometres above the surface. At that height Earth's gravity is still about 90 percent as strong as it is on the ground. If gravity had switched off, the station would fly straight off into space instead of circling the planet.

What is actually happening is that the station and everyone inside it are falling, all the time, and moving sideways so fast that they keep missing the Earth. Everything falls together at the same rate, so nothing presses against anything else, and the crew have nothing to push against. That is what floating is: not the absence of gravity, but falling with no floor coming to meet you.

You can feel a hint of it in a lift that starts to descend quickly, when your stomach seems to lift for a moment. For that instant you and the floor are accelerating downwards together, and the floor is pushing on you less.

Experiment: two very different masses, dropped together

Safe. Do it over grass, carpet or a table, not over your feet, and use unbreakable objects.

1. Take two identical plastic bottles with lids. Fill one with water and leave the other empty. Cap both.
2. Weigh them if you have a scale. The full one will be several times heavier.
3. Hold one in each hand at exactly the same height, arms outstretched, and release both at the same instant. Listen as much as watch.
4. Repeat three times, swapping hands, until you are confident about what you heard.
5. Now repeat with a bottle and a single flat sheet of paper.

What to expect: The two bottles land at the same time, and you hear one sound rather than two. The paper drifts down long afterwards.

Why it happens: The full bottle is pulled down much harder, because gravity pulls in proportion to mass. But it also has much more inertia, so the same proportion more force is needed to accelerate it. The two effects cancel exactly, and both bottles gain speed at the same rate. The paper behaves differently only because its large surface meets much more air resistance, which is the same reason Scott's feather would have lost on Earth and did not lose on the Moon.

Experiment: work out your weight across the solar system

No equipment beyond a bathroom scale and a calculator.

1. Weigh yourself and write down your mass in kilograms. A bathroom scale reads mass in kilograms even though we call it weighing.
2. Multiply your mass by 9.8 to get your weight on Earth in newtons.
3. Multiply your mass by 1.6 for the Moon, and by 3.7 for Mars.
4. Divide your Moon answer by your Earth answer and see what fraction you get.
5. Write down what your mass would be in each place.

What to expect: A 50 kg person weighs about 490 N on Earth, 80 N on the Moon and 185 N on Mars. The Moon fraction comes out at about one sixth. Mass stays at 50 kg everywhere.

Why it happens: Weight is the pull of the nearest large mass, and the Moon has far less mass than Earth, so it pulls far less hard. Your body has not changed at all, which is exactly why mass is the more useful quantity for describing an object and weight is the more useful one for describing a situation.

Common misconceptions

"There is no gravity in space." Gravity reaches everywhere and is what holds the Moon in its orbit. At the space station's altitude it is still about 90 percent as strong as at the surface. Astronauts float because they are falling continuously, not because gravity is absent.

"Heavier things fall faster." Only when air resistance is in play. A hammer and a feather land together on the airless Moon, and two capped bottles of very different mass land together on Earth.

"Mass and weight are the same thing measured in different units." Mass is an amount of matter and does not change. Weight is a force and changes with location. Your mass on Mars is identical to your mass at home; your weight is about 38 percent of it.

"Gravity only pulls downwards." It pulls towards the centre of the mass doing the pulling. Down is simply the direction of the Earth's centre from wherever you happen to be standing, which is why down in Australia points the opposite way in space from down in Canada.

Summing up

• Gravity is an attraction between any two masses, stronger with more mass and weaker with more distance.
• Earth pulls with about 9.8 newtons per kilogram, often rounded to 10.
• Mass is measured in kilograms and never changes; weight is a force in newtons and changes with location.
• Weight equals mass times gravitational field strength.
• The Moon pulls about one sixth as hard as Earth, and Mars about 38 percent as hard.
• Astronauts float because they are in continuous free fall, not because gravity has gone.
• With air resistance removed, everything falls at the same rate regardless of mass.

Lifting something against gravity takes energy, and that word has been doing quiet work for several lessons. It is time to define it.

Sources

1. NASA Glenn Research Center. (n.d.). Weight equation. Beginner's Guide to Aeronautics. grc.nasa.gov
2. NASA. (n.d.). What is microgravity? nasa.gov
3. NASA Glenn Research Center. (n.d.). Mass. grc.nasa.gov
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Gravity force lab. phet.colorado.edu

The ball that never comes back to your hand

Hold a bouncing ball at shoulder height, about 1.5 metres, and drop it. It comes back up to perhaps 1 metre. Drop it again from there and the second bounce reaches maybe 65 centimetres. Keep going and the bounces shrink until the ball is rattling on the floor and then lying still.

Nobody took anything away. Nobody added anything. And yet the ball has, apparently, less of something after each bounce than it had before.

Physics insists that nothing was lost, and this lesson is about what that claim actually means, because on the face of it the bouncing ball looks like a straightforward contradiction of it.

Key idea: Energy is never created or destroyed. It moves from place to place and changes form, and some of it always ends up spread out as heat where nothing can use it.

What energy is, and what it is measured in

Energy is what makes things happen. Nothing moves, heats, glows, grows or sounds without energy being transferred, which is why it turns up in every other topic in this course.

It is measured in joules, written J, named after James Prescott Joule. One joule is roughly the energy needed to lift a small apple one metre against gravity, which tells you that a joule is a small unit. Food labels use kilojoules, thousands of joules, and electricity bills use kilowatt hours, which are millions.

The forms energy takes

Form	What it is	Example
Kinetic	Energy of anything moving	A rolling ball, wind, a running child
Gravitational potential	Energy stored by being high up	A book on a shelf, water behind a dam
Elastic potential	Energy stored by stretching or squashing	A drawn bow, a wound spring, a squashed ball
Chemical	Energy stored in the arrangement of atoms	Food, fuel, a battery
Thermal	Energy of the random motion of particles	A hot drink, a warm room
Light	Energy carried by electromagnetic waves	Sunlight, a torch beam
Sound	Energy carried by vibrations through matter	A shout, a drumbeat
Electrical	Energy carried by moving charge	Current in a wire
Nuclear	Energy stored in the nucleus of an atom	The Sun, a nuclear power station

These are not nine different substances. They are nine descriptions of where the same quantity currently is and what it is doing. A ball on a shelf and the same ball falling have the same energy in two different accounts.

Energy chains

The useful way to describe an event is to follow the energy from store to store, writing arrows between them.

A torch being switched on. Chemical energy in the battery becomes electrical energy in the wires, which becomes light energy from the bulb, and also thermal energy, because the bulb gets warm.

A child on a swing. At the highest point the swing is momentarily still, and all the energy is gravitational potential. At the lowest point it is moving fastest, and the energy is kinetic. Rising again turns kinetic back into gravitational potential. Every cycle, a little goes to sound and to warming the air and the ropes, which is why a swing that nobody pushes gradually stops.

Eating breakfast and running for a bus. Chemical energy in the food becomes chemical energy stored in your body, then kinetic energy in your legs, and a great deal of thermal energy, which is why you get hot when you run.

What matters here: Every chain ends with thermal energy. Always. It is never the only output, but it is always one of them.

Conservation, and why the ball still loses

The law of conservation of energy says the total amount of energy in a closed system stays constant. Energy can move and change form, but the books always balance.

So follow the ball properly.

1. Held at 1.5 metres, the ball has gravitational potential energy.
2. Falling, that becomes kinetic energy. Just before impact, nearly all of it is kinetic.
3. At the moment of impact the ball squashes, and the kinetic energy briefly becomes elastic potential energy in the deformed rubber.
4. The ball springs back, turning most of that elastic energy into kinetic again, which carries it upwards.
5. But not all of it. Some went into the sound you heard, which is energy that travelled off through the air. Some went into warming the ball and the floor very slightly, because squashing and un-squashing rubber heats it. Some went into pushing air aside on the way down.

Add up the height of the bounce, the sound and the warming and you get back the energy you started with. Nothing vanished. What happened is that a portion of it moved into a form that cannot lift the ball: heat, spread thinly through the ball, the floor and the air.

That is what people mean by wasted energy. It is not destroyed energy. It is energy that has been shared out so widely and thinly that no practical machine can gather it back up and use it. The technical word is dissipated, and it is why perpetual motion machines do not work: every real machine leaks energy into heat, and once it has spread out, it stays spread out.

Useful and wasted, in numbers

An old filament light bulb takes in 100 joules of electrical energy every second and turns roughly 5 of them into light. The other 95 become heat. A modern LED bulb takes in about 10 joules per second to make the same amount of light, so far more of what it takes in ends up as the thing you actually wanted.

The fraction that comes out as what you wanted is called efficiency. The filament bulb is about 5 percent efficient at making light, which is another way of saying it is an excellent heater that happens to glow.

Neither bulb destroys or creates a single joule. They differ only in how much of the input lands in the useful pile.

Experiment: measure the energy a ball keeps

Safe. Do it against a wall you can mark with a pencil, or with someone holding a ruler.

1. Tape a long ruler or a metre stick vertically against a wall, or mark heights on the wall with a pencil.
2. Hold a bouncy ball with its lowest point exactly at 100 cm and let it go without throwing it.
3. Have a partner watch at eye level and note the height of the top of the first bounce.
4. Repeat three times and take the middle reading.
5. Now repeat the whole thing on three surfaces: a hard floor, a carpet, and a folded towel.
6. For each surface, work out the bounce height as a percentage of 100 cm.

What to expect: On a hard floor a good bouncy ball may return 70 to 80 percent of its drop height. On carpet it will be much less, and on a folded towel it may barely bounce at all.

Why it happens: The percentage is telling you how much of the original gravitational potential energy came back as gravitational potential energy. The rest went to sound and heat. A soft surface squashes and does not spring back, so it converts much more of the arriving energy into warmth in its fibres, which is precisely why crash mats and running shoes are made of it. Nothing was destroyed in any of the three runs; the surfaces differ only in how much of the energy they send onward and how much they dissipate.

Experiment: turn movement into heat with your hands

1. Press your palms together and rub them back and forth fast for fifteen seconds. Notice the temperature.
2. Take a metal paperclip and bend it back and forth at the same spot, twenty times, quickly.
3. Immediately touch the bent spot to your lip or the back of your hand, which are far more sensitive than fingertips. Do not use a paperclip that has snapped, as the ends can be sharp.

What to expect: Your palms get noticeably warm. The bend in the paperclip feels distinctly hot.

Why it happens: In both cases you supplied energy by moving, and friction or repeated bending turned it into thermal energy in the material. This is the wasted branch of an energy chain made deliberate and obvious. Notice how one sided it is: you can turn movement into heat with almost no effort, and turning that heat back into movement would need an engine and would only recover a fraction. That one-way tendency is why energy chains always end at heat.

Common misconceptions

"Energy is used up." It is transferred, not consumed. When a phone battery goes flat the chemical energy has become light, sound and heat that have left the phone. The total is unchanged; it is simply no longer where you can use it.

"Wasted energy has been destroyed." It has been dissipated, spread thinly as heat through the surroundings. Destroyed and unusable are different things, and only the second one ever happens.

"A bouncing ball loses energy, so conservation of energy is wrong." Measure the sound and the warming as well as the height and the total balances. The bounce is lower because some energy left the ball, not because some ceased to exist.

"Heat and temperature are the same as energy." Thermal energy is one form energy can take. The next lesson separates heat from temperature properly, because they are not the same thing either.

Where this leaves us

• Energy is what makes things happen, and it is measured in joules.
• It comes in forms including kinetic, gravitational potential, elastic potential, chemical, thermal, light, sound, electrical and nuclear.
• Events are best described as chains: energy moving from one store to another.
• The total energy in a closed system never changes, whatever else happens.
• Every real chain sends some energy to heat, spread thinly through the surroundings, which is what wasted means.
• Efficiency is the fraction of the input that comes out as the thing you wanted.

Heat has now turned up in every single energy chain in this lesson. It deserves its own.

Sources

1. Khan Academy. (n.d.). Energy. Middle school physics. khanacademy.org
2. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Energy forms and changes. phet.colorado.edu
3. Urone, P. P., and Hinrichs, R. (2020). Work, power, and the work-energy theorem. Physics. OpenStax, Rice University. openstax.org
4. Wikipedia contributors. (n.d.). Conservation of energy. Wikipedia. en.wikipedia.org

A cup of tea and a bathtub

A cup of tea sits at 80 degrees Celsius. A bath in the next room sits at 40 degrees. The tea is twice as hot on the thermometer, and it would scald you.

Now ask a different question: which one contains more thermal energy? The bath, by an enormous margin. It holds perhaps four hundred times as much water, and every one of those particles is carrying energy. Pouring the bath into a swimming pool would warm the pool more than pouring the tea in would.

Hotter and more energy are not the same claim. Getting the two apart is what this lesson does first.

Key idea: Temperature is how fast the particles are moving on average. Heat is energy on the move because of a temperature difference. A small hot thing can be at a high temperature and still carry little energy.

Temperature

Temperature measures the average kinetic energy of the particles in a substance. Faster particles, higher temperature. It is measured in degrees Celsius for everyday purposes.

The word average matters. In any cup of water some particles are moving much faster than others; the thermometer reports the average of the whole crowd. That is also why the size of the sample makes no difference to temperature: a teaspoon of the bath and the whole bath read the same.

There is a floor. Cool anything far enough and the particle motion drops to its absolute minimum, at about −273 degrees Celsius, called absolute zero. Nothing can be colder, because nothing can be slower than as slow as possible. Laboratories have got extremely close to it and never reached it.

Heat

Heat is energy transferred from a hotter place to a cooler place. It is not a substance stored in objects; it is the flow itself. Objects store thermal energy, and heat is what we call that energy while it is moving.

Two rules follow, and they run the rest of the lesson.

1. Heat always flows from hotter to colder, never the other way on its own.
2. The flow continues until the temperatures are equal, at which point the objects are in thermal equilibrium and nothing more happens.

This is why there is no such thing as coldness flowing into something. A cold drink does not fill your hand with cold; your hand loses energy to the drink. The direction is always the same, and only the size of the temperature difference changes how fast it goes.

Three ways energy gets from hot to cold

Method	How it works	Where it happens	Everyday example
Conduction	Vibrating particles knock into their neighbours and pass energy along	Mainly solids, especially metals	A spoon handle warming in a hot drink
Convection	Warmed fluid expands, becomes less dense, rises, and cooler fluid flows in to replace it	Liquids and gases only	A radiator warming a whole room
Radiation	Energy travels as infrared waves, needing no material at all	Anywhere, including a vacuum	The Sun warming your face through a window

Conduction is a chain reaction of collisions. Heat one end of a metal rod and the particles there vibrate harder, knock their neighbours, and the disturbance travels along. Metals do this exceptionally well, which is why saucepans are metal and their handles are not. Air does it terribly, which is why anything full of trapped air is a good insulator: a duvet, a woolly jumper, loft insulation, the fur on an animal. None of those materials is warm. They simply slow the escape of energy from something that is.

Convection needs the material itself to move, so it cannot happen in solids. Warm a liquid or a gas and it expands, becoming less dense than the cooler fluid around it, so it floats upwards. Cooler fluid sinks to take its place, is warmed in turn, and the loop keeps going. That loop is a convection current. It is why a heater placed near the floor warms a whole room while one near the ceiling would not, why the top of a bus is warmer than the bottom, and why a hot air balloon rises.

Radiation is the odd one out because it needs no matter whatsoever. Energy from the Sun crosses about 150 million kilometres of near-perfect vacuum in a little over eight minutes and arrives at your face. It travels as infrared, which sits just beyond red on the electromagnetic spectrum. Dark, matt surfaces absorb and emit it well; shiny, light surfaces reflect it, which is why a survival blanket is silver and why a white roof stays cooler than a black one.

Remember: Conduction needs contact. Convection needs a fluid that can move. Radiation needs nothing at all.

The metal handle that is not actually cold

Reach into a drawer and touch a metal spoon and a wooden spoon. The metal feels colder. Both have been sitting in the same drawer for a week, so both are at exactly the same temperature, and a thermometer will confirm it.

What you are feeling is not their temperature. It is the rate at which they take energy from your hand. Metal conducts extremely well, so it pulls warmth from your skin quickly, and the sensation of rapid heat loss is what your nerves report as cold. Wood conducts badly, so it takes very little, and it feels neutral.

Put both in a warm oven for ten minutes and the same property reverses the sensation: the metal will feel far hotter, because it delivers energy to your hand quickly. Your skin does not have a thermometer in it. It has a heat-flow detector, and that is a genuinely different instrument.

Experiment: race two cups to room temperature

Safe if you use warm tap water rather than boiling water. Ask an adult before using anything hotter than the tap.

1. Fill two identical mugs with the same amount of warm water from the tap, filling them at the same moment.
2. Wrap one mug completely in a towel or a woolly jumper, including a loose cover over the top. Leave the other bare.
3. If you have a thermometer, take both starting temperatures. If not, you will judge by touch at the end.
4. Wait thirty minutes without disturbing either.
5. Unwrap the towel and compare, either by thermometer or by dipping a clean finger into each.

What to expect: The wrapped mug is clearly warmer. Over thirty minutes the difference is easy to feel and typically several degrees.

Why it happens: The towel is full of trapped air, and air is a poor conductor. It slows conduction out through the sides and it stops convection currents carrying warm air away from the surface. The lid matters too, because without it the fastest particles evaporate off the top and take their energy with them. Notice the towel did not add anything: both mugs are cooling, and one is simply cooling more slowly. Insulation never makes something warmer, it only makes heat leave more slowly.

Experiment: watch a convection current

Safe with warm tap water and food colouring.

1. Fill a large clear glass or jug with cold water and let it stand for five minutes until it is completely still.
2. Fill a small bottle or a narrow glass with warm tap water and add several drops of food colouring so it is strongly coloured.
3. Very gently lower the small container into the big one so it sits on the bottom without tipping. A pair of tongs or a slow steady hand works.
4. Watch the coloured water for two minutes without touching the glass.
5. Repeat the whole experiment with cold coloured water instead of warm.

What to expect: The warm coloured water rises in a plume to the top and spreads out there. The cold coloured water stays put or creeps along the bottom.

Why it happens: Warming water makes its particles spread slightly further apart, so the same mass takes up more space and the water becomes less dense. Less dense fluid floats on more dense fluid, exactly as a cork floats on water, so the warm plume rises. That is one half of a convection current; the cooler water sinking around it to take its place is the other half. This is the mechanism that circulates air in a room, water in a kettle, and, on a vastly larger scale, air in the atmosphere and water in the oceans.

Common misconceptions

"Metal is colder than wood." In the same drawer both are at the same temperature. Metal conducts energy away from your hand faster, and your skin reports the speed of that loss, not the temperature.

"Cold flows into things." Only energy flows, and it always flows from hotter to colder. Ice does not fill a drink with cold; the drink loses energy to the ice.

"A jumper is warm." A jumper is at room temperature until you put it on. It works by trapping air, which conducts badly, so your own body heat leaves more slowly. It supplies no warmth of its own.

"Temperature and thermal energy are the same." Temperature is the average speed of the particles. Thermal energy also depends on how many particles there are, which is why a bath at 40 degrees holds far more than a cup of tea at 80.

What you now know

• Temperature is the average kinetic energy of particles; heat is energy transferred because of a temperature difference.
• Heat always flows from hotter to colder, and stops when the temperatures match.
• Conduction passes energy by particle collisions and works best in metals.
• Convection carries energy by the movement of a fluid, driven by warm fluid becoming less dense and rising.
• Radiation carries energy as infrared waves and needs no material, which is how the Sun reaches us.
• Insulators work by trapping air and slowing conduction and convection; they add no warmth themselves.
• Your skin senses the rate of heat flow, not temperature, which is why metal feels colder than wood.

Radiation travels as a wave. That word has been used loosely for two lessons now, and the next module gives it a proper definition.

Sources

1. NASA. (n.d.). Earth. NASA Science. science.nasa.gov
2. Wikipedia contributors. (n.d.). Heat transfer. Wikipedia. en.wikipedia.org
3. Wikipedia contributors. (n.d.). Temperature. Wikipedia. en.wikipedia.org
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Energy forms and changes. phet.colorado.edu

The wave that travels round a stadium

Forty thousand people in a stadium stand up, throw their arms in the air, and sit down again, each a fraction of a second after the person to their left. Seen from the far side, a wave sweeps right round the ground and comes back to where it started.

Nobody moved seats. Every single person ended up exactly where they began, having gone up and come down. Something unmistakably travelled all the way round the stadium, and it was not any of the people.

That is the whole idea of a wave, and once you have it, water waves, sound and light all become versions of the same thing.

Key idea: A wave transfers energy from place to place without carrying the material with it.

Two kinds of wave

Waves are sorted by the direction the material wobbles compared with the direction the wave travels.

• In a transverse wave the material moves at right angles to the wave's direction. The stadium wave travels sideways round the ground while the people move up and down. Water waves, waves on a rope, and light are all transverse.
• In a longitudinal wave the material moves back and forth along the same line the wave travels. Squeeze one end of a long spring and a squashed region runs down its length. Sound is longitudinal, and that will matter a great deal in the next lesson.

Both kinds obey everything that follows. The measurements are the same; only the direction of the wobble differs.

The parts of a wave

• A crest is a high point of the wave; a trough is a low point.
• Amplitude is the distance from the middle rest position up to a crest. It is measured from the middle, not from trough to crest, which is a common slip and gives an answer twice too big.
• Wavelength is the distance from one point on the wave to the matching point on the next: crest to crest, or trough to trough. It is measured in metres.
• Frequency is how many complete waves pass a point each second, measured in hertz, written Hz. Five waves per second is 5 Hz.

Amplitude and frequency describe different things and are worth keeping apart. Amplitude tells you how much energy the wave carries: a bigger amplitude means a louder sound or a brighter light or a more destructive sea. Frequency tells you how often the wobble repeats: for sound it becomes pitch, and for light it becomes colour.

The wave equation

wave speed = frequency × wavelength

The reason is worth thinking through rather than memorising. If four complete waves pass you every second, and each one is 3 metres long, then in one second 12 metres of wave has gone by. Speed is distance per second, so the speed is 12 metres per second, which is 4 multiplied by 3.

Worked example 1. A wave has a frequency of 5 Hz and a wavelength of 2 m. Find its speed.

Step 1. speed = frequency × wavelength.

Step 2. 5 × 2 = 10.

Step 3. The speed is 10 metres per second.

Worked example 2. A sound travels at 340 m/s with a wavelength of 0.68 m. Find the frequency.

Step 1. Rearrange: frequency = speed ÷ wavelength.

Step 2. 340 ÷ 0.68 = 500.

Step 3. The frequency is 500 Hz.

Worked example 3. A radio station broadcasts at 100 million Hz. Radio waves travel at 300 million m/s. Find the wavelength.

Step 1. Rearrange: wavelength = speed ÷ frequency.

Step 2. 300,000,000 ÷ 100,000,000 = 3.

Step 3. The wavelength is 3 metres, which is roughly why car radio aerials are the length they are.

In short: In a given material the speed is fixed, so frequency and wavelength trade off against each other. Higher frequency means shorter wavelength, and the other way round.

How fast do waves actually go?

Wave	Where	Approximate speed
Sound	Air at about 20 degrees Celsius	343 metres per second
Sound	Water	Roughly four times faster than in air
Light	Vacuum	300,000 kilometres per second
Ripples	A tray of water	Under a metre per second

The gap between sound and light is why you see lightning before you hear thunder. The light arrives essentially instantly and the sound takes about three seconds to cover a kilometre, which gives the familiar rule for estimating how far away a storm is.

Experiment: make waves on a rope

Safe. You need a skipping rope, a washing line, or a long piece of soft cord, and somewhere with room to swing it. Keep clear of lamps and faces.

1. Tie one end of the rope to a door handle, or have someone hold it still, and stretch it out so it is slack but straight.
2. Flick your end sharply upwards once and watch the single hump run along the rope to the far end.
3. Now move your hand steadily up and down, about once a second, and keep going. Watch the shape that forms.
4. Keep the timing the same but move your hand through a much bigger distance. Note what changes and what does not.
5. Now go back to the small movement but shake much faster, three or four times a second. Note what changes.
6. Put a small piece of tape on the rope halfway along and watch what it does while the waves run past.

What to expect: The single flick travels away from you and does not come back with your hand. Steady shaking makes a repeating wave. A bigger hand movement makes taller humps but the same number of them. Faster shaking makes more humps, and they are closer together. The tape moves up and down but stays in the same place along the rope.

Why it happens: Every result here is one of the definitions made visible. Bigger hand movement is bigger amplitude, and the number of waves per second, the frequency, did not change. Faster shaking is higher frequency, and because the speed along a given rope is fixed by the rope's tension, higher frequency has to mean shorter wavelength, which is why the humps crowd together. And the tape is the stadium spectator: it goes up and down, it stays in its seat, and something travels past it anyway.

Experiment: ripples and a floating crumb

1. Fill a large baking tray or a washing-up bowl with water about 3 cm deep and let it settle completely still.
2. Drop a small piece of cork, a breadcrumb or a scrap of paper onto the surface near the middle.
3. Dip one fingertip in and out at one end of the tray, once per second, and watch the ripples spread.
4. Watch the floating crumb carefully as the ripples pass under it.
5. Now dip faster and watch what happens to the spacing of the ripples.

What to expect: Ripples spread out across the tray. The crumb bobs up and down almost on the spot and is not carried to the far end. Faster dipping gives ripples that are closer together.

Why it happens: The ripples carry energy across the tray, which is obvious because they can make the crumb move at all. What they do not carry is the water. Each bit of water rises and falls and returns to where it started, exactly like the stadium crowd. The crowding of the ripples at higher frequency is the wave equation again: same water, same speed, more waves per second, so each one has to be shorter.

Common misconceptions

"Waves carry water forwards." They carry energy forwards. The water goes round in small circles and stays put, which is why a floating crumb bobs instead of being delivered to the far side of the tray. Surfers are pushed by breaking waves in shallow water, which is a different and more complicated situation.

"Amplitude is the distance from trough to crest." It is measured from the middle rest position to a crest, which is half of trough to crest. Using the full height doubles every answer.

"A louder sound travels faster." Loudness is amplitude and does not change the speed. In a given material at a given temperature, all sounds travel at the same speed, which is why a band stays in time at the back of a hall.

"Frequency and wavelength are independent." In a fixed material they are locked together by the wave equation. Raise the frequency and the wavelength must shorten, because the speed cannot change.

Looking back

• A wave transfers energy without transferring matter; the material returns to where it started.
• Transverse waves wobble at right angles to their direction of travel; longitudinal waves wobble along it.
• Amplitude is measured from the rest position to a crest and tells you the energy carried.
• Wavelength is crest to crest; frequency is waves per second, measured in hertz.
• Wave speed equals frequency times wavelength, and the equation rearranges for either.
• In a given material the speed is fixed, so higher frequency always means shorter wavelength.

Next: the longitudinal wave you meet most often, and why you cannot hear anything in space.

Sources

1. Urone, P. P., and Hinrichs, R. (2020). Types of waves. Physics. OpenStax, Rice University. openstax.org
2. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Wave on a string. phet.colorado.edu
3. Khan Academy. (n.d.). Waves. Middle school physics. khanacademy.org
4. Wikipedia contributors. (n.d.). Wavelength. Wikipedia. en.wikipedia.org

The bell that could not be heard

Around 1660 Robert Boyle set a ringing bell inside a sealed glass vessel and used an air pump to draw the air out. As the air thinned, the sound of the bell faded, and faded, until it could barely be heard at all, while the clapper could still plainly be seen striking.

Nothing had happened to the bell. It was vibrating exactly as before. What had been removed was the air, and without air there was nothing to carry the vibration to the listener's ear.

That single experiment separates sound from light for good. Light crossed the glass and the vacuum without difficulty; sound could not cross the vacuum at all.

Key idea: Sound is a vibration passed from particle to particle. Remove the particles and there is nothing left to pass it along.

What a sound wave actually is

Every sound starts with something vibrating: a guitar string, a drum skin, your vocal folds, a speaker cone.

When the speaker cone pushes forwards, it squashes the air particles just in front of it into a slightly crowded region called a compression. When it pulls back, it leaves a slightly thinned region called a rarefaction. The cone moves back and forth many times a second, so a train of compressions and rarefactions travels outwards.

This is a longitudinal wave: the air particles move back and forth along the same line the sound travels, unlike the up and down of a rope wave. Each particle jiggles a tiny distance and stays roughly where it started. What travels across the room is the pattern of crowding and thinning, not the air itself. If air actually travelled from a speaker to your ear you would feel a wind, and you do not.

Your eardrum is pushed inwards by each compression and outwards by each rarefaction. That tiny drumming is turned by the rest of your ear into signals your brain reads as sound.

Sound needs a medium, and prefers a stiff one

Because sound is passed from particle to particle, the material it is travelling through matters enormously.

Material	Approximate speed of sound	Why
Vacuum	No sound at all	No particles to pass the vibration on
Air at about 20 degrees Celsius	343 metres per second	Particles are far apart, so the message travels slowly
Water	About 1480 metres per second	Particles are touching, so each passes it on sooner
Steel	Around 5000 metres per second	Particles are tightly bonded and pass it on almost immediately

Read that table against the particle model from Module 1 and it falls straight out. In a gas the particles have to fly across a gap before they can hit the next one. In a liquid they are already touching. In a solid they are bonded together, so a push on one is felt by its neighbour almost instantly. Closer and more tightly held means faster sound, which is exactly the opposite of what most people guess.

This is why putting your ear to a rail lets you hear a distant train before you hear it through the air, and why whales can communicate across enormous distances of ocean.

Why this matters: Sound travels fastest in solids, slower in liquids, slowest in gases, and not at all in a vacuum. Space really is silent.

Pitch and loudness are two separate measurements

What you hear	What it measures	Change it by
Pitch, how high or low the note is	Frequency, in hertz	Making the source vibrate faster or slower
Loudness, how strong the sound is	Amplitude of the wave	Making the source vibrate through a bigger distance

A short, tight, thin guitar string vibrates quickly, giving a high frequency and a high note. A long, slack, thick string vibrates slowly, giving a low note. Pluck either one harder and the string swings further, the compressions are more compressed, the amplitude is greater, and the note is louder. The pitch does not change.

Human hearing runs from about 20 Hz at the low end to about 20,000 Hz at the high end, and the top of that range drops steadily with age, which is why children can often hear sounds that adults in the same room cannot. Dogs hear well above the human ceiling, which is what a silent dog whistle exploits, and bats navigate using frequencies far higher still.

Echoes, and using them to measure

Sound reflects off hard surfaces. A reflected sound that arrives late enough to be heard separately is an echo.

Because you know the speed of sound, an echo can measure distance. Send a sound, time how long it takes to come back, and remember the crucial detail: it travelled to the wall and back, so the distance to the wall is half the total.

Worked example. You shout at a cliff and hear the echo 2 seconds later. Sound travels at 340 m/s. How far away is the cliff?

Step 1. Total distance travelled = speed × time = 340 × 2 = 680 metres.

Step 2. That is there and back, so halve it: 680 ÷ 2 = 340 metres.

Step 3. The cliff is 340 metres away.

Ships map the sea floor this way, sending a pulse downwards and timing its return, a technique called sonar. Hospitals use the same idea at much higher frequencies to look inside the body, which is what an ultrasound scan is. Forgetting to halve is the standard mistake, and it doubles every answer.

Experiment: change pitch and loudness independently

Safe. A ruler and a rubber band do the whole thing.

1. Hold a ruler flat on the edge of a table with about 20 cm hanging over the edge, pressing the other end down firmly.
2. Twang the free end and listen to the note. Watch the ruler blur as it vibrates.
3. Slide the ruler so only 10 cm hangs over and twang again with the same force. Listen to the pitch.
4. Go back to 20 cm and twang gently, then twang hard. Listen to what changes and what does not.
5. Now stretch a rubber band between two fingers and pluck it. Stretch it tighter and pluck again.

What to expect: A shorter overhang gives a higher note. A harder twang gives a louder note at the same pitch. A tighter rubber band gives a higher note.

Why it happens: A shorter or tighter piece of material vibrates more times per second, which is a higher frequency, which your ear reports as a higher pitch. Twanging harder does not change how often it vibrates, only how far it swings each time, which is amplitude, which your ear reports as loudness. Steps 3 and 4 are the whole distinction, done twice, with only one variable changed each time.

Experiment: hear a spoon become a church bell

Safe and startling. Use string, not wire.

1. Tie the middle of a metal spoon to the centre of a piece of string about a metre long.
2. Let the spoon hang and swing it against the edge of a table. Listen to the ordinary clinking sound.
3. Now wind one end of the string around your left index finger and the other end around your right, and press both fingertips gently into your ears. Do not push them in hard.
4. Let the spoon hang freely and swing it against the table edge again.
5. Try it with a larger metal object, such as a metal coat hanger, tied the same way.

What to expect: Through the air it is a small clink. Through the string it becomes a deep, ringing, resonant sound like a large bell, far louder and richer than you expected.

Why it happens: The first time, the vibration reaches you through air, whose widely spaced particles pass it on poorly and spread it in all directions. The second time, the string carries the vibration directly to your ears through a solid path where the particles are bonded together. Almost none of the energy leaks away sideways, so much more of it arrives, and it arrives faster. This is the same reason a doctor's stethoscope uses a tube rather than open air, and why putting your ear against a door tells you more than standing near it.

Common misconceptions

"Explosions in space would be loud." Space is close to a vacuum, so there is nothing to carry the compressions. Boyle's bell showed this in about 1660, and no film has ever obeyed it.

"Sound travels faster in air because air is thinner and easier to move through." The opposite is true. Sound needs particles to pass the vibration between them, so closely packed, tightly bonded particles carry it far faster. Steel beats water, and water beats air.

"Turning the volume up makes the sound reach you sooner." Loudness is amplitude and has no effect on speed. Every sound in a room travels at the same speed, which is why an orchestra does not fall out of time with itself.

"Air travels from the speaker to your ear." The pattern travels; the air stays put, jiggling back and forth over a tiny distance. If air actually crossed the room you would feel a draught from every conversation.

The takeaway

• Sound is a longitudinal wave made of compressions and rarefactions, produced by something vibrating.
• It needs a medium, so there is no sound in a vacuum.
• It travels fastest in solids, slower in liquids and slowest in gases, because closer particles pass the vibration on sooner.
• Pitch is frequency; loudness is amplitude; changing one does not change the other.
• Human hearing runs roughly from 20 Hz to 20,000 Hz, and the upper limit falls with age.
• An echo can measure distance, but the sound travelled there and back, so halve the total.

Light crossed Boyle's vacuum without any trouble at all. That is the last lesson of this module.

Sources

1. National Oceanic and Atmospheric Administration. (n.d.). Sound in the ocean. NOAA National Ocean Service. oceanservice.noaa.gov
2. NASA Glenn Research Center. (n.d.). Sound waves. Beginner's Guide to Aeronautics. grc.nasa.gov
3. Urone, P. P., and Hinrichs, R. (2020). Speed of sound, frequency, and wavelength. Physics. OpenStax, Rice University. openstax.org
4. Wikipedia contributors. (n.d.). Sound. Wikipedia. en.wikipedia.org

The straw that snaps in half

Stand a plastic straw in a glass of water and look at it from the side, level with the surface. The straw appears to break cleanly in two at the waterline, with the lower part offset sideways from the upper part.

Lift it out and it is perfectly straight. Nothing bent, and nothing was ever bent. What bent was the light, on its way from the straw to your eye, and this lesson works out exactly why and by how much.

Key idea: Light travels in straight lines until it meets a boundary. At a boundary it can bounce, and it can bend, and both are completely predictable.

What light is

Light is a transverse wave, and unlike sound it needs no material at all. It crosses the vacuum between the Sun and the Earth without difficulty, which is exactly what Boyle's bell in the last lesson could not do.

In a vacuum it travels at about 300,000 kilometres per second. That is fast enough to go round the Earth about seven and a half times in one second, and it is the fastest speed anything can travel. Sunlight takes a little over eight minutes to reach us.

Visible light is a narrow band of a much larger family called the electromagnetic spectrum, which also contains radio waves, microwaves, infrared, ultraviolet, X-rays and gamma rays. All of them are the same kind of wave differing only in wavelength and frequency, and all travel at the same speed in a vacuum. Your eyes happen to respond to one thin slice of it.

Within that slice, wavelength is colour. Red has the longest wavelength your eye can detect and violet the shortest, with orange, yellow, green and blue in between.

Light travels in straight lines

Because light travels in straight lines, an object in its way leaves a region behind it that the light cannot reach. That region is a shadow, and its shape is a projection of the object.

Straight-line travel is also why you cannot see round corners without a mirror, why a pinhole makes an image, and why a torch beam is a beam rather than a general glow. In diagrams we draw light as rays, straight lines with arrows showing the direction of travel.

Note the direction of those arrows carefully. Light travels from a source, bounces off objects, and goes into your eye. Your eye is a detector, not an emitter. Nothing comes out of it, which is why you cannot see in a completely dark room no matter how long you wait.

Reflection, and the line you measure from

When light hits a surface it can bounce off. The rule is short and exact:

The angle of incidence equals the angle of reflection.

Both angles are measured from an imaginary line drawn at right angles to the surface at the point where the light hits, called the normal. This is the part people get wrong. Measure from the surface itself and every number will be the complement of the right one: a ray hitting at 30 degrees to the surface is at 60 degrees to the normal, and the answer you report will be wrong by exactly that swap.

Worked example. A ray strikes a mirror at 25 degrees to the normal. Where does it go?

Step 1. The angle of incidence is 25 degrees, measured from the normal.

Step 2. By the law of reflection, the angle of reflection is also 25 degrees.

Step 3. It leaves on the other side of the normal, so the two rays make an angle of 50 degrees with each other.

Two kinds of reflection matter in ordinary life.

• Specular reflection happens on a very smooth surface such as a mirror or still water. Parallel rays arrive and leave parallel, so the pattern of the light is preserved and you see an image.
• Diffuse reflection happens on a rough surface such as a wall, paper or skin. The law of reflection still holds at every single point, but the surface tilts differently from point to point, so the rays scatter in all directions. No image forms, and that is precisely why you can see a wall from anywhere in the room instead of only from one spot.

The point: A wall does not disobey the law of reflection. It obeys it at every point on a surface that is pointing in thousands of slightly different directions.

Refraction: the bend at the boundary

Light changes speed when it moves from one transparent material into another. It travels fastest in a vacuum, very slightly slower in air, and about three quarters as fast in water. In glass it is slower still.

If the light hits the boundary straight on, it slows down and carries straight on. If it arrives at an angle, one side of the beam reaches the slower material before the other, and that side is held back first, so the beam swings round. That swing is refraction.

There is a rule of thumb worth memorising.

• Going into a slower material, such as air into water or glass, light bends towards the normal.
• Coming out into a faster material, such as water into air, light bends away from the normal.

A helpful picture: imagine a car driving at an angle from tarmac onto sand. The wheel that reaches the sand first slows down while the other is still on tarmac, so the car slews round. Light does the same thing for the same reason.

Now the straw is explained. Light leaves the underwater part of the straw, speeds up as it crosses into the air, and bends away from the normal. Your brain, which has assumed since birth that light travels in straight lines, traces those rays straight back and places the underwater part of the straw somewhere it is not. The break you see is the offset between where the straw really is and where your brain has put it.

The same effect makes a swimming pool look shallower than it is, and it is why a spear-fisher must aim below the fish rather than at it.

Splitting white light

Different colours slow down by slightly different amounts when they enter glass, so they bend by slightly different amounts. Violet bends most and red bends least. Send white light through a triangular prism and the colours fan out into a spectrum, an effect called dispersion.

Isaac Newton did this in the 1660s and then did the crucial second half of the experiment: he sent the fanned-out colours through a second prism and recombined them into white light. That ruled out the idea that the prism was somehow adding colour to the light. The colours were in the white light all along.

A rainbow is the same thing on a larger scale, with raindrops doing the work of the prism, which is why you see one only when the Sun is behind you and rain is falling in front of you.

Experiment: bend the light and move a coin

Completely safe, and there are two results in one setup.

1. Put a coin flat in the bottom of an opaque mug, near the far edge from you.
2. Lower your head slowly until the rim of the mug just hides the coin. Do not move from that spot.
3. Have someone gently pour water into the mug without moving it or splashing the coin.
4. Keep your eye exactly where it was and watch.
5. Then, in a clear glass of water, stand a straw or a pencil and look at it from the side.
6. Look at it again from directly above, straight down the length of it.

What to expect: The coin appears, rising into view without moving. The straw looks broken from the side, and looks perfectly normal from directly above.

Why it happens: Light from the coin that would have travelled below your line of sight is now bent as it leaves the water, swinging away from the normal and up into your eye. Your brain traces it back in a straight line and places the coin higher than it really is. The straw is the same effect on a longer object. The final step is the check that proves the explanation: looking straight down, the light crosses the boundary head on, at no angle, so there is nothing to bend and the straw looks straight. If the water were somehow distorting the object itself, the view from above would be bent too.

Experiment: test the law of reflection

Safe. Use a small mirror and keep it flat on the table.

1. Lay a small flat mirror upright against a stack of books on a sheet of paper, so it stands vertically with its base on the paper.
2. Draw a line along the base of the mirror, then draw a line at right angles to it, out from the middle. That second line is the normal.
3. In a darkened room, shine a narrow torch beam along the paper towards the point where the normal meets the mirror. A torch with a slit of card taped over it gives a narrow beam.
4. Mark the incoming beam with two pencil dots and the outgoing beam with two more.
5. Join the dots, then measure both angles from the normal with a protractor.
6. Repeat at three different incoming angles.

What to expect: The two angles match, within a degree or two, every time.

Why it happens: This is the law of reflection measured rather than asserted. Notice how much easier the measurement is when you use the normal: measuring from the mirror surface would give you angles that also match each other, but they would be the complements, and every calculation in a physics course assumes the angle from the normal. Any small mismatch in your readings is the mirror not standing quite square to the paper, which is worth checking rather than shrugging off.

Common misconceptions

"We see because something comes out of our eyes." Light travels from a source, reflects off objects, and enters the eye. Nothing leaves it. A perfectly dark room stays dark no matter how hard you stare.

"A mirror reverses left and right." It reverses front and back. Your mirror image's nose points towards you while your real nose points away. Left and right only seem swapped because you imagine turning yourself around to face the way the image faces.

"Rough surfaces do not obey the law of reflection." They obey it at every point. The surface simply faces slightly different directions at different points, so the reflected rays scatter, and no image forms.

"The prism adds colour to white light." Newton settled this by recombining the spectrum back into white with a second prism. The colours were already present; the prism only separates them by bending each one differently.

Pulling it together

• Light is a transverse wave that needs no medium and travels at about 300,000 kilometres per second in a vacuum.
• Visible light is one narrow band of the electromagnetic spectrum, and within it wavelength is colour.
• Light travels in straight lines, which is why shadows form and why we draw rays.
• In reflection, the angle of incidence equals the angle of reflection, both measured from the normal.
• Smooth surfaces give images; rough surfaces scatter light and give none, while still obeying the same law.
• Refraction is bending caused by a change of speed at a boundary: towards the normal when slowing, away when speeding up.
• White light is a mixture, and a prism separates it because each colour bends by a slightly different amount.

One form of energy is still unaccounted for. The last module follows charge through a wire and then finds out that it makes magnets.

Sources

1. NASA. (n.d.). Introduction to the electromagnetic spectrum. NASA Science. science.nasa.gov
2. NASA. (n.d.). Visible light. NASA Science. science.nasa.gov
3. Urone, P. P., and Hinrichs, R. (2020). Reflection. Physics. OpenStax, Rice University. openstax.org
4. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Bending light. phet.colorado.edu

The tap water that bends

Turn on a cold tap until you have a thin, smooth stream of water no thicker than a pencil lead. Rub a balloon briskly on your hair for about ten seconds, then hold it a couple of centimetres from the stream without touching it.

The water bends. It curves visibly towards the balloon and keeps curving for as long as you hold it there.

Nothing touched the water. There is no wind and no magnet. What is reaching across that gap is an electric force, and understanding it is the beginning of everything from a torch to a power station.

Key idea: Electric charge comes in two kinds. Like charges push apart, unlike charges pull together, and the force works across a gap.

Charge, and how a balloon gets some

Atoms contain positively charged protons in the nucleus and negatively charged electrons around the outside. Normally the numbers match and the atom is neutral overall.

Electrons on the outside can be scraped off by rubbing. Rub a balloon on hair and electrons transfer from your hair to the balloon. The balloon now has more electrons than protons, so it is negatively charged. Your hair has lost electrons, so it is positively charged, which is why it stands up: every strand is now positive and every strand is pushing every other strand away.

Two rules cover all of it.

• Like charges repel. Two negative objects push apart; so do two positive ones.
• Unlike charges attract. A negative object and a positive object pull together.

The bending water is a subtler case, because tap water is neutral overall. What happens is that the balloon's negative charge pushes the electrons in each water molecule slightly to the far side, leaving the near side slightly positive. The near, positive side is attracted and the far, negative side is repelled, but the near side is closer, so attraction wins and the stream leans in. The same explanation covers a charged balloon sticking to a neutral wall.

Charge that has been separated and is sitting still is called static electricity. It stays put on materials that do not let charge move, which is why the effect works with balloons, plastic combs and dry hair, and hardly at all on a metal doorknob or on a humid day when moisture in the air carries the charge away.

Current: charge that flows

Static charge sits. Current is charge on the move, and it is what does useful work.

In a metal wire, some electrons are free to drift between the atoms. Give them a push and they flow, and that flow is a current. It is measured in amperes, usually shortened to amps, symbol A, using a meter called an ammeter.

Two more quantities complete the picture.

Quantity	What it means	Unit	A water analogy
Current	How much charge flows past a point each second	Ampere, A	How much water flows through the pipe per second
Voltage	The push that drives the charge round	Volt, V	The pressure from the pump
Resistance	How much the component opposes the flow	Ohm	How narrow the pipe is

The analogy is not perfect and you should not lean on it too hard, but it gets three things right. More pressure gives more flow. A narrower pipe gives less flow. And nothing flows at all unless the loop is complete.

One historical wrinkle worth knowing. Circuit diagrams show current flowing from the positive terminal round to the negative, a convention fixed before anyone knew what was actually moving. The electrons in a metal wire in fact drift the other way. Everything you calculate still works, because the convention is consistent, but if the direction ever seems backwards, this is why.

A circuit needs a complete loop

A circuit is a closed path around which charge can flow. It needs an energy source such as a cell or a battery, a conducting path such as wires, and usually something that uses the energy, such as a lamp or a motor. Break the path anywhere and everything stops, everywhere, instantly. That is what a switch does: it makes and breaks the loop deliberately.

Component	What it does
Cell	Provides the voltage that pushes charge round
Battery	Two or more cells joined together, giving a bigger push
Lamp	Turns electrical energy into light and heat
Switch	Makes or breaks the loop
Resistor	Deliberately opposes the flow to control the current
Ammeter	Measures current, and is placed in the loop itself
Voltmeter	Measures voltage, and is placed across a component

Series and parallel

In a series circuit there is a single loop and everything sits on it, one after another.

• The same current flows through every component, because there is nowhere else for it to go.
• The voltage from the cell is shared out among the components.
• Adding more lamps makes them all dimmer, because the same push is divided among more of them.
• Remove one lamp and the loop is broken, so everything goes out. Old Christmas tree lights worked this way and were maddening.

In a parallel circuit the path splits into branches and each component sits on its own.

• Each branch gets the full voltage of the cell.
• The current divides between the branches and recombines afterwards.
• Adding more lamps does not dim the others, because each has its own full push.
• Remove one lamp and the others stay lit, because their loops are still complete.

Houses are wired in parallel, which is exactly why switching off a bedroom lamp does not plunge the kitchen into darkness, and why a blown bulb affects only itself.

What matters here: Series means one path shared; parallel means separate paths. Almost every prediction about brightness or about removing a component follows from that one distinction.

Safety, which is not negotiable

Everything in this lesson uses single small batteries, which are safe. Mains electricity is a completely different matter. The supply in a wall socket is around 120 or 230 volts depending on the country, hundreds of times the push of a AA cell, and it kills people every year.

• Never put anything into a wall socket except a proper plug.
• Never open a plug, a socket, or any mains-powered appliance.
• Never experiment with anything that plugs into the wall.
• Never connect the two ends of a battery directly with a bare wire. There is nothing to limit the current, and the wire and the battery can both get hot enough to burn.
• Keep water away from any electrical experiment.

Experiment: static electricity, three ways

Completely safe and needs only a balloon. Works best on a dry day; damp air spoils it.

1. Blow up a balloon and tie it. Rub it briskly on clean, dry hair for about ten seconds.
2. Hold it near, but not touching, small torn scraps of paper on a table. Watch what they do.
3. Hold it against a wall and let go.
4. Turn a cold tap to a thin, smooth stream and hold the balloon a couple of centimetres away from it.
5. Now rub two balloons on your hair and hang them from threads a few centimetres apart. Watch what they do to each other.

What to expect: Paper scraps jump up to the balloon. The balloon sticks to the wall for a while and then falls. The water stream bends towards it. The two hanging balloons swing apart and stay apart.

Why it happens: Rubbing moves electrons from your hair to the balloon, making the balloon negative. Near a neutral object, that negative charge pushes the object's own electrons away, leaving the near surface slightly positive, and the closer positive side is attracted more strongly than the further negative side is repelled. That is the paper, the wall and the water, all one explanation. The two balloons are the other rule: both are negative, like charges repel, and they push each other apart. The balloon eventually falls off the wall because the extra electrons gradually leak away into the air, especially if the air is humid.

Experiment: build a working circuit

Ask an adult to help with this one. They should supply the parts and check the connections before you switch anything on. Use only a single AA or AAA cell of 1.5 volts and a small torch bulb rated for it. Never use mains electricity, and never connect the two ends of the battery to each other with just a wire.

1. You need one AA cell, a small torch bulb, and two pieces of insulated wire with the ends stripped, or two strips of aluminium foil folded into narrow bands.
2. Tape one wire end to the flat negative end of the cell and touch its other end to the metal side of the bulb.
3. Touch the bottom tip of the bulb to the raised positive end of the cell.
4. Note whether the bulb lights, then break the contact at any one point and watch what happens.
5. Now put a paperclip, a plastic ruler, a pencil lead, a rubber band and a coin one at a time into the loop by touching it between the wire and the bulb. Record which ones let the bulb light.

What to expect: The bulb lights only when the loop is complete. Breaking it anywhere puts the light out immediately. The paperclip and the coin let it light; the plastic ruler and the rubber band do not; the pencil lead lights it dimly.

Why it happens: A circuit works only as a complete loop, and where you break it makes no difference at all, which tells you the current is not being used up as it goes round. The materials that let the bulb light are conductors, which have electrons free to move; the ones that do not are insulators, which hold their electrons tightly. Metals are conductors and most plastics and rubbers are insulators, which is precisely why a wire is metal wrapped in plastic. Pencil lead is graphite, a form of carbon that conducts moderately well, which is why it glows dimly rather than not at all.

Common misconceptions

"Current gets used up as it goes round a circuit." It does not. The same current flows all the way round a series loop. Energy is transferred at the lamp, but the charge itself keeps going. Breaking the loop after the lamp stops it just as completely as breaking it before.

"A balloon sticks to a wall because the wall is charged." The wall is neutral. The charged balloon pushes the wall's electrons back a little, leaving the near surface slightly positive, and the closer attraction beats the more distant repulsion.

"Batteries store electricity." They store chemical energy and convert it to electrical energy when a circuit is completed. They do not contain a reservoir of charge waiting to be poured out.

"Series and parallel are just different drawings." They behave completely differently. Removing one lamp from a series circuit kills them all; removing one from a parallel circuit leaves the rest lit. Houses are wired in parallel for exactly that reason.

Where this leaves us

• Charge comes in two kinds: like charges repel and unlike charges attract, across a gap.
• Rubbing transfers electrons, leaving one object negative and the other positive, which is static electricity.
• A charged object attracts a neutral one because it separates that object's charges slightly, and the nearer attraction wins.
• Current is flowing charge, measured in amperes; voltage is the push, in volts; resistance opposes the flow, in ohms.
• A circuit works only as a complete loop, and the current is the same all the way round a series loop.
• Series shares one path and one voltage; parallel gives each branch its own full voltage, which is how houses are wired.
• Mains electricity is dangerous and is never a subject for experiments.

Send a current through a wire and something else happens around it, something nobody expected until 1820. That is the last lesson.

Sources

1. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Circuit construction kit: DC. phet.colorado.edu
2. Urone, P. P., and Hinrichs, R. (2020). Ohm's law. Physics. OpenStax, Rice University. openstax.org
3. Wikipedia contributors. (n.d.). Series and parallel circuits. Wikipedia. en.wikipedia.org
4. Khan Academy. (n.d.). Middle school physics. khanacademy.org

The compass needle that twitched during a lecture

In 1820, in Copenhagen, Hans Christian Oersted was demonstrating something to a room of students when he noticed a compass needle on the bench move as he connected a wire to a battery. Disconnect the wire and the needle swung back.

Nobody had expected that. Electricity and magnetism had been studied for centuries as two separate subjects with nothing to do with one another. A moving charge, it turned out, produces a magnetic field, and that single observation is the reason electric motors, loudspeakers, hard drives and power stations exist.

This lesson works up to that discovery from the beginning: what a magnet is, what a field is, and what happens when you put a current in the picture.

Key idea: A magnetic field is made by moving charge, whether that charge is moving inside a lump of iron or through a wire you control.

Poles and fields

Every magnet has two poles, called north and south. The names come from compasses: the end that points towards the Earth's north is the north-seeking pole, shortened to north.

The rules are the same shape as the ones for charge, but they are a separate phenomenon.

• Like poles repel. North pushes north away, and south pushes south away.
• Unlike poles attract. North and south pull together.

One thing about magnets has no equivalent in electricity. Cut a magnet in half and you do not get a separate north and a separate south. You get two smaller magnets, each with its own north and south. Keep cutting and it keeps happening, right down to the smallest piece you can manage. Poles always come in pairs.

The region around a magnet where its force can be felt is its magnetic field. It is invisible, so we draw it as field lines, which by convention run out of the north pole, curve round, and back into the south pole. Where the lines are closest together the field is strongest, which is why the pull is fiercest right at the poles and weak in the middle of a bar magnet.

Only a few materials are magnetic: iron, nickel, cobalt, and alloys containing them, of which steel is by far the most common. Aluminium, copper, gold, silver, brass and tin are all metals and a magnet ignores every one of them. Magnetic and metallic are not the same word, and a magnet is a useful tool for telling steel from aluminium in a scrapyard for exactly that reason.

The Earth is a magnet

A compass needle is a small magnet, balanced so it can swing freely. It settles pointing roughly north and south because the whole planet behaves as a very large, very weak magnet.

That planetary field is not a bar magnet buried in the middle. It is generated by the motion of molten iron in the Earth's outer core, a churning flow of conducting liquid that produces the field in much the same way a current in a wire does. Because the flow changes, the field changes too: the magnetic poles wander over time and the field strength varies from place to place, which is why navigation charts have to be updated.

Two consequences worth knowing.

1. Magnetic north is not the same as geographic north. The angle between them is called declination, it differs depending on where you stand, and serious navigation corrects for it.
2. The magnetic pole up in the Arctic actually behaves as a south pole. It must, because the north-seeking end of your compass needle is attracted to it, and unlike poles attract. The naming is a historical accident that nobody has bothered to fix.

Oersted's discovery, and the electromagnet

A current in a straight wire produces a magnetic field in circles around the wire. It is weak, which is why nobody had noticed it before Oersted put a sensitive compass close enough.

Two changes make it strong enough to be useful.

1. Wind the wire into a coil. Each turn adds its field to the others, and the fields inside the coil line up and reinforce. A coil like this is called a solenoid, and its field looks remarkably like a bar magnet's, with a north end and a south end.
2. Put an iron core inside the coil. Iron responds strongly to the field and adds its own, which can multiply the strength many times over.

The result is an electromagnet, and three things control how strong it is.

Change	Effect on strength
More current	Stronger
More turns of wire on the coil	Stronger
An iron core instead of air	Much stronger

An electromagnet can do three things a permanent magnet cannot, and all three are why it matters.

• It can be switched off. A scrapyard crane picks up a car, moves it, and drops it by cutting the current.
• Its strength can be varied. Turn the current up or down and the pull follows.
• Its poles can be swapped. Reverse the current and north and south change places, which is what makes an electric motor turn and a loudspeaker cone push and pull.

The upshot: An electromagnet is a magnet with a switch, a volume control, and a reverse gear.

Experiment: map an invisible field and find north

Safe. Do not use a phone or a laptop near strong magnets, and keep magnets away from bank cards.

1. Lay a bar magnet or a strong fridge magnet on a table and cover it with a sheet of paper.
2. Sprinkle iron filings thinly over the paper, or use the fine dust from a pencil sharpener full of steel shavings. Tap the paper gently.
3. Look at the pattern that forms and note where the lines are most crowded.
4. Now straighten a steel paperclip and stroke it fifty times with one pole of a magnet, always in the same direction, lifting the magnet clear at the end of each stroke.
5. Lay the magnetised paperclip on a small piece of cork, foam or a plastic bottle cap, and float it in a bowl of still water away from any metal.
6. Wait for it to settle and compare its direction with a phone compass app or a known landmark. A sewing needle works better than a paperclip, but ask an adult before handling one.

What to expect: The filings form curved lines running from one end of the magnet to the other, crowded at the poles and sparse in the middle. The floating paperclip slowly swings round and settles pointing roughly north and south.

Why it happens: Each iron filing becomes a tiny magnet and lines up with the field, so the pattern is a picture of the field lines. The crowding at the poles is the field being strongest there. Stroking the paperclip in one direction lines up the magnetic regions inside the steel so that they reinforce rather than cancel, turning it into a weak permanent magnet. Floated free of friction, it does what any small magnet does in a large field: it turns until it is aligned with the Earth's, which is exactly how a compass works.

Experiment: build an electromagnet

Ask an adult to help and to check the setup before you connect it. The wire and the battery can become warm, so connect it for only a few seconds at a time and disconnect between tests. Use a single 1.5 volt AA cell, never a larger battery and never mains electricity.

1. You need an iron nail about 8 cm long, about a metre of thin insulated copper wire with the ends stripped, one AA cell, and a pile of steel paperclips.
2. Wind the wire neatly around the nail, turn beside turn, about twenty times. Leave a good length free at each end.
3. Before connecting anything, hold the nail near the paperclips. Nothing should happen.
4. Hold one bare wire end to each end of the cell for no more than five seconds, and dip the nail tip into the paperclips. Count how many it lifts, then disconnect.
5. Add another twenty turns of wire to the nail and repeat the count.
6. Take the nail out, keeping the coil's shape, and repeat the count with nothing but air inside the coil.

What to expect: With no current the nail lifts nothing. With current it lifts several paperclips. Forty turns lift noticeably more than twenty. Without the iron nail inside, the coil lifts very few, perhaps none.

Why it happens: The current makes a magnetic field around every part of the wire. Coiling it stacks those fields so they add up inside the coil, and more turns means more adding, which is why forty beats twenty. The iron nail responds strongly to that field and contributes its own, which is why removing it costs you most of the strength. And the moment you disconnect, the field vanishes and the paperclips drop, which is the property no permanent magnet has and the one that makes electromagnets useful.

Common misconceptions

"All metals are magnetic." Only iron, nickel, cobalt and alloys containing them, such as steel. Aluminium, copper, gold and silver are all ignored by a magnet, which is why a magnet can sort steel cans from aluminium ones.

"Cutting a magnet in half separates the poles." It gives you two complete magnets, each with a north and a south. Poles always come in pairs, however small the piece.

"There is a giant bar magnet inside the Earth." The field is generated by molten iron moving in the outer core. Because that flow changes, the poles wander and navigation charts need updating.

"Magnetism and electricity are separate subjects." Oersted's compass needle showed in 1820 that they are not. A moving charge always makes a magnetic field, and that link is the basis of every motor and generator.

What you now know

• Magnets have north and south poles; like poles repel and unlike poles attract, and poles always come in pairs.
• A magnetic field is drawn as lines running from north to south outside the magnet, crowded where the field is strongest.
• Only iron, nickel, cobalt and their alloys are magnetic; most metals are not.
• A compass works because the Earth generates a magnetic field from molten iron moving in its outer core.
• Oersted found in 1820 that a current produces a magnetic field, linking electricity and magnetism for good.
• An electromagnet is a coil with an iron core, and its strength depends on current, turns and core.
• Electromagnets can be switched off, varied and reversed, which permanent magnets cannot.

That is the course. You started by proving air is matter with a paper towel and a glass, and you have finished by making a magnet out of a nail and switching it off again. Between those two experiments you have the particle model, the periodic table, conservation of mass, three laws of motion, conservation of energy, three ways heat travels, and the behaviour of waves, sound, light, charge and magnetism. The final exam draws on all of it.

Sources

1. National Geographic Society. (n.d.). Magnetism. National Geographic Education. education.nationalgeographic.org
2. National Oceanic and Atmospheric Administration. (n.d.). National Centers for Environmental Information: geomagnetism. ncei.noaa.gov
3. PhET Interactive Simulations, University of Colorado Boulder. (n.d.). Magnets and electromagnets. phet.colorado.edu
4. Wikipedia contributors. (n.d.). Electromagnet. Wikipedia. en.wikipedia.org