Middle School Physical Science

The paper towel that refuses to get wet

A paper towel tucked high inside an upside-down clear cup can stay dry when the cup goes into a bowl of water. The opening is under water, but the towel sits in a pocket of trapped air. Tilt the cup and bubbles can escape. Water then rises farther into the cup.

The cup was never empty. Air occupied it before you lowered it. Water pushes on that air and compresses it a little, so some water can enter even when no air escapes. In a shallow bowl, with the towel held near the closed end, the water may not reach the paper. A wet towel is possible if the cup tilts, the paper hangs too low or water splashes onto it. The observation needs an explanation, not a promise that every attempt ends the same way.

Key idea: Matter has mass and occupies space. Invisible air is matter, and changing its volume does not make it stop being matter.

Mass, volume and density answer different questions

Mass tells you how much matter an object contains in this introductory model. We measure it in grams or kilograms. A kitchen scale estimates mass from the force on its sensor, so its reading has limited precision. Volume tells you how much space a sample occupies. We use millilitres, litres or cubic centimetres. One millilitre is one cubic centimetre.

A kilogram of feathers and a kilogram of lead have equal masses. Their volumes differ greatly. To compare how much mass fits into a given volume, calculate density = mass divided by volume. Liquid water near room temperature has a density of about 1 gram per cubic centimetre. That is an approximation: temperature and dissolved material affect the value.

Try a supplied example. A sealed block has mass 60 g and outside volume 100 cubic centimetres. Divide 60 by 100 to get 0.6 g per cubic centimetre. This is the block's average density, including any sealed spaces inside it. If it keeps its shape, does not absorb water and is free to move, we expect it to float in water because its average density is lower than water's. A hollow object can therefore float even if its walls are made of a dense material.

Do not apply that prediction blindly to a sponge. Water can enter its pores, replacing air, so its dry mass and outside volume do not completely describe what happens after soaking. Nor does a heavy object necessarily sink: both its mass and the volume of water it can displace matter. Surface effects can also matter for very small objects. Here we use density comparisons for ordinary freely floating objects, without those extra effects.

Light, sound and heat are not substances that you add like sand. Light carries energy; sound carries energy through a disturbance in matter; heat means energy transferred because of a temperature difference. The air carrying a sound is matter, but the sound is not an extra material mixed into the air. Failure to register on your kitchen scale is not a test for whether something is matter. One dust grain may be too small for that scale to detect.

A model you can draw, with limits you must remember

A model is a simplified representation used to explain observations and make predictions. Here you draw dots or circles for atoms and molecules. Those drawings are not photographs of tiny solid marbles. Different materials contain different kinds of particles, and forces between them affect their spacing and motion. Instruments provide evidence about atoms, including images made by scanning tunnelling microscopes; unaided eyes cannot resolve individual atoms.

1. Ordinary matter consists of extremely small particles. A water molecule is one such particle. It contains atoms bonded together. In this lesson we do not need to draw the parts inside every molecule.
2. Particles have thermal motion. At everyday temperatures, particles in a solid vibrate around positions, while those in a liquid or gas can move past one another. For the same substance in the same state, higher temperature generally means greater average energy of this motion. Individual particles do not all move at the same speed.
3. Particle spacing and interactions matter. Gas particles at ordinary room conditions are much farther apart than particles in liquids and solids. In a liquid, close neighbours interact strongly enough to resist a large reduction in volume.

The drawings leave out details. A circle's edge does not show a rigid shell that can never move closer to another circle. Saying that liquid particles are close together is useful. Saying that they are already touching and therefore cannot be compressed at all goes beyond what the model establishes.

Why air squeezes much more than water

Imagine two sealed, leak-free syringes with the same starting volume, one containing air and the other water with no air bubbles. This is a paper comparison, not an instruction to force a blocked syringe. Pressing a plunger increases pressure, the push per unit area. With air, that can noticeably reduce the space occupied by the same collection of particles. Their average separation decreases; the particles do not vanish or get smaller.

With water, the particles are already close together. Compressing the liquid means forcing those neighbours closer, which meets much greater resistance. Under a comparable modest increase in pressure, water's volume decreases far less than air's. The change may be too small to see with a classroom syringe. Water is slightly compressible, not perfectly incompressible. The US Geological Survey explicitly describes its small volume change under high pressure.

A water-filled syringe that moves noticeably does not immediately disprove this explanation. Ask whether it contains an air bubble, whether water leaks past a seal, or whether the equipment itself flexes. Each can move a plunger without a large compression of the liquid. You need to identify what changed before explaining why.

Now work a particle sketch. Draw twelve dots scattered through a rectangle. In a second rectangle half as large, draw the same twelve dots with the same dot size. Only the spacing has changed. That is a useful model of gas compression. Drawing six dots instead would represent losing particles, not compressing a sealed sample. Trying the same large volume reduction for liquid water at the same modest pressure would be an inaccurate prediction.

Why this matters: Compressibility is a comparison of volume changes under pressure. "Too small for us to notice" and "exactly zero" are different claims.

What spreads, and what carries it?

Diffusion is spreading caused by random particle motion. If many dye particles start in one small region of water, their random movements tend to spread them into regions with fewer dye particles. A particle does not know which way to go. More leave the crowded region simply because more start there. Once the dye is evenly mixed, particles keep moving even though you no longer see a changing colour pattern.

Movement of the whole fluid also transports particles. A draft can carry toast smells across a room, while diffusion mixes particles over shorter distances. Likewise, a swirl in a cup carries dye with the moving water. Convection includes fluid motion associated with temperature differences. A warm cup cooling at its sides can contain currents even when you do not stir it. Fast spreading across a room or a cup is not proof that diffusion did all the transport.

Dissolving is another process. When a small amount of sugar dissolves, molecules leave the sugar crystal and become dispersed among water molecules. Water and sugar interact; the process is not just grains dropping into empty holes. After complete dissolution, the sugar is too finely dispersed to see as grains. Compare the water alone with water plus added sugar and the mass increases. Compare the same container, water and sugar together before and after dissolving, without losing material, and their combined mass stays the same within measurement uncertainty. The comparison you choose changes the question you are answering.

Experiment: watch trapped air

Use a clear rigid plastic cup, a paper towel, a bowl and cold water. Work over a sink or tray, keep water away from electrical equipment, and get adult help if handling the setup is difficult.

1. Wedge a small crumpled towel near the closed end of the cup. Turn the cup upside down above the tray to check that it stays in place.
2. Put enough water in the bowl to cover the cup's opening when you lower it. Keep the paper well above the opening.
3. Lower the cup straight down without tilting. Look through its side for the boundary between trapped air and water.
4. Lift it out with the opening still facing down. Dry the rim before checking the paper.
5. Repeat with a dry towel. This time tilt the submerged opening slowly until air bubbles escape, and watch the water level inside.

What to expect: The upright trapped pocket often keeps the towel dry; tilting lets water rise as air leaves. Record what you actually see. A bubble is a visible boundary between air and water, not an individual air particle.

Why it happens: Water pressure increases with depth. The trapped air is compressed until its pressure balances the water pressure at the boundary. It occupies less volume but still fills the remaining pocket. Tilting can let air escape and water replace it. This experiment shows that air occupies space and can change volume. It does not establish that no water entered during the first trial.

A second experiment: compare colour spreading

This task adapts an American Chemical Society activity. Have an adult supply comfortably warm, not hot, tap water. Use plastic cups on a tray, wear splash goggles and avoid tasting the mixtures. Food colouring can stain.

1. Put equal volumes of cool and warm water into two identical clear cups. Place them side by side away from drafts.
2. Let visible pouring swirls settle. Add one similar-sized drop of the same food colouring to each, from close to the surface, without stirring.
3. Watch for five minutes. Sketch the shapes at the start, after one minute and after five minutes. Record streaks, sinking plumes or loops as well as overall spreading.
4. Repeat if practical, using fresh water and reversing the positions of the cups. Check whether the same pattern recurs.

What to expect: Colour often spreads faster in the warmer cup, but the exact pattern and timing vary. Higher temperature generally increases diffusion. Currents from temperature or density differences, the added drop and residual motion can also carry dye. Waiting briefly does not prove all currents have stopped.

What you can conclude: You observed visible dye distribution under two sets of conditions. You did not directly measure molecular speeds or isolate diffusion. If a plume crosses the cup rapidly, describe it as bulk movement of coloured water. Random molecular motion still occurs within that moving water.

Common misconceptions

"Air is empty space." Air contains particles with mass. It occupies volume, as the trapped pocket shows. An empty space with no matter would be a vacuum.

"No visible compression means none is possible." A liquid's change can be much smaller than the markings on your equipment can reveal. That is a measurement limit, not an absolute rule.

"A dissolving solid loses its mass." Its particles become dispersed. Count the sugar as well as the water in both the before and after comparison.

"No stirring means pure diffusion." Fluid currents can exist without a spoon. Distinguish motion of the fluid from random motion within it.

What to carry forward

Remember: Mass, volume and density describe different features of matter. A model connects those measurements to particle motion, spacing and interactions. It also has limits: particles are not rigid marbles, liquids are not perfectly incompressible, and a coloured current is not a direct view of molecules.

Close the lesson and explain why the same gas particles can fit into a smaller volume. Then explain why that does not mean water can shrink just as easily. When you return later, sketch the trapped-air cup and label where some water can enter without reaching the towel. If you draw no water inside at all, revisit the pressure explanation.

Sources

1. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Chemistry 2e, section 1.2, Phases and classification of matter, opening definitions and Atoms and Molecules. OpenStax, Rice University. Matter and particle models
2. US Geological Survey, Water Science School. (2026, August 24). Water compressibility, Pressure and temperature can affect compressibility. Small compression of water
3. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, sections 11.4, Variation of pressure with depth in a fluid, and 11.7, Archimedes' principle. OpenStax. Pressure with depth; Average density and floating
4. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, sections 12.7, Molecular transport phenomena, and 14.6, Convection. OpenStax. Diffusion and its timescale; Fluid currents
5. American Chemical Society. (2024, July 18). Molecules in motion, Lesson 1.2, Explore and Explain. Middle School Chemistry. Colour-spreading activity
6. American Chemical Society. (2024, July 30). Why does water dissolve sugar?, Lesson 5.4, Explain Step 4. Middle School Chemistry. Intact molecules and attractions in dissolving
7. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 14.1, Heat, definition and internal-energy discussion. OpenStax. Heat as energy transfer

Ice at zero degrees, water at zero degrees

Imagine a cup containing pure ice and liquid water, both close to 0 degrees Celsius at normal atmospheric pressure. Energy enters from the warmer room. Some ice melts, yet the mixture can remain near 0 degrees while ice and water coexist. More energy has entered without a matching increase in temperature.

This is a model of a well-mixed sample close to thermal equilibrium, meaning its parts have nearly the same temperature. Ice straight from a freezer may be colder than 0 degrees. A thermometer near a warm cup wall can read differently from one surrounded by ice. Dissolved substances and changes in pressure also matter. Do not expect every real cup to give an exact, unchanging display.

Key idea: During melting, energy changes the arrangement and interactions of particles. It need not raise their average kinetic energy, the energy associated with motion. Melting ice actually takes up less volume than the same mass of ice, so "added energy always pulls particles farther apart" cannot be the explanation.

Compare motion, arrangement and volume

Water molecules remain water molecules in ordinary ice, liquid water and water vapour. Their arrangements and freedom to move change. The table describes common materials under everyday conditions; it is not a claim that all matter has only three possible states.

A litre of liquid poured carefully from a bottle into a bowl changes shape with little change in volume, provided temperature stays similar and none is lost. Its particles can rearrange while staying close together. Liquid flow does not require the large separations found in a gas. A block of ice retains its shape because its particles do not continually exchange neighbours as they do in liquid water.

Some solids have a repeating crystal pattern. Others, including ordinary glass, are amorphous: they lack that long-range repeating order. Do not decide whether something is a solid just by drawing neat rows of dots. Also, close particles are not rigid balls whose surfaces must touch. Both liquids and solids can be compressed slightly. The word "fixed" in an introductory description of their volume means nearly constant under the conditions being compared.

Six directions for a change of state

Follow the sample when deciding whether it takes in or gives out energy. Melting ice takes energy from the surrounding warmer material. Freezing water gives energy to its colder surroundings. The refrigerator must remove that energy; freezing is not the disappearance of energy.

These directions apply to the ordinary phase changes discussed here. They describe the energy needed for the change, not every other energy transfer that might happen at the same time. Evaporating sweat, for instance, takes energy from skin and the surrounding air. That can cool the skin.

Spacing alone cannot tell you the direction of energy transfer. Ordinary ice has an open structure. When it melts, that arrangement breaks down and the molecules pack more closely on average, yet melting still needs energy. When it freezes, the more open structure forms and energy is released. The attractions and arrangement of particles belong in the explanation alongside their motion.

Work through a heating curve

Use a paper model of a pure water sample at constant normal atmospheric pressure, with temperature nearly uniform throughout. Draw temperature vertically and energy added horizontally. The ideal curve has sloping parts separated by flat parts. This is not an instruction to heat water or contain steam at home.

1. Warm the ice to about 0 degrees Celsius. Energy increases thermal motion and the temperature rises.
2. Melt the ice near 0 degrees. Ice and water coexist. Added energy changes the structure and interactions, while the temperature stays approximately constant. The amount of ice decreases.
3. Warm the liquid towards 100 degrees. After melting finishes, further energy raises the liquid's temperature.
4. Boil the water near 100 degrees. Added energy changes liquid into vapour. During this ideal constant-pressure stage, the temperature remains approximately constant.
5. Warm the vapour if it is retained in suitable equipment. Further energy can raise its temperature after the liquid has vaporized. Vapour escaping from an open cup is no longer all part of the sample being measured.

Now compare two points on the melting plateau. At the first, a quarter of the original ice has melted; at the second, half has melted. The temperature can be the same at both points, but the second sample has absorbed more energy. Temperature is related to average particle kinetic energy, not a count of all the energy stored in a sample. Energy associated with interactions has changed.

On a graph against time, the lengths of the stages also depend on how quickly energy enters and escapes. A more powerful heater can shorten a plateau without requiring a higher melting temperature. Uneven heating, heat loss, impurities and thermometer response can make an actual graph less tidy than this ideal one. Dissolved salt changes the freezing behaviour of water, so a salt-water sample is not the pure-water model.

What matters here: A flat temperature reading does not mean no energy enters. Check whether a phase change is using the transferred energy.

State depends on conditions

At normal atmospheric pressure, about 1 atmosphere, pure water melts near 0 degrees Celsius and boils near 100 degrees Celsius. These are useful reference values, not universal temperatures for all samples of water. Boiling point depends on external pressure. On a mountain, lower atmospheric pressure lets water boil at a lower temperature.

During boiling, bubbles of water vapour can grow within the liquid because its vapour pressure matches the surrounding pressure. At a lower surrounding pressure, that condition is reached at a lower temperature. In a classroom comparison, water boiling below 100 degrees on a high mountain is therefore not evidence that the thermometer must be broken.

Melting temperatures also depend on pressure and composition. Use a substance's melting or boiling point to compare samples only when those conditions are specified. The amount of a pure sample changes how much energy a phase change requires; doubling the amount does not itself double the melting temperature. The ideal melting plateau here describes a pure crystalline substance, not every kind of solid.

Evaporation happens at a surface

A liquid does not need to boil before molecules can escape from its surface. At a given temperature, molecular energies vary. Some surface molecules have enough energy to escape their neighbours' attractions and enter the gas. This is evaporation. It can occur below the boiling point whenever the liquid is present. A cold puddle can shrink without bubbling.

Molecules can also return from vapour to liquid. In a closed container, evaporation and condensation can eventually balance. Both continue, but the amount of liquid no longer changes. "Evaporation happens" therefore does not guarantee that a sample will dry out. In an open room, the net loss depends on temperature, exposed area, humidity and air movement.

Other conditions alike, a larger exposed surface gives more places for molecules to escape, so a shallow pool generally loses water faster than the same amount in a narrow cup. Moving air carries water vapour away from the surface. Humid air slows net drying because more molecules return to the liquid. These are comparisons under conditions, not a timetable for when every cup will be empty.

Why ice floats and condensation appears

Ordinary ice occupies more volume than the same mass of liquid water near freezing. Because density is mass divided by volume, that larger volume means lower density. This explains why ordinary ice floats in liquid water. The key comparison is density, not whether the ice feels heavy in your hand.

A tightly filled closed container can be damaged when water freezes because the ice needs more room. Treat that as an explanation to reason about, not an experiment to try. Do not freeze a sealed bottle to make it burst. Also, ice on a pond does not guarantee that fish survive every winter; that broader ecological outcome is not established by a density comparison.

For condensation, start with water vapour already in the air. Cooling it near a sufficiently cold surface can produce liquid droplets. Whether droplets appear depends on the amount of water vapour as well as the temperature. The dew point is the temperature to which that air must cool to become saturated. A cup whose surface is not cold enough for the room's humidity may stay dry.

Water vapour itself is invisible. A visible mist is made of tiny liquid droplets suspended in air. You can see this in breath on a cold day or condensation on a cold surface. There is no need to approach a boiling kettle or its steam to distinguish the states.

Experiment: look for condensation

Use two clear plastic cups on a tray, water, ice and a paper towel. Wear splash goggles, wipe spills and keep the tray away from electrical equipment. This adapts the cold-cup demonstration from the American Chemical Society.

1. Put cool water and a few ice cubes into one cup. Put room-temperature water in the other. Leave space at the top of both.
2. Dry the outside of each cup carefully, checking that you have not splashed water onto it.
3. Leave both in the same room for five to ten minutes. Watch the outside surfaces and record any droplets.
4. Dry a small patch on the cold cup. See whether droplets reappear while it stays cold.

What to expect: In sufficiently humid air, the colder cup is more likely to develop droplets. Very dry air may produce no visible result. The room-temperature cup provides a comparison, although the two cups also exchange energy with the room at different rates.

Why it happens: Water vapour from the surrounding air can condense on the cold surface, releasing energy to the surroundings. The cup also receives energy through other routes, so its warming is not proof that condensation alone warmed it. If both cups are wet immediately, consider splashes. If neither gets wet, record that result and explain why low humidity or insufficient cooling could account for it.

Experiment: compare two exposed surfaces

1. Place equal measured amounts of water, about two tablespoons each, in a clean wide plastic dish and a narrow plastic cup.
2. Set them together on a tray away from direct sun and drafts. Record the starting amounts and exposed surfaces.
3. Check after two hours and again the next day. Record water remaining rather than assuming either has emptied.

What to expect: The wider surface generally promotes faster loss if other conditions are similar. Temperature, humidity, airflow and container shape can affect the comparison. Different depths and container materials may also change cooling, so this home setup does not isolate surface area perfectly.

For a worked interpretation, suppose the dish loses more water. That agrees with the surface-area prediction but does not prove area was the only influence. If it does not, check the placement and exposed area before deciding that evaporation has stopped working. Repeat under more similar conditions when possible.

Common misconceptions

"Melting always moves particles farther apart." Ice is a counterexample: the liquid occupies less volume while taking in energy. Arrangement and interactions matter.

"All solids have particles in perfect rows." Crystals have repeating order; amorphous solids do not. Both can retain their shape.

"Water always boils at exactly 100 degrees." That is an approximate value for pure water at normal atmospheric pressure. Pressure and dissolved material affect the comparison.

"A cold cup must become wet." Condensation depends on humidity and surface temperature. A dry cup can be a valid observation.

The short version

Solids, liquids and gases differ in particle arrangement and freedom of motion. Liquids remain close-packed while flowing and are only slightly compressible. During an ordinary phase change, particles retain their chemical identity while their interactions and arrangements change.

Remember: Follow the energy and state the conditions. Melting ice takes in energy even though its volume decreases. A temperature plateau describes a pure sample changing phase near equilibrium at constant pressure. Evaporation can occur below boiling, and its net rate depends on the surroundings.

Return later to two questions without looking: why can melting ice have the same temperature after absorbing more energy, and why might a cold cup stay dry? Use particle interactions for the first and humidity plus surface temperature for the second.

Sources

1. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Chemistry 2e, section 10.3, Phase transitions, including Boiling Points, Melting and Freezing, and Heating and Cooling Curves. OpenStax, Rice University. Phase changes and heating curves
2. Flowers, P., et al. (2019). Chemistry 2e, sections 1.2, Phases and classification of matter, and 10.5, The solid state of matter, opening paragraphs. OpenStax. State properties; Crystalline and amorphous solids
3. American Chemical Society. (2024, July 19). Changing state: Freezing, Lesson 2.4, Engage Step 1 and Explain Steps 4-5. Middle School Chemistry. Ice structure and expansion
4. American Chemical Society. (2024, July 19). Changing state: Condensation, Lesson 2.3, About this Lesson, Engage and Extend Steps 13-14. Middle School Chemistry. Cold-cup observations and humidity
5. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 13.6, Humidity, evaporation, and boiling, opening discussion and Figure 13.32. OpenStax. Dew point and evaporation
6. Flowers, P., et al. (2019). Chemistry 2e, sections 10.4, Phase diagrams, and 11.4, Colligative properties. OpenStax. Pressure and phase boundaries; Dissolved substances and phase-change temperatures

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.

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.

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 published a table of the known elements, arranging them mainly by atomic mass while grouping elements with similar behaviour. He left gaps for elements not yet discovered and predicted some of their properties. The modern table uses atomic number instead of atomic mass, but still makes patterns in chemical behaviour visible.

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.

The IUPAC periodic table lists 118 named elements, from hydrogen to oganesson. Many occur naturally on Earth; others have been produced in laboratories. The table gives each element its own place, whether it is common like oxygen or made in tiny amounts for research.

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.

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 contains different elements chemically combined. For the compounds we will study here, their atoms occur in fixed ratios. The formula records that ratio.

• Water, H₂O. Each water molecule has two hydrogen atoms joined to one oxygen atom. The small 2 applies to H; no small number after O means one.
• Sodium chloride, NaCl. One sodium for each chlorine in the compound. This is the main substance in table salt.
• Carbon dioxide, CO₂. One carbon to two oxygen.

Compare sodium chloride with the elements that form it. Sodium is a soft, shiny, very reactive metal. Chlorine is a poisonous, greenish gas. Sodium chloride is a white crystalline solid. These descriptions refer to different substances, even though sodium and chlorine atoms are present in the compound.

The difference comes from how the particles are bonded and arranged. In sodium chloride, sodium has lost an electron and chlorine has gained one. These charged particles are called ions. Positive sodium ions and negative chloride ions attract each other in a repeating crystal. NaCl records their one-to-one ratio; it does not mean the crystal consists of separate pairs like water molecules.

Knowing which elements are present is useful, but it is not enough to describe every property of a compound. Chemists also use its bonding and structure. The crystal arrangement helps explain salt's shape, for example. So do not copy the properties of sodium metal and chlorine gas onto salt, and do not conclude that predicting properties is impossible.

The point: A compound has properties of its own, which can differ greatly from those of its elements. A formula is not a safety test. Never taste an unknown substance or try to make salt from sodium and chlorine.

Mixture or compound?

Imagine water evaporating from salt water. Salt crystals remain. The water and salt have been separated without turning sodium chloride into sodium metal and chlorine gas. That second task would require a chemical change. Crushing a salt crystal also leaves sodium chloride: smaller pieces are not simpler substances.

A mixture does not have to look patchy. Salt water may look uniform throughout, yet you can make one sample saltier than another. Pure sodium chloride has a definite composition. Use composition and the kind of separation involved to classify a sample, rather than relying on its appearance alone.

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. Atomic number increases as you read across. Patterns in properties repeat from one period to the next; this does not mean every property changes smoothly.
• Columns are called groups. Members often have similar chemical behaviour. Similar does not mean identical: the table gives clues to investigate, not a promise that every member reacts in exactly the same way.

Three groups are worth knowing by name.

Most metals sit on the left and in the middle; most nonmetals sit toward the upper right. Hydrogen is an exception to that map: it usually sits above the alkali metals in group 1, but is a nonmetal. Elements such as silicon, near the stair-step boundary, are called metalloids because they have a mix of metallic and nonmetallic properties.

Many metals are shiny when clean, conduct heat and electricity well, and can be shaped without breaking. These are useful tendencies, not a complete identification test. An object may have a coating or contain several materials. A metal spoon is often an alloy, a material made with a metal and other elements, rather than one pure element.

Try reading one square. Oxygen has symbol O and atomic number 8, so each oxygen atom has eight protons. It lies in period 2 and group 16. The larger mass value printed in many tables answers a different question about atomic mass; it is not the proton count. Find carbon next: C, atomic number 6, period 2, group 14. The two elements share a row, but not a column.

Observation: compare everyday materials

Use intact objects at room temperature. This task needs no heating, tasting, bending or breaking. Keep magnets away from electronics, and use a large, securely enclosed fridge magnet rather than loose small magnets.

1. Choose a metal spoon, aluminium foil, a plastic spoon and a wooden spoon. Record any material information on their packaging.
2. Predict which objects the magnet will attract. Write your predictions before testing.
3. Bring the magnet close to each object and record whether you can observe attraction. Do not scratch or force it against the object.
4. Compare the result with your predictions. Can a metal fail to show attraction in this test?
5. Make a separate column headed "Pure element, compound or mixture?" Write "not enough information" wherever the material label does not settle that question.

What to expect: Aluminium foil should show no noticeable attraction to the fridge magnet. The metal spoon's response depends on its material. Your observations can therefore challenge the claim that every metal sticks to a magnet, even if you cannot identify the spoon's exact alloy.

Why it happens: Iron, cobalt and nickel are familiar examples of materials with strong magnetic responses. Other materials can have much weaker responses that this simple test cannot detect. "No noticeable attraction" is a report of your observation, not proof of absolutely no magnetic effect. Wood and plastic are materials containing compounds, not individual nonmetal elements listed in the periodic table.

Read a fizzy drink label

A label can help you classify substances, but some ingredient names describe mixtures. Read the label without opening the container.

1. Find a bottle of fizzy water or a soft drink and read the ingredients list.
2. Write down each ingredient. Classify named pure substances as elements or compounds; mark broad names such as "flavourings" as needing more information.
3. If carbon dioxide is listed, write its formula and count the atoms of each element in one molecule.

Check your reasoning: Pure water, sucrose (table sugar) and carbon dioxide are compounds. CO₂ describes one carbon atom and two oxygen atoms per molecule. A drink containing several substances is a mixture, even when it looks uniform. A list saying "fruit juice" does not give one chemical formula because juice contains several substances.

One label does not tell you how common free elements are in everyday life. Oxygen and nitrogen in air are elemental substances: their molecules contain only one kind of atom. The air as a whole is a mixture. Count the kinds of atoms in a substance, not simply the number of atoms in a molecule.

Common misconceptions

"A compound is just a mixture of its elements." Sodium chloride contains sodium and chlorine chemically combined. Its properties differ from those of sodium metal and chlorine gas because its particles have different bonding and arrangement.

"All metals stick to a fridge magnet." Aluminium is a metal but shows no noticeable attraction in this test. Magnetism alone cannot sort every material into metal or nonmetal.

"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 contains one kind of atom and cannot be broken down chemically; the IUPAC table lists 118 named elements.
• Symbols use a capital first letter and a lower case second, and several come from Latin names.
• The compounds studied here have fixed ratios of elements. Their properties depend on bonding and structure as well as composition.
• Physical methods separate a mixture into substances; breaking a compound into simpler substances requires chemical change.
• The periodic table orders elements by atomic number, which counts protons; rows are periods and columns are groups.
• Elements in a group often behave similarly. Patterns helped Mendeleev predict properties of undiscovered elements.

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

Sources

1. International Union of Pure and Applied Chemistry. (2022). Periodic table of the elements, 4 May release. Element names, symbols and atomic numbers. IUPAC
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. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Atomic structure and symbolism, section 2.3, Chemical Symbols and Table 2.3. Chemistry 2e. OpenStax
4. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). The periodic table, section 2.5, opening history and group descriptions. Chemistry 2e. OpenStax
5. American Chemical Society. (2024). Energy levels, electrons, and ionic bonding, lesson 4.5, Steps 1, 2 and 6. Middle School Chemistry. ACS
6. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Ionic bonding, section 7.1, opening discussion and The Formation of Ionic Compounds. Chemistry 2e. OpenStax
7. Urone, P. P., and Hinrichs, R. (2022). Ferromagnets and electromagnets, section 22.2, Ferromagnets. College Physics 2e. OpenStax

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

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

Where did the missing mass go?

A cup of vinegar and baking soda fizzes, and carbon dioxide leaves in bubbles. If the cup then weighs less, has the reaction destroyed matter? Before answering, decide what you weighed. The cup and its remaining contents are only part of the story.

A system is the collection of things you choose to study. Draw an imaginary boundary around the cup and its contents. Gas can cross that boundary into the room. Draw a larger boundary that also includes the escaped gas, and you can account for the material that left. Choosing the boundary is the first step in a mass investigation.

Key idea: In ordinary chemical reactions, the total mass of the products equals the total mass of the reactants to the accuracy relevant here. Atoms are rearranged into new combinations. Count all the participating matter, including gases.

Atoms are rearranged; measurements have limits

A chemical reaction changes how atoms are joined. It does not turn one element's atoms into another element's atoms. Think of taking apart a model house and building a boat with the same building bricks. The shape changes, but the collection still contains the same bricks. This model helps you count atoms; real atoms bond according to chemical rules, unlike bricks that you can connect however you choose.

A closed system exchanges no matter with its surroundings. A properly sealed container can approximate one even while energy passes through its walls. An open system can gain or lose matter. Its contents really can gain or lose mass when material crosses the boundary. That does not mean the reaction has created or destroyed matter.

Conservation of mass is the rule we use for these chemical and physical changes. It is supported by experiments, and the atomic model explains it. It is not a promise that two readings on a kitchen scale will display exactly the same number. A scale has a limited resolution, the smallest change it can display, and other measurement uncertainties. Identical readings do not prove exact equality; different readings do not by themselves identify the cause.

Working with the numbers

A worked example. Treat these as rounded classroom masses: 12 grams of carbon combines completely with 32 grams of oxygen, forming only carbon dioxide. What mass of carbon dioxide forms?

Step 1. Count both reactants, including the gas: 12 + 32 = 44 grams.

Step 2. The problem says both amounts react completely and there is just one product. That product therefore accounts for the full 44 grams.

Step 3. If you collect only some of the gas, your collected sample will weigh less than 44 grams. The calculated amount formed and the amount successfully collected are different quantities.

A second one, running backwards. A sealed flask initially contains only 10 grams of substance A and an unknown mass of B. Both react completely to form 27 grams of a single product. These masses exclude the flask. How much B was there?

Step 1. Write the mass balance: 10 + B = 27.

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

Step 3. Check: 10 + 17 = 27 grams. If you had included the flask in the last measurement but not the first, this subtraction would not answer the question.

Conservation gives the total mass of all the final material. It does not tell you how that mass is divided among several products, or how much starting material remains when one reactant runs out. For example, adding extra baking soda does not guarantee that all of it reacts if there is too little acid in the vinegar.

A burning log and a rusting nail

Case one: a log leaves much less ash than its starting mass. Burning involves oxygen from the air as well as wood. Carbon dioxide and water vapour are major products, but real wood smoke also contains other gases and small particles. Some material can remain as unburned wood or deposits. Comparing only wood with ash misses both an input and several outputs.

To balance the account, include the wood and oxygen consumed on the starting side. Include all gases, particles, ash and other remaining material on the finishing side. There is no need to assume a particular ash yield: it varies with the wood and the burning conditions. This is an explanation to work through on paper, not an instruction to light a fire.

Case two: a nail and its attached rust gain mass. Iron reacts in the presence of oxygen and water. Rust contains material that came from outside the original nail, so the combined nail and retained rust can weigh more. If rust flakes off or iron is carried away, the object you later weigh need not be heavier. Record what stayed and what left.

The upshot: First check the system boundary and the measurements. Uncounted gas is one possible explanation for an apparent mismatch. Spilled liquid, lost solids, a forgotten cup and limited instrument resolution also matter.

Balancing an equation without changing the substances

Chemists record reactants and products with chemical formulas. For complete combustion of methane in oxygen, the balanced equation is:

CH₄ plus 2 O₂ gives CO₂ plus 2 H₂O

Count the left side first: one carbon atom and four hydrogen atoms in CH₄, plus four oxygen atoms in two O₂ molecules. On the right, CO₂ contains one carbon and two oxygen atoms. Two water molecules contain four hydrogen and two more oxygen atoms. The totals are one carbon, four hydrogen and four oxygen on each side.

The large numbers before formulas are coefficients. They multiply a whole formula. The small lowered numbers are subscripts; they describe the substance itself. To balance an equation, change coefficients while keeping the formulas fixed. Changing H₂O to H₂O₂ would replace water with hydrogen peroxide, not balance the original reaction.

The vinegar reaction does not turn all its material into gas. Baking soda reacts with acetic acid in vinegar to form carbon dioxide, water and sodium acetate. Much of the material remains in solution, and there may be unreacted ingredients. Gas formation can increase the volume of an enclosed mixture without increasing its total mass.

Experiment: keep the same sealed system

Start with dissolving, a physical change that lets you practice weighing without producing gas. Ask an adult to help. Use a dry, unbreakable screw-top container, its lid, a small dry plastic cup that fits inside it, 50 millilitres of room-temperature water, half a teaspoon of table salt and a kitchen scale. Do not taste the materials. Keep water away from the scale's electronics.

1. Put the water in the larger container and the salt in the small cup. Stand the small cup inside the container with the salt above the water. Choose containers that let it remain dry until you tip it.
2. Close the lid. Dry the outside. The weighed system includes the container, lid, small cup, salt, water and enclosed air.
3. Set the scale on a firm, level surface and check that its empty reading is zero. Place the entire assembly on it, touching nothing else. Record the displayed unit and reading. Lift and replace the assembly twice to see whether the readings repeat.
4. Remove the assembly from the scale. Without opening it, gently tip it so the salt mixes with the water. Swirl until the salt dissolves. Do not add or remove anything.
5. Let the assembly rest, return it to the same position on the scale and repeat the three readings. Check for leakage. If liquid escaped, record that the closed-system condition failed.

What to expect: If no matter enters or leaves, the total mass stays the same to the accuracy relevant to this activity. The readings should be consistent with that prediction within the scale's measurement limits. A display that changes in whole grams cannot resolve every smaller change. Repeated readings help reveal variability; they do not measure every possible error.

Why it happens: Dissolving disperses the salt through the water. It does not remove it from the sealed assembly. The outside shape of the container also stays nearly unchanged, which helps keep the surrounding air's effect on the weighing similar. If you cannot arrange this setup, use the numerical examples and explain what each weighing must include.

Why an inflating bag is harder to weigh

Imagine the vinegar reaction inside a flexible, sealed bag. If nothing leaks, the bag and everything inside retain their total mass, while carbon dioxide formation can enlarge the bag. That does not guarantee an unchanged scale reading. Air pushes upward on objects, an effect called buoyancy. A larger bag displaces more surrounding air, increasing that upward force and potentially reducing the indicated mass even without a leak.

The size of this effect depends on the change in displaced volume and the air density. Whether the scale shows it also depends on the scale's resolution and other uncertainties. A lower reading could reflect buoyancy, a leak, or both. Opening the bag changes the gas contents and may change its volume as well, so subtracting the readings does not isolate the mass of carbon dioxide.

Use this bag example as a reasoning problem. Do not seal a gas-producing reaction in a rigid container or carry out an inflating-bag experiment for this lesson. The open-cup investigation below lets the gas leave freely.

Experiment: track an open reaction

With adult help and splash goggles, work in a well-ventilated room. Use an open plastic cup of at least 250 millilitres, a second small cup, a dry tray that fits on your scale, half a teaspoon of baking soda and 10 millilitres of household vinegar. Leave the reacting cup uncovered, keep your face away from it and wash your hands afterwards. A scale displaying tenths of a gram may show more detail than one displaying whole grams, but neither guarantees a detectable change.

1. Put the baking soda in the large cup and the vinegar in the small cup. Place both cups on the tray. Check that the assembly is within the scale's capacity.
2. Weigh the entire tray, both cups and both ingredients together. Record the reading and the smallest displayed step. Do not subtract a cup mass or press tare between the before and after measurements.
3. Move the tray off the scale. Pour the vinegar into the baking soda while holding the small cup over the tray. Return the small cup, including any liquid still in it, to the tray.
4. When vigorous fizzing has stopped, weigh the whole tray and both cups again. Keep any droplets on the tray as part of the weighed system. Record the elapsed time and anything that spilled beyond the tray.
5. Compare the two readings. Write down what crossed the system boundary and which measurement limitations could affect your conclusion.

What to expect: Escaping carbon dioxide tends to reduce the mass remaining on the tray. A small reaction may produce a change your scale cannot resolve. Some carbon dioxide can remain dissolved, and the end of visible fizzing does not prove that every bit has escaped. Evaporation, splashes beyond the tray and measurement uncertainty can also affect the comparison. Do not label the entire measured decrease as pure carbon dioxide without accounting for these possibilities.

Check the bookkeeping. Suppose a supplied example has a tray and two cups totalling 80 grams, plus 14 grams of ingredients. The initial total is 94 grams. If the measured final total is 93 grams, the indicated decrease is 1 gram. If you accidentally leave off a 6-gram cup, the reading becomes 87 grams: an apparent 7-gram decrease. Six of those grams belong to omitted equipment, not escaped gas. These are invented arithmetic data, not predicted results for your experiment.

Common misconceptions

"Burning destroys matter." Ash is only part of the output. Include oxygen consumed and all material that leaves or remains.

"Gases have no mass." Gas particles contribute mass even when you cannot see them. Gas density depends on conditions, so there is no single mass for a litre of every gas.

"A sealed container must give identical readings." Sealing prevents matter exchange only if the seal holds. Instrument limits and forces such as air buoyancy still affect measurements.

"Dissolving makes matter disappear." Salt remains in the solution. If nothing is spilled or exchanged with the surroundings, the total mass remains unchanged.

"Mass and volume are conserved together." Equal total mass does not require equal volume. Rearrangement and changes of state can change how much space the material occupies.

The takeaway

• Count every reactant and product, including gases, when applying conservation of mass.
• For an open system, track matter crossing the boundary. For a closed system, check that nothing enters or leaves.
• Weigh the same equipment before and after. A cup omitted from one measurement can imitate a large mass loss.
• Distinguish a predicted mass from an instrument reading. Resolution, leaks, spills and air buoyancy can affect what you observe.
• Balance chemical equations by changing coefficients, not the formulas of the substances.

Later, try explaining a lower reading in an open cup and a lower reading for a sealed, expanding bag without looking back. The first can involve matter leaving; the second also calls for checking how the weighing itself changed. For either one, name the system before deciding what the number means.

Sources

1. Flowers, P., Theopold, K., Langley, R., and Robinson, W. R. (2019). Sections 2.1, 4.1, 11.3 and 17.6, atomic theory, balancing equations, solubility and corrosion. Chemistry 2e. OpenStax, Rice University. Atomic theory; Balancing equations; Corrosion; Solubility.
2. Clark, M. A., Douglas, M., and Choi, J. (2018). The laws of thermodynamics, opening definitions of open and closed systems. Biology 2e, section 6.3. OpenStax. System definitions
3. American Chemical Society. (n.d.). Lesson 4.1: Conservation of mass. Inquiry in Action. Measurement limits, dissolving and including both cups in a mass comparison. ACS
4. American Chemical Society. (2024, July 30). Lesson 6.2: Controlling the amount of products in a chemical reaction. Middle School Chemistry. Vinegar reaction products and open-cup quantities. ACS
5. Harris, G. L. (2019). Selected laboratory and measurement practices and procedures to support basic mass calibrations (NISTIR 6969, 2019 edition). NIST. SOP 2, Appendix A, and SOP 29, section 3. Lesson investigations apply these measurement principles; they are not NIST calibration procedures. NIST
6. United States Environmental Protection Agency. (2025, December 17). Smoke from residential wood burning. Opening description of gases and fine particles in smoke. EPA

Nine point five eight seconds

On 16 August 2009, in Berlin, Usain Bolt ran 100 metres in 9.58 seconds, setting a men's 100-metre world record.

Divide one number by the other and you get 100 ÷ 9.58, or about 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.

The distance and finishing time let you calculate that average, but they do not tell you how his speed changed during the race. To find the average for a smaller part, you would need the distance and elapsed time for that part. Even that smaller average would describe an interval, not one exact instant.

Key idea: Average speed is total distance travelled divided by total elapsed time. It describes the chosen interval; it does not by itself tell you the speed at a particular instant.

The formula, and its two rearrangements

average speed = total distance travelled ÷ elapsed time

Elapsed time means the time from the beginning to the end of your chosen interval, including any pauses. It must be greater than zero. Distance means the length of the path travelled, so a return trip adds distance rather than cancelling it.

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. Use units consistently: a distance in kilometres and a time in minutes give km/min until you convert them.

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

Multiplying both sides of the first formula by time gives distance = average speed × time. Dividing that result by average speed gives the time formula, provided the average speed is greater than zero. Use the average for the same interval as the distance and time. If speed is constant, that speed is also the average.

Worked example. A cyclist covers 4500 metres in 300 seconds. Find her average speed. Then suppose she travels at a constant 15 m/s for another 45 seconds: how far does she go in that new interval?

Step 1. Average 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 15% of 300 seconds, and 675 metres is 15% of 4500 metres. Keeping the same speed makes those proportions match.

Converting between the units. A constant 1 m/s covers 3600 metres in an hour. That is 3.6 kilometres, so 1 m/s = 3.6 km/h. Multiply an m/s value by 3.6 to get km/h; divide a km/h value by 3.6 to get m/s. Bolt's average of about 10.44 m/s becomes about 37.6 km/h. This changes the unit, not the motion.

Average speed against speed right now

A car covers 120 kilometres in 2 hours, including a twenty-minute stop. Its average speed is 60 km/h. The moving time is 100 minutes, or 5/3 hours, so its average while moving is 120 ÷ (5/3) = 72 km/h. The whole-trip average and the moving-only average answer different questions.

Instantaneous speed means speed at one moment. A speedometer indicates this speed, which may stay steady or change. Knowing the completed trip's average does not guarantee the same average on a future trip. An arrival-time estimate needs an assumption about the average speed you will achieve.

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. Omitting it gives 1000 ÷ 500 = 2 m/s, the moving-only average. You also cannot usually add the speeds of different stages and divide by the number of stages: that gives every stage equal weight even if their durations differ.

For example, 2 m/s for 10 seconds followed by 4 m/s for 30 seconds covers 20 + 120 = 140 metres in 40 seconds. The average is 3.5 m/s, not (2 + 4) ÷ 2 = 3 m/s. If each speed lasts the same time, their simple arithmetic mean does work. Total distance divided by total elapsed time works in both cases.

Distance-time graphs

For the main graphs in this lesson, put elapsed time along the bottom and cumulative distance travelled up the side. Cumulative means a running total of the path length. Imagine a trip counter that starts at zero and adds every metre, including any metres travelled back towards the start. It never counts backwards.

Describe motion relative to a fixed reference frame. Here we use the ground and track the overall motion of the walker or vehicle. A line that rises by 10 metres in 2 seconds has a slope of 10 ÷ 2 = 5 m/s. That is the average speed over those 2 seconds. A straight section represents constant speed in the graph's model; on a curve, the local steepness indicates speed at that moment.

These are separate examples on the same axes, not three stages of one trip. For cumulative-distance graphs:

• A straight sloping line means constant speed. Equal distance covered in each equal slice of time.
• A steeper line on the same scales means a faster speed, because more distance is covered in the same time. Compare numerical slopes if the axis scales differ.
• 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.

A truly flat interval on this cumulative-distance graph means no path length is being added, so the object is stopped relative to the ground. A few equal measured values are less conclusive: a small movement may be too small for your instrument to detect. A straight line joining two measured points is also a model between those readings, not proof that speed stayed constant throughout.

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 cumulative-distance graph consists of straight sections from (0 seconds, 0 metres) to (20 seconds, 100 metres), then horizontally to (30 seconds, 100 metres), then up to (50 seconds, 160 metres).

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. Without the stop, the same distance in the 40 moving seconds would average 4 m/s. Including the stop lowers the average; it does not always place the answer between the two moving speeds. A long enough stop could make it lower than both.

Why this matters: Read the axis label before interpreting the slope. Cumulative distance records how much ground has been covered; position records where the object is.

Three different meanings hidden in the word distance

Suppose you walk 10 metres east from a doorway, then return to it along the same straight path. Your cumulative distance finishes at 20 metres. Your final position is back at zero. Your displacement, the change from initial to final position, is zero too. Walking back does not erase the outward part of the journey.

On the doorway trip, choose east as positive. Position rises from 0 to +10 metres and falls back to 0. A downward position-time slope means motion in the negative direction. For motion confined to that straight line, the size of the local slope, ignoring its sign, gives speed at that moment. Displacement is final position minus initial position. A displacement-from-start graph has the same slopes as the position graph because it subtracts the same initial position from every reading.

Now imagine a toy vehicle going around a circular track centred on a post. Its radial distance from the post stays equal to the track's radius while its cumulative distance increases. A flat graph of distance from the post therefore does not prove that the vehicle is stationary. Similarly, a single horizontal position coordinate cannot reveal motion perpendicular to that coordinate.

A graph labelled "distance from the start" needs the same care. After moving away from its start, an object could follow part of a circle centred there, keeping that distance fixed. If the problem instead specifies motion along one straight line, a constant distance from the start throughout an interval does mean stopped. Use the stated path and quantity, not the word distance alone.

Experiment: measure your own walking speed and graph it

Use a clear, level path away from traffic and obstacles, a tape measure, and a stopwatch. Walk at a comfortable pace. Ask a partner to handle the timing so you can watch the path. If walking is not suitable, use the supplied graph activity below.

1. Measure a straight 20-metre path and mark 0, 5, 10, 15 and 20 metres. If space is limited, use 4 metres with marks every metre, and use those actual distances in every calculation.
2. Choose one part of your body, such as your torso, to track at every mark. Start the timer as it crosses the start. Record the starting pair: 0 seconds and 0 metres.
3. Walk steadily without turning back. Your partner records the cumulative stopwatch reading as you pass each remaining mark. Do not reset the watch at the intermediate marks.
4. Divide the measured full path length by the total elapsed time for the average speed. Plot the five time-distance pairs, labelling the vertical axis cumulative distance travelled in metres.
5. Repeat, stopping at the middle mark for about five seconds. Record both the arrival and departure times at that same distance, as well as the other readings. The extra pair is necessary to show the pause.
6. Join successive plotted points with straight lines as an approximation. Find each interval's average speed from the change in cumulative distance divided by the elapsed time for that interval.

What to expect: A roughly steady walk produces points near a straight sloping line. The arrival and departure points at the pause have equal cumulative distance and different times, giving a flat segment. Timing reactions and changes in walking pace can affect your measured slopes, especially on a short path.

Why it happens: Equal distances in equal times produce equal slopes. During the pause, time passes without added travel. If the two trials have the same moving times, the trial with the pause has a lower whole-trip average. If your walking pace changes between trials, compare the recorded times before drawing that conclusion.

Common misconceptions

"Every flat distance graph means stopped." A flat cumulative-distance interval does. A flat radial-distance interval can describe motion around a fixed point. Read the full axis label and the path assumptions.

"Returning home makes total distance zero." It makes displacement zero. Every part of the return trip still adds to the distance travelled.

"Average speed is always the simple mean of the stage speeds." That method works for equal-duration stages. For unequal durations, calculate each stage's distance and divide their total by all the elapsed time, including stops.

"A speedometer shows the whole-trip average." Its usual speed reading indicates speed now. A separate trip-average display, if present, answers a different question.

"Metres per second and kilometres per hour are close enough." The numerical values for the same speed differ by a factor of 3.6. A person moving at 1.4 m/s is moving at 5.04 km/h.

Recap

• Average speed is distance travelled divided by elapsed time. Use the same interval when rearranging to find distance or time.
• Multiply an m/s value by 3.6 to express that same speed in km/h; divide to convert back.
• Average speed is total distance over total time, and any stops count in the time.
• On a cumulative-distance graph, a straight rising section represents constant speed, a flat interval represents a stop, and increasing local steepness means speeding up.
• Position, displacement and radial distance answer different questions. Fixed radial distance alone does not establish that an object is stopped.

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

Sources

1. Urone, P. P., and Hinrichs, R. (2020). Physics, sections 2.1 to 2.3. OpenStax. Definitions and graph interpretation: distance and displacement; speed and velocity; position-time graphs.
2. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 6.2, figure 6.7. OpenStax. Circular motion at fixed radius: centripetal acceleration.
3. National Institute of Standards and Technology. (2025, updated August 18). Guide to the SI, chapter 4, tables 2 and 5, and SP 330, section 4, table 8. Unit definitions: metres per second and kilo; hours and seconds.
4. World Athletics. (2025). Men's 100 metres, records and all-time world list, in the competition statistics document dated 16 August 2025 (PDF page 15). The table records Bolt's 2009 performance: World Athletics statistics.

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.

The pulls can stretch the rope even while its middle stays in place. To explain whether the rope as a whole starts moving, add the forces on it with their directions. Equal pulls in opposite directions give a total of zero. A large pull on each end does not necessarily mean a large total force.

Key idea: Net force tells you how motion changes, not whether an object is already moving. Zero net force allows an object to stay still or continue at the same speed in the same direction.

Here we track an object's overall movement from the ground, treating the ground as a suitable stationary reference for these short everyday examples. Spinning and changes of shape need more information about where the forces act. A zero total force alone does not rule those out.

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. Using one scale, a longer arrow represents a larger force. Equal arrows pointing opposite ways cancel in the total only when they represent forces on the same object. The book's push on the table does not belong in a diagram of forces on the book.

Note the support force, because it is easy to forget. For a book resting on a level table, we model the upward support and downward weight as equal. The book has no vertical acceleration. This equality depends on the situation: an extra downward hand push would require more support. A tilted surface's normal force is tilted too. "Normal" means perpendicular, not always vertically upward.

Adding forces along a line

The net force is the total of the external forces acting on your chosen object, taking direction into account. For forces along one line, pick one direction as positive, call the other negative, and add. In the horizontal examples below, weight and support balance vertically. We list all the horizontal forces used in each model.

Example 1. A box sliding right is pushed right with 30 N while friction acts 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. The box accelerates right, so its rightward speed increases.

Acceleration describes how quickly velocity changes, and velocity includes direction as well as speed. A rightward net force does not always mean speeding up. If a cart is moving left while a rightward net force acts, it initially slows down. Always compare the direction of the net force with the direction of travel.

Example 2. A parachutist falling vertically has 700 N of weight pulling down and 700 N of air resistance pushing up. Treat these as the only significant forces.

Step 1. Down positive: +700 and −700.

Step 2. Add: 0.

Step 3. Net force is zero, so her downward velocity stays constant while the forces remain balanced. This is terminal velocity. It can be very fast. A parachute can reduce the terminal speed by increasing drag; reaching terminal velocity by itself does not make a fall safe.

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

The second row needs both conditions: constant speed and a straight path. On a level road, the road's forward force on the driven tyres balances resistance, and the vertical forces balance too. The engine turns the wheels, but the road supplies the external forward force on the car. When all forces cancel, there is no acceleration.

Now compare the last row. A car turning at the same speed still changes velocity because its direction changes. It needs a net force toward the centre of the circle. On a flat road, sideways friction can provide that force. Friction therefore does more than slow objects down.

You can picture the difference on paper: draw arrows along a straight path, then along a circle. Equal arrow lengths show equal speeds. Along the circle, the arrow directions change. A speedometer alone cannot tell you that the net force is zero.

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

A book sliding across a table slows after your hand leaves it. Your hand no longer pushes, but sliding friction still acts on the book. This is evidence of an opposing force, not evidence that motion uses up a stored supply of force. With zero net force, motion would continue at constant velocity.

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.

There is friction even before sliding begins. Imagine a resting box that can resist up to 90 N before slipping. Push with 40 N and static friction can supply 40 N back. Push with 75 N and it can supply 75 N back. You do not subtract the maximum 90 N from every push. Once the box slides, use its actual sliding friction, which may differ from the maximum static value.

Air resistance is also called drag. For an unchanged shape and air conditions, it generally increases with speed through the air. In a simple vertical fall, weight initially exceeds drag and the object speeds up. As drag approaches weight, acceleration becomes smaller. If the forces balance, the object falls at terminal velocity. Short drops need not last long enough to reach it. Our falling-object model ignores the relatively small buoyant force of air.

Experiment: a gentle push, then no hand

Use a small empty plastic food container, a dry level table and a towel. Keep the test area away from the edge and clear of breakable objects. Use only gentle pushes, and stop if the container catches or tips. This compares observations; your hand is not a calibrated force meter.

1. Start with the container still. Press gently sideways, increasing the push only enough to start a short slide.
2. Once it slides, remove your hand. Observe whether its speed changes while the hand is no longer touching it.
3. Repeat three times. Sketch the forces during a slide after release: weight, support and friction. Treat air resistance as small.
4. Lay the towel flat and repeat with the same container. Record what actually happens, including catching or uneven motion.
5. Explain why these trials cannot give a numerical friction force: the starting pushes and speeds were not measured.

What to expect: A sliding container usually slows after release. The towel may change the motion, but do not assume a fixed ranking of surfaces. The materials, their condition and how the container contacts them matter. A rough-looking surface does not always give the largest friction.

Why it happens: After release, sliding friction acts opposite the slide. Before release, while the container remains at rest, static friction can balance a small sideways push. Different stopping distances could reflect different starting speeds as well as different resistance. Repeat observations help you notice variation, but they do not remove that uncertainty.

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. Stand on the floor in a clear space away from fans. Hold both at waist height, the flat sheet roughly horizontal, and release together without pushing.
3. Watch which lands first. Repeat three times and record any fluttering or uneven release.
4. Draw the downward weight and upward drag for each during its fall. Use the same weight-arrow length for the two sheets.

What to expect: The crumpled sheet usually reaches the floor first. A flat sheet can turn or flutter, so its landing time can vary. A single trial is not a precise measurement of acceleration or terminal speed.

Why it happens: Crumpling changes shape without appreciably changing mass or weight. The flat sheet generally experiences greater drag at the same speed because of its shape and larger area facing the air. Equal weights do not guarantee equal net forces. In a vacuum at the same location, with the same initial motion, both would have the same gravitational acceleration.

Common misconceptions

"A moving object needs a forward net force." A forward net force changes velocity. Steady straight-line motion needs zero net force. An applied push may still be needed to balance resistance.

"Balanced forces mean the object is stationary." A resting lamp and a car moving at 60 km/h in a straight line can both have balanced forces. The forces tell you whether velocity changes, not what velocity it already has.

"A constant speed means balanced forces." Turning changes velocity even when speed stays constant. Direction must also stay unchanged for the net force to be zero.

"Heavier things always fall faster." With only gravity acting at the same location, objects have the same gravitational acceleration regardless of mass. The paper trial compares equal masses with different shapes, so a landing-time difference cannot be explained by one sheet being heavier.

"Friction always points backward." It opposes relative slipping at a contact. During walking, static friction from the ground can push your foot forward while preventing it from slipping backward. The direction depends on the contact, not just the direction your body travels.

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 give zero acceleration: still if initially still, the same speed and direction if initially moving.
• Unbalanced forces change motion: speeding up, slowing down, or changing direction.
• Static friction can balance a push before slipping; sliding friction opposes the slide between surfaces.
• In the weight-and-drag model, terminal velocity occurs when those forces balance during a fall.

Before calculating, name the object and draw the forces acting on it. After calculating, compare the net-force direction with its current motion. That final comparison is what lets you explain a speeding box, a slowing trolley and a turning car using the same idea.

Sources

1. NASA Glenn Research Center. (n.d.). Newton's laws of motion, first and second law sections. Beginner's Guide to Aeronautics. NASA
2. NASA Glenn Research Center. (n.d.). Falling object with air resistance. Beginner's Guide to Aeronautics. NASA
3. Urone, P. P., and Hinrichs, R. (2022). Newton's second law of motion: Concept of a system, section 4.3. College Physics 2e. OpenStax
4. Urone, P. P., and Hinrichs, R. (2022). Newton's third law of motion: Symmetry in forces, section 4.4, walking and driven-wheel examples. College Physics 2e. OpenStax
5. Urone, P. P., and Hinrichs, R. (2022). Normal, tension, and other examples of forces, section 4.5. College Physics 2e. OpenStax
6. Urone, P. P., and Hinrichs, R. (2022). Friction, section 5.1. College Physics 2e. OpenStax
7. Urone, P. P., and Hinrichs, R. (2022). Drag forces, section 5.2. College Physics 2e. OpenStax
8. Urone, P. P., and Hinrichs, R. (2022). Centripetal acceleration, section 6.2. College Physics 2e. OpenStax
9. Urone, P. P., and Hinrichs, R. (2022). The second condition for equilibrium, section 9.2, opening discussion of turning forces. College Physics 2e. OpenStax

The coffee cup on the dashboard

A driver brakes at a junction and a loose coffee cup slides towards the front of the dashboard. The cup and car were moving together before braking. Afterwards, the car slows more quickly than the cup. You can explain that forward slide without inventing a forward push on the cup.

Friction from the dashboard can slow the cup, but it may not provide enough force to slow it at the same rate as the car. Relative to the road, both can be slowing while the cup moves forward relative to the car. The statement "the cup did not slow at all" would require an extra assumption that its horizontal forces were negligible. This is a thought example, not an experiment to try in a vehicle.

Isaac Newton's Principia was published in 1687. Its laws of motion connect forces with changes in motion. Here we apply their familiar school form to ordinary objects, treating motion relative to the ground as a useful approximation to a nonaccelerating reference frame. A braking car is an accelerating frame, so we first explain the cup from the roadside view.

Key idea: Choose the object and the reference frame, then add the forces acting on that object. A change in velocity depends on their net effect, not just on whether an engine is running.

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.

Use these examples to separate inertia from the forces that change motion.

• The coffee cup. A cup needs a backward net force to slow. Friction can provide some of it; inertia is not an extra forward force.
• Seat belts. A belt exerts a force that helps slow a passenger with the vehicle. The first law explains why the passenger's motion cannot change without a net force.
• A resting book. Earth pulls down and the table pushes up. With those forces balanced, the book remains at rest. Zero net force does not mean no forces exist.
• A spacecraft between planets. Turning off its engine removes thrust, and atmospheric drag is usually negligible far from planets. Gravity from the Sun and planets still acts, changing the spacecraft's velocity. Coasting means travelling without propulsion; it does not mean constant velocity.

Imagine a different, ideal case in which the spacecraft's net external force is zero. It would keep the same velocity: the same speed and direction in a nonaccelerating reference frame. For a real flight, negligible drag alone does not establish that condition. A craft can speed up, slow down or turn under gravity while its engine is off. NASA's account of interplanetary trajectories describes coasting along orbits and speed changes during gravity assists.

Pause and test the distinction. "No thrust," "negligible drag" and "zero net force" are three different statements. Which one guarantees constant velocity in the model? Only the last. Before using the first law to predict a straight path at constant speed, account for gravity and any other external forces.

The second law: how much change, exactly

Net external force equals mass times acceleration for an object of constant mass. Written as a formula: F_net = m × a. Here m is mass in kilograms, a is acceleration in metres per second per second, and F_net is the total external force in newtons, with direction included.

Acceleration describes a change in velocity, including slowing or turning. Its direction is the direction of the net force, which need not be the direction of travel. At the same mass, a larger net force produces greater acceleration. At the same net force, greater mass produces less acceleration. A larger push alone does not settle the result if friction changes too.

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

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

Step 1. Rearrange: acceleration = net 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: the mass increased from 2 kg to 5 kg, a factor of 2.5. Acceleration fell from 5 to 2 metres per second per second, so it became 1/2.5, or two fifths, of its previous value. Both calculations use the same net force.

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

Step 1. Net force = mass × acceleration.

Step 2. 1200 × 2 = 2400.

Step 3. The answer is 2400 N in the direction of the acceleration. This is the resultant force on the car, not a claim about engine power or one individual force.

Worked example 4. A 4 kg cart has a 14 N force to the right and a 6 N force to the left. Its vertical forces balance. First subtract the opposite horizontal forces: 14 - 6 = 8 N to the right. Then divide by mass: 8 ÷ 4 = 2 metres per second per second to the right. Using 14 N alone would give 3.5 and would ignore a force in the problem.

If that cart initially travels left, the rightward acceleration first slows its leftward motion. If it starts at rest, it begins moving right. The same acceleration can therefore describe different changes in speed depending on the starting velocity. When the two horizontal forces are both 6 N, their sum is zero and the cart keeps its existing velocity.

What matters here: Draw force arrows on one chosen object before calculating. Subtraction works for forces along one line in opposite directions. In general, forces must be combined with their directions; simply adding every force size will not work.

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 two forces act on different objects at the same time. A useful label names both participants: "table on book" or "book on table." Reversing those names identifies the partner force. Both forces belong to the same interaction; "reaction" does not mean a delayed response.

To calculate the net force on the book alone, include the table's upward push and Earth's downward pull. They balance when the book rests on a level table, but they are not a third-law pair: both act on the book and come from different interactions. The partner of Earth's pull on the book is the book's pull on Earth. The partner of the table's push on the book acts on the table.

A system is the object or collection of objects you choose to study. For one object, its interaction partner acts elsewhere and cannot cancel a force in that object's force sum. If you choose both interacting objects as one system, their mutual forces are internal and cancel in the total force sum. That does not prevent the objects from moving relative to each other. The system boundary decides which force sum you are calculating.

Experiment: the coin and the card

Work over a tray on a stable table, with a plastic cup, stiff card and coin. Keep small objects away from young children and pets, and do not put the coin in your mouth. Use adult help if needed. You can instead sketch predictions without handling the materials.

1. Stand the empty plastic cup on the tray and lay the card flat across its opening.
2. Place the coin near the centre, directly above the cup's opening.
3. Pull the card horizontally out from under the coin with a quick movement. Keep hands and faces out of its path.
4. Record whether the coin falls into the cup, lands on the rim or moves off to one side.
5. Reset the same arrangement and pull more slowly. Repeat each condition a few times, keeping the starting position and materials alike.

What to expect: A quick pull often leaves the coin near enough to its starting horizontal position to fall into the cup. A slower pull can carry it farther sideways. Neither outcome is guaranteed: friction, the card's bend, the pull and the coin's starting position matter.

Why it happens: While the surfaces touch, friction can accelerate the coin horizontally. The velocity change depends on the force and how long it acts, not on time alone. A brief contact can give a small sideways change. Once the support is gone, gravity makes the coin fall. It may still move sideways while falling; landing in the cup does not prove zero horizontal motion.

You have not measured a contact duration or friction force. Do not assign a precise time to the flick from watching it. Compare repeated observations and explain a possible reason for a missed cup. A prediction is useful even when the result prompts you to examine an assumption.

A balloon rocket: what would a comparison establish?

Consider this setup on paper. An inflated balloon is taped to a straw threaded on a level string. When air escapes backwards through the neck, the balloon can move forwards along the string. It pushes on the escaping air, and that air pushes back. A rocket also expels material and does not require surrounding air to produce thrust. Gravity and other external forces must still be counted.

Now examine the claim "half as much air always gives half as much acceleration." It is not a valid use of the second law. Changing inflation can change the thrust, how long air escapes, the moving mass and the balloon's shape. Resistance at the straw and string also matters. A shorter travel distance does not directly measure acceleration.

A claim about adding mass needs a condition too: for the same net force, more mass gives less acceleration. Taping another object onto a balloon does not establish that the net force stayed the same. This comparison may be interesting to observe, but it is not a controlled numerical test of mass alone.

Use supplied values to isolate the calculation instead. In an ideal cart model, net force is fixed at 0.6 N. A 0.2 kg cart accelerates at 0.6 ÷ 0.2 = 3 metres per second per second. A 0.3 kg cart accelerates at 0.6 ÷ 0.3 = 2. These are model values, not measurements from a balloon trial. A real balloon also loses air mass as it moves; we have not calculated its changing motion with one fixed mass.

Common misconceptions

"Action and reaction must balance on me." Only one member of each interaction pair acts on you. The other acts on your interaction partner. Their cancellation in a combined system's total does not mean that your own net force is zero.

"Any push must make a resting box move." Static friction may balance your push. A nonzero net force produces acceleration; an applied push and the net force are different quantities.

"A rocket needs outside air to push against." It pushes on exhaust material. A vacuum removes the need to account for atmospheric drag, but it does not remove gravitational forces.

"An engine-off spacecraft has no acceleration." Gravity can change its velocity while it coasts. The first law requires zero net external force for exactly constant velocity, not merely zero thrust.

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: for constant mass, net external force equals mass times acceleration.
• Use force directions and count only forces acting on the chosen object or system.
• Third law: forces always come in equal and opposite pairs, acting on two different objects.
• An interaction pair does not balance on one object. It cancels as an internal pair when both objects belong to one system.
• A spacecraft can coast under gravity. No thrust is not the same condition as zero net force.

Close the text and draw the forces on the resting book. Then identify the partner of each force on a separate object. On another day, explain why a coasting spacecraft can turn and solve the cart example again with a 10 N rightward force and 6 N leftward force. For a 4 kg cart, the result is 1 metre per second per second to the right. If you used 10 N alone, revisit the force sum.

Sources

1. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, sections 4.2, Newton's first law of motion: Inertia, and 4.3, Newton's second law of motion: Concept of a system. OpenStax. First law and inertia; Net external force and acceleration
2. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 4.4, Newton's third law of motion: Symmetry in forces, including Example 4.3 discussion. OpenStax. Interaction pairs and system boundaries
3. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 8.1, Linear momentum and force, Momentum and Newton's Second Law. OpenStax. Force, contact time and constant mass
4. NASA. (2025, January 16). Basics of space flight, Chapter 3: Gravity and mechanics, Gravitation; NASA. (2024, November 4). Chapter 4: Trajectories, Hohmann Transfer Orbits and Gravity Assist Trajectories. Gravity in space; Coasting trajectories
5. Newton, I. (1687). Philosophiae naturalis principia mathematica, title page. The Newton Project, University of Oxford, normalized transcription published 2009. Historical publication date. Principia front matter
6. Urone, P. P., and Hinrichs, R. (2022). College Physics 2e, section 5.1, Friction, opening discussion and static-friction limit; section 6.4, Fictitious forces and non-inertial frames, opening car example and reference-frame discussion. OpenStax. Friction between surfaces; Choosing a reference frame

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.

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

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 holds 0.25 kg of tea at 80 degrees Celsius. A bath holds 100 kg of water at 40 degrees Celsius. The tea has the higher temperature. Its Celsius reading is twice as large, but that does not mean it is "twice as hot": zero Celsius is not the point where thermal motion disappears.

Now ask how much energy each could release while cooling to 20 degrees Celsius. Treat the tea as water. The bath has 400 times the mass, so even though its temperature would fall by only 20 degrees compared with the tea's 60 degrees, it could release much more energy. Temperature alone cannot tell you how much energy a sample can transfer.

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

Key idea: Temperature is related to the average kinetic energy of random particle motion. Heat is energy transferred because of a temperature difference. A small hot sample can release less energy than a much larger warm sample of the same material.

Temperature

Temperature tells you how hot or cold something is and is measured with a thermometer. In our particle model, higher temperature means greater average kinetic energy of random motion. Kinetic energy is energy of motion, not speed itself: it also depends on particle mass. Compare water with water, and warmer water has faster-moving molecules on average.

The word average matters. In a cup of water, particles have a range of speeds. Temperature reflects the collective state, not the speed of any one molecule. A teaspoon taken from a well-mixed bath initially has the same temperature as the bath, although it can cool faster after removal.

The Kelvin temperature scale starts at absolute zero, 0 K, which equals minus 273.15 degrees Celsius. Use this as the lower limit for the ordinary materials studied here. The simple moving-particle model helps explain cooling, but it is not a complete description of matter near absolute zero.

Heat

Heat is energy transferred because of a temperature difference. Thermal energy refers here to internal energy associated with particles' random motion and interactions. Heat names a transfer, not something stored. Energy can also be transferred by work, such as stirring water, so not every energy transfer is heat.

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

1. Net heat transfer is from hotter to colder when objects exchange energy without an external device moving energy the other way.
2. Equal temperatures mean thermal equilibrium: there is no net heat transfer between the objects. Particles still move and exchange energy.

A cold drink does not fill your hand with cold; your warmer hand loses energy to the drink. The rate depends on more than temperature difference. Material, contact area and thickness matter too. If two objects can exchange energy and no outside source keeps them at different temperatures, they approach the same temperature.

Three ways energy gets from hot to cold

During conduction, energy passes through interactions between neighbouring particles without the material flowing along with it. In a solid, atoms vibrate about their positions. Metals also contain mobile electrons that help carry energy, which makes many metals good conductors. This explains why a saucepan may have a metal base and a plastic handle. Some pans have metal handles too, so a handle's appearance is no guarantee that it is safe to touch.

Air is a poor conductor. Wool and similar insulating materials hold air in small pockets that also limit its circulation. They slow energy transfer; they do not create energy. The same insulation can slow cooling of a warm drink or warming of an ice pack.

Convection carries energy with flowing material. In natural convection, warmed air expands and becomes less dense than nearby cooler air. Buoyancy makes it rise, while cooler air moves in. Continued heating and cooling can maintain a circulation called a convection current. This helps a heater near the floor distribute warmth. A fan or pump can also drive convection, even without warm fluid rising. Our classroom examples use liquids and gases, not a rigid solid spoon.

Radiation carries energy as electromagnetic waves, which can cross empty space. Sunlight includes visible light and infrared radiation; it is not all infrared. When a surface absorbs radiation, its internal energy can increase. Objects near room temperature emit mainly infrared, which your eyes cannot see.

A shiny metallic survival blanket reflects much of the infrared from your body and reduces energy loss by radiation. Visible colour alone does not tell you how a surface behaves in infrared. A surface that looks white to your eyes is not necessarily a good infrared reflector.

Remember: Conduction needs matter. Convection needs material that can flow. Radiation can cross empty space.

The metal handle that is not actually cold

Consider a metal spoon and a wooden spoon left in the same room, away from sunlight or a heater, until both reach room temperature. If the room is cooler than your hand, the metal usually feels colder.

The metal conducts energy away from the contact area faster, cooling your skin more quickly. Wood transfers energy more slowly. Touch therefore does not provide a reliable comparison of the objects' temperatures: the feeling also depends on how quickly your skin gains or loses energy.

The direction reverses when an object is hotter than your skin: it transfers energy into your hand. A good conductor can then cause a burn quickly. Do not test this by touching heated objects. Use a suitable thermometer to measure temperature.

Experiment: race two cups to room temperature

Ask an adult to help prepare mildly warm water and check that it is safe to handle. Use stable mugs on a tray and a thermometer designed for measuring water. Do not use boiling water or test unknown water temperatures with your fingers.

1. Pour equal amounts of water from one batch into two identical mugs. Record their starting temperatures.
2. Wrap the sides and base of one mug in a dry towel. Leave the other bare. Give both the same loose cover, so the side insulation is the main difference.
3. Keep the mugs together away from sunlight, heaters and draughts. If you have no suitable thermometer, make a prediction on paper instead.
4. Wait thirty minutes without disturbing either.
5. Measure both final temperatures in the same way. Subtract each final reading from its starting reading to find its temperature drop.

What to expect: The insulated mug should usually show a smaller temperature drop. The difference depends on the mugs, towel, water and room, so no particular number of degrees is guaranteed. Repeat the comparison if the readings are too close to distinguish with your thermometer.

Why it happens: Air trapped in the towel slows conduction and limits air circulation within the insulation. Covers also reduce evaporation, which carries energy away with escaping water molecules. Giving both mugs matching covers helps you investigate the towel itself. The towel supplies no energy; it changes how quickly energy escapes from warmer water to the cooler room.

Experiment: watch a convection current

Use an adult's help, a stable clear plastic container, a dropper, food colouring and mildly warm water checked by the adult. Protect the surface with a tray.

1. Fill the clear container with room-temperature water and let it become still.
2. Mix a few drops of colouring into a small cup of mildly warm water.
3. Fill the dropper with this coloured water. Place its tip near the bottom and release a little very slowly. Avoid squirting a jet.
4. Watch the coloured water for two minutes without moving the container.
5. Repeat with fresh room-temperature water in the container and coloured water at the same temperature. Use the same amount of colouring and the same release method.

What to expect: The warm coloured water may form a rising plume. Compare that pattern with the second trial. Movement in both trials can come from the dropper, so a rising streak alone is not proof that temperature caused it.

Why it happens: Over this room-temperature-to-warm range, water expands when warmed. The same mass occupies more space, so its density falls and it can rise through denser water. Other water moves into the space it leaves. This shows buoyant motion that can contribute to natural convection. Do not generalize it to every temperature: liquid water behaves differently close to freezing. A continuously heated pan can sustain circulation; this small plume eventually mixes and loses its temperature difference.

Common misconceptions

"Metal must be colder than wood if it feels colder." Objects at the same temperature can feel different because they change your skin's temperature at different rates.

"Cold flows into things." Ice does not fill a warmer drink with cold. There is a net transfer of energy from the drink 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 related to average kinetic energy, whereas a sample's thermal energy also depends on how much material it contains and the material's properties. The bath can release more energy than the cup even though it is cooler.

What you now know

• Temperature is related to average particle kinetic energy; heat is a transfer caused by a temperature difference.
• At thermal equilibrium, net heat transfer between the objects is zero.
• Conduction transfers energy through matter without bulk flow.
• Convection carries energy with moving fluid; buoyancy, a fan or a pump can drive that flow.
• Radiation uses electromagnetic waves, including visible light and infrared, and can cross a vacuum.
• Insulation slows energy transfer and can keep a warm object warm or a cool object cool.
• Touch depends on heat transfer as well as temperature. Use a thermometer to compare temperatures.

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. American Chemical Society. (2024). Heat, temperature, and conduction. Middle School Chemistry, lesson 2.1. ACS
2. Urone, P. P., and Hinrichs, R. (2022). Temperature and kinetic theory. College Physics 2e, sections 13.1 and 13.4. OpenStax. Temperature; Kinetic theory.
3. Urone, P. P., and Hinrichs, R. (2022). Heat; temperature change and heat capacity. College Physics 2e, sections 14.1 and 14.2. OpenStax. Heat; Heat capacity.
4. Urone, P. P., and Hinrichs, R. (2022). Conduction; convection. College Physics 2e, sections 14.5 and 14.6. OpenStax. Conduction; Convection.
5. Urone, P. P., and Hinrichs, R. (2022). Radiation. College Physics 2e, section 14.7, opening paragraphs and figure 14.24. OpenStax. Radiation.
6. Urone, P. P., and Hinrichs, R. (2022). Thermal expansion of solids and liquids. College Physics 2e, section 13.2, figure 13.13 and discussion of water. OpenStax. Water and temperature.
7. U.S. Department of Energy. (2011). Guide to cool roofs (DOE/EE-0384), p. 1, solar reflectance and thermal emittance; and (n.d.), Types of insulation, How? section. Reflectance and emission; Insulation.

The wave that travels round a stadium

Picture a row of stadium spectators standing up and sitting down in turn. The rising pattern travels along the row, although nobody changes seats. Follow one person and you see an up-and-down movement. Follow the pattern and you see movement along the stands.

A pulse on a rope makes the same distinction visible. A pulse is a single travelling disturbance, such as a hump made by one flick of your hand. Each small section of rope pulls on its neighbour. The disturbance travels and carries energy, while each section moves near its own resting place.

The spectators are an analogy for the moving pattern. They use their own muscles to stand up; they do not pass the energy for standing from person to person. In the rope, forces between neighbouring sections really do transfer energy along it. The rope is the wave's medium, the material through which it travels.

Key idea: Track the travelling disturbance separately from the local motion of the material. A wave can carry energy without carrying each piece of its medium along with the wave.

That statement does not mean waves can never move matter overall. Real water waves can cause drift. The simple picture of material returning to its starting place is a useful model for small waves, not an exact rule for every situation.

Two kinds of wave

For a mechanical wave, compare the direction of the material's vibration with the direction of wave travel. A vibration is a repeated back-and-forth motion.

• In a transverse mechanical wave, the material moves at right angles to the wave's direction. A small wave can travel along a stretched rope while the rope moves up and down.
• In a longitudinal wave, the material vibrates along the direction of travel. Push and pull the end of a stretched spring along its length. Crowded regions, called compressions, travel along it, alternating with more spread-out regions. Sound in air is also longitudinal.

Water surface waves involve both up-and-down and back-and-forth motion. A water particle can follow an approximately circular or oval path. Drawing only the surface height hides part of this motion. A surface wave is therefore not a purely transverse example like our ideal rope wave.

Light is transverse too, but no rope or other material has to vibrate. Its electric and magnetic fields vary at right angles to the direction of travel. These electromagnetic waves can cross a vacuum. Sound and rope waves need a medium; light does not.

The parts of a wave

Imagine a snapshot of a symmetric repeating rope wave. These hypothetical values describe three neighbouring high and low points at one instant. Positive displacement means above the rest line; negative means below it.

If you want to sketch this example, draw a horizontal rest line and mark the three positions along it. Put the crests 1 cm above that line and the trough 1 cm below it. Join them with a smooth wave shape. Label the vertical rest-to-crest distance and the horizontal crest-to-next-crest distance separately.

• A crest is a high point of the wave; a trough is a low point.
• Amplitude is the greatest distance from the rest position for the rope's motion. On this symmetric wave, measure from the rest line to a crest or to a trough. Trough-to-crest height is twice the amplitude.
• Wavelength is the distance along the direction of travel between neighbouring matching points: crest to next crest, or trough to next trough. Use a length unit such as metres or centimetres.
• Frequency is how many complete waves pass a point each second, measured in hertz, written Hz. Five waves per second is 5 Hz.

The table describes a snapshot of a repeating rope wave. Position means distance along the rope, not time. The values let you find amplitude and wavelength. To find frequency, you must also watch how often the motion repeats. One snapshot without timing information cannot give you the frequency.

Try reading a snapshot: suppose crests occur at 2 cm, 8 cm and 14 cm along a rope. Subtract neighbouring positions: 8 - 2 = 6 cm, so the wavelength is 6 cm. The distance from the first to the third crest is 12 cm, which spans two wavelengths. If each crest is 1 cm above the rest line, the amplitude is 1 cm, not 6 cm.

A longitudinal wave has a wavelength too: measure from the centre of one compression to the centre of the next. Its displacement amplitude is the greatest distance a bit of the medium moves from its rest position along the direction of travel. A graph of sound pressure can also have peaks, but its vertical axis is pressure, not the height of the air.

Amplitude tells you the size of a disturbance, not its repetition rate. Compare small repeating waves on the same rope with the same tension and frequency. A larger amplitude carries more energy each second. You need those conditions: amplitude alone cannot tell you the total energy carried by any wave. Frequency and how long the source runs can also matter.

For sound, a greater pressure amplitude at the listener generally makes the same tone louder. Frequency mainly controls the pitch of a pure tone. For light of one visible frequency, frequency helps determine its perceived colour, while field amplitude relates to intensity. Mixed light can produce colours that do not correspond to one frequency.

The wave equation

wave speed = frequency × wavelength

For a repeating travelling wave, follow a crest. In the time between two crests passing you, the pattern advances one wavelength. If four cycles pass each second and the wavelength is 3 metres, a crest advances 12 metres in one second. That gives a wave speed of 12 metres per second. We are calculating the speed of the pattern, not the speed of a bit of rope moving up and down.

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. Multiply 5 cycles per second by 2 metres per cycle: 5 × 2 = 10 metres per second.

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. Divide both sides of speed = frequency × wavelength by wavelength. This leaves frequency = speed ÷ wavelength.

Step 2. 340 ÷ 0.68 = 500.

Step 3. The frequency is 500 Hz. Check by multiplying back: 500 × 0.68 = 340 m/s. Here 340 m/s is a supplied rounded speed, not the speed of sound under every condition.

Worked example 3. A radio station broadcasts at 100 million Hz. Use the approximate radio-wave speed in air of 300 million m/s. Find the wavelength.

Step 1. Divide speed = frequency × wavelength by frequency. This gives wavelength = speed ÷ frequency.

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

Step 3. The wavelength is about 3 metres. The millions cancel in the division, leaving 300 ÷ 100 = 3. This is a distance between matching parts of the radio wave, not the height of its electric field.

Remember: If wave speed stays the same, increasing frequency decreases wavelength. At 12 m/s, a frequency of 3 Hz gives a wavelength of 4 m. Doubling the frequency to 6 Hz gives 12 ÷ 6 = 2 m. The same distance now contains twice as many cycles.

The condition about speed matters. Small waves on the same uniform rope have approximately the same speed if its tension stays fixed. Tension means how strongly the rope is pulled tight. A tighter pull changes the speed; a heavier rope per metre also changes it.

Water surface waves are more complicated. Their speed can depend on wavelength as well as water depth and surface tension, the tendency of the surface to resist stretching. Waves of different wavelengths travelling at different speeds show dispersion. The wave equation still applies to each repeating wave. Do not assume that two ripples have equal speeds just because both travel through water.

How fast do waves actually go?

Light travels almost as fast through air as through a vacuum. That is why the light from a distant lightning flash arrives before its thunder. Using 343 m/s for the sound, 1000 ÷ 343 is about 2.9 seconds per kilometre. Light covers that distance in only a tiny fraction of a second. These are approximate travel-time comparisons, not a reason to go outside to watch a storm.

Experiment: make waves on a rope

Use a soft rope without hard handles or attached weights. Work with an adult in a clear space, away from faces, lamps and walkways. Keep movements small, and do not wrap the rope around anyone. If you lack suitable space or help, use the table and the paper activity instead.

1. With the rope at rest, put a small tape mark near its middle. Have the adult hold one end still. Hold the other end so the rope is gently stretched, without a hard pull.
2. Make one small up-and-down movement. Follow the hump towards the other end. Then watch for a returning pulse.
3. Wait for the rope to settle and repeat. This time follow the tape, not the hump. Describe each motion separately.
4. Try a few steady up-and-down movements. Keep roughly the same pull and timing, then slightly increase your hand's travel. Record what changes.
5. Return to the small movement and repeat a little faster. Watch the first waves travelling away before returning waves overlap them. If the pattern is unclear, record that rather than guessing a wavelength.

Prediction and comparison: A pulse should pass the tape while the tape moves mainly up and down near its original place. It does not travel down the rope with the hump. A pulse can reflect at the held end and return; at an ideally fixed end, an upward pulse returns inverted. A real hand-held end may move, so the reflection need not look perfect.

For small waves with the same tension, a larger hand motion should increase the outgoing amplitude. Faster repeated motion should increase frequency and shorten wavelength. Changing your pull at the same time makes the comparison harder, because it also changes speed. Reflected waves can overlap outgoing waves and make a pattern that no longer looks like separate moving humps.

Experiment: ripples and a floating marker

Place a shallow tray on a stable surface away from electrical equipment. Use a small floating scrap of paper. Wipe up spills and wash your hands afterwards. This observation tests a simple picture; it cannot measure the full motion of each water particle.

1. Add water about 3 cm deep. Let it settle, place the paper near the middle, and watch whether it drifts even before you make a ripple.
2. Touch the surface gently with one fingertip near an end of the tray. Watch the outward ripple before it reaches the walls.
3. Repeat after the water settles. Follow the paper this time. Does it bob? Does it move sideways? Does it travel with the crest all the way across?
4. Try a few gentle repeated touches. Record the shape and spacing you can actually see. Repeat with faster touches, without claiming that the speed stayed constant.

What to look for: The moving crest can pass the marker while the marker mainly bobs or moves over a much smaller distance. That difference helps separate wave travel from local motion. The marker may also drift. Finger movements can create currents, air movement can push the paper, and waves themselves can cause drift. Reflections from the tray walls add further motion.

A drifting marker does not mean the travelling wave has stopped carrying energy. It means the claim that water returns exactly to its starting place is too simple for the observation. Nor does a bobbing marker prove that there is no sideways motion. Write what you saw and which explanation it supports, leaving small or unclear motions unresolved.

Common misconceptions

"A wave is a lump of material travelling from end to end." A rope pulse travels past successive pieces of rope. Those pieces move locally. Water surface waves add motion and drift that the simplest rope picture does not describe, but a moving crest still need not be the same parcel of water all the way across.

"Amplitude is the distance from trough to crest." For a symmetric rope wave, amplitude is measured from the middle rest line to an extreme. If the full height is 6 cm, the amplitude is 3 cm.

"A louder sound must arrive sooner." Ordinary sounds travel at approximately the same speed through air under the same conditions. Greater pressure amplitude does not make an ordinary tone catch up with a quieter one. Very strong disturbances such as shock waves are outside this simple model.

"Being in the same material guarantees a fixed speed." The rope's tension matters, and water ripples can show dispersion. First check the conditions. Only then use a fixed speed to predict how frequency and wavelength trade off.

Looking back

• A travelling disturbance carries energy. Follow a piece of the medium separately to see its local motion; do not assume that real water waves cause no drift.
• Transverse vibrations are at right angles to travel; longitudinal vibrations are along it. Light has vibrating fields and needs no material medium.
• Amplitude measures the disturbance's size. Wavelength measures the spacing of a repeating pattern. Frequency counts cycles per second, in hertz.
• Wave speed equals frequency times wavelength, and the equation rearranges for either.
• At the same wave speed, higher frequency means shorter wavelength. State that condition when making the comparison.

Return tomorrow: without looking back, sketch a repeating rope wave and label amplitude and wavelength. Then calculate its speed for 4 Hz and 1.5 m, and explain whether the rope itself moves along at that speed. Check afterwards: 4 × 1.5 = 6 m/s is the travelling pattern's speed. The rope moves mainly across that direction. Redraw any label you missed and explain your correction aloud.

Sources

1. Moebs, W., Ling, S. J., and Sanny, J. (2016). University Physics, Volume 1. OpenStax. Sections 16.1, 16.3, 16.4, 16.5 and 17.2 cover wave measurements, string speed, energy, reflections and sound speed. Travelling waves; String speed; Energy; Reflections; Sound speed
2. NASA, Science Mission Directorate. (2010, updated 2023). Anatomy of an electromagnetic wave. NASA Science
3. Georgi, H. (1993). The Physics of Waves, section 11.5, especially pp. 287-291. Prentice Hall; text hosted by MIT OpenCourseWare. Water-wave motion and dispersion. Textbook PDF
4. Kumar, N., Cahl, D. L., Crosby, S. C., and Voulgaris, G. (2017). Bulk versus spectral wave parameters: Implications on Stokes drift estimates, regional wave modeling, and HF radars applications. Journal of Physical Oceanography, 47, 1413-1431. Introduction, p. 1413, explains wave-induced mass transport. NOAA repository and full paper
5. Urone, P. P., and Hinrichs, R. (2022). Color and color vision. College Physics 2e, section 26.3. OpenStax. Colour mixtures and perception
6. Ling, S. J., Sanny, J., and Moebs, W. (2016). Huygens's principle, Figure 1.25. University Physics, Volume 3, section 1.6. OpenStax. Transverse light waves

A watch still running, but no longer heard

Robert Boyle suspended an open watch by a thread inside a glass vessel. In Experiment 27 of a book first published in 1660, he reported that its sound faded as air was pumped out. Observers could still see the watch's hand and balance moving when they could no longer hear it. When he let air back in, they heard the watch again.

The return of the sound matters. A watch that had stopped would also become silent. Seeing its moving parts and restoring the sound by admitting air helped Boyle test that explanation. His later bell trial in the same account gave little or no change in loudness. It was not the simple fading-bell demonstration often attributed to him.

Modern classroom demonstrations often use an electric bell inside a glass jar. Its sound grows much quieter as a pump removes air. These pumps leave some air behind, and supports can still carry vibration. Less sound also passes between the thin air and the jar. The demonstration supports the need for a material path; it does not create a perfect vacuum. Light still passes through the jar.

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 compresses the air just in front of it. The particles become more crowded in a region called a compression; the particles themselves do not shrink. When the cone pulls back, it leaves a less crowded 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's back-and-forth motion is along the direction the wave travels. A rope can instead move sideways to the wave's direction. In air, imagine a small region moving back and forth as the sound passes. Its molecules also have their own random thermal motion. The travelling pattern of pressure is not a stream of air carried all the way from the speaker to you.

Sound in liquids is also longitudinal. Solids can carry both longitudinal and transverse vibrations, depending on how they are disturbed. In this lesson, the compressions and rarefactions describe the longitudinal kind. A vibrating guitar string may move sideways while producing longitudinal sound in the air around it.

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.

Two properties work together. Stiffness describes how strongly a material pushes back when deformed. Density is mass per unit volume. Greater stiffness tends to raise wave speed; more mass to move tends to lower it, if stiffness is unchanged. The result depends on both. Particle spacing alone cannot tell you the speed.

The table gives examples, not a rule that every solid beats every liquid or gas. Different solids, different wave types and different temperatures give different speeds. In air, sound travels faster when the temperature rises. The quoted steel value describes a longitudinal wave through the bulk material; a thin rod or a sideways vibration can give a different value.

Why this matters: Choose the speed for the material, wave type and conditions. Sound needs matter, but it does not require air specifically. Water and solid objects can also carry it. An ideal vacuum has no material path for a sound wave.

Pitch and loudness describe different experiences

A guitar string's frequency depends on its vibrating length, tension and mass per unit length. Shortening the same string while keeping its tension about the same raises its pitch. Tightening it also raises pitch. At the same length and tension, a string with more mass per unit length gives a lower note. Change one property at a time to make a fair comparison.

Amplitude describes the size of an oscillation. For sound in air, pressure amplitude is the size of the pressure change above or below its average. Intensity is the sound energy passing through a unit area each second. A greater pressure amplitude gives greater intensity in the same medium. At the same frequency, that usually sounds louder to the same listener. Loudness is a perception, not another name for amplitude: equal intensities at different frequencies need not sound equally loud.

Plucking the same string a little harder usually makes it louder with little change in pitch. This is an approximate comparison for small vibrations, not a promise about every possible pluck. Listen for the difference between a higher note and a stronger version of the same note.

The usual textbook range for young people with healthy hearing is roughly 20 Hz to 20,000 Hz. Actual limits vary, and sensitivity to high frequencies often declines with age. The range is not a test that every learner must pass. You can study frequency using a diagram even if a sound is outside your own hearing range.

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.

Here the speed is a supplied rounded value and the cliff and listener stay in place. The two seconds include both legs of the journey. If you divided the time first, you would get the same answer: 2 ÷ 2 = 1 second each way, then 340 × 1 = 340 metres. An answer of 680 metres counts the return journey as extra distance to the cliff.

Ships can send a pulse towards the sea floor and time its return. This is active sonar. Passive sonar instead listens for sound already present. For a straight-down pulse, the calculated distance is from the instrument to the reflecting bottom. Use the speed in water, not the speed in air. Some medical ultrasound images also use echoes, at frequencies above human hearing, to locate boundaries inside the body.

Experiment: change pitch and loudness independently

Use a flexible plastic ruler without cracks or sharp edges. Make small movements, keep your face clear of its free end, and stop if it starts to slip or bend sharply. You can also compare the predictions on paper if handling or hearing the ruler is difficult.

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. Move the tip aside by a similarly small distance and release it. Listen for a pitch change.
4. Keep the overhang at 10 cm. Release it from a small deflection, then a slightly larger one. Keep your listening position the same.
5. Repeat the pair of trials. Record which note seems higher and which seems louder. If you cannot hear a note at one length, record that instead of inventing a result.

What to expect: The shorter overhang vibrates faster. At a fixed length, a slightly larger starting deflection usually produces a louder sound with roughly the same pitch. Some long rulers vibrate too slowly to give a clear audible note.

Why it happens: Shortening the overhang changes the ruler's vibration frequency. Changing its starting deflection mainly changes amplitude in these small-motion trials. The ruler, your hand and the table all affect the result. A changed grip can add a rattle or change how the ruler vibrates. This comparison illustrates pitch and loudness; it does not measure frequency, pressure amplitude or sound speed.

Experiment: hear a spoon become a church bell

Use a small metal spoon and soft string. Tap gently and stop if the sound is uncomfortable. Keep the string loose around your fingers, keep the spoon below your face, and do not put anything into your ear canals.

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 gently tap it against a table leg. Listen with your hands away from your ears.
3. Loop each end loosely around an index finger. Place your hands over the openings of your ears, keeping your fingers outside them.
4. Let the spoon hang freely and make another gentle tap. Compare what you hear.
5. Move your hands away and repeat. Try to keep the tap strength similar.

What to expect: The spoon often sounds fuller and more bell-like when your hands cover your ears.

Why it happens: The string and your hands provide a direct route for vibrations into your head and towards the inner ear. More of the vibration can reach you by this route than through the surrounding air. Energy is still lost. This is a comparison of what reaches your ears, not a measurement of how fast sound travels. A louder result alone cannot establish a faster speed.

Common misconceptions

"Sound can cross an empty gap if it is loud enough." A pressure wave needs matter throughout its path. Increasing its amplitude cannot give an ideal vacuum that missing material. Sound can travel inside a spacecraft's air and structure, so the claim is about the vacuum gap, not every place in space.

"Closer particles always mean faster sound." Speed depends on stiffness and density together. Steel, water and air follow the order in the table, but that is not a universal ranking of all solids, liquids and gases.

"Turning the volume up makes sound reach you sooner." For ordinary sounds travelling along the same path through the same air, speed is nearly unchanged. A quiet sound may be harder to detect, but detection and travel time are different questions.

"A pressure graph shows air moving up and down." Its vertical axis shows pressure, not the path of an air particle. In a sound wave travelling horizontally, the air's organised motion is back and forth horizontally. A graph can look like a rope wave while representing a different kind of motion.

The takeaway

• Sound in air is a longitudinal wave of compressions and rarefactions, produced by vibration.
• It needs a medium, so a sound wave cannot cross an ideal vacuum.
• Speed depends on the material and conditions. Stiffness and density both matter.
• Pitch is closely linked to frequency. Loudness depends on the sound reaching the listener and on hearing.
• Roughly 20 Hz to 20,000 Hz is a textbook hearing range, not a guarantee for each person.
• An echo can measure distance, but the sound travelled there and back, so halve the total.

Try from memory: A speaker keeps the same frequency but produces larger pressure changes at your ear. Which usually changes: pitch, loudness or travel speed? Explain before checking. The expected change is greater loudness; the frequency and ordinary sound speed stay about the same. Return tomorrow and explain why an echo calculation needs half the measured time.

Sources

1. Boyle, R. (1682). New experiments physico-mechanical, touching the spring of the air, and its effects (3rd ed., Experiment XXVII, pp. 103-108; first published 1660). M. Flesher for R. Davis. EEBO-TCP transcription A29007. Primary text
2. University of Maryland, Department of Physics. (n.d.). H1-01: Bell in vacuum. Lecture Demonstration Facility. Description and Background. Modern demonstration and limits
3. Urone, P. P., and Hinrichs, R. (2020). Speed of sound, frequency, and wavelength; Sound intensity and sound level. Physics, sections 14.1 and 14.2. OpenStax. Sound waves; Amplitude and intensity
4. Moebs, W., Ling, S. J., and Sanny, J. (2016). Speed of sound. University Physics Volume 1, section 17.2 and Table 17.1. OpenStax. Materials and wave types
5. Urone, P. P., and Hinrichs, R. (2022). Hearing; Ultrasound. College Physics 2e, sections 17.6 and 17.7. OpenStax. Pitch and loudness; Echo imaging
6. University of New South Wales, Music Acoustics. (n.d.). How does a guitar work? Sections on sound and strings. String vibration
7. Exploratorium. (n.d.). Secret bells. Science Explorer. Spoon and string activity
8. National Oceanic and Atmospheric Administration. (2026). What is sonar? National Ocean Service. Active and passive sonar

The straw that snaps in half

A straight straw leaning in a clear cup of water can look bent or displaced near the waterline. Move your head and the apparent bend changes. Take the straw out and check its shape: the straw itself has not snapped.

The light reaching your eye has changed direction. To explain the view, you need to follow its route through the water, the cup and the air. We will start with a simpler route through a flat water surface, then use the same idea to interpret the straw.

Key idea: Rays help us trace light through everyday objects. At a boundary, some light can reflect and some can pass through. The direction of the transmitted light depends on the materials and the angle at which it arrives.

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. The previous lesson's watch experiment showed that removing air weakened the sound reaching observers while they could still see the moving watch.

The wave consists of changing electric and magnetic fields. In a freely travelling light wave, these fields point across the direction of travel. That is what makes it transverse: no material rope or row of air particles is needed to carry the disturbance.

In a vacuum, light travels at about 300,000 kilometres per second. Visible light belongs to a much larger family, the electromagnetic spectrum. Radio waves, microwaves, infrared, ultraviolet, X-rays and gamma rays are other parts of that family. They all travel at the same speed in a vacuum. Their wavelength and frequency identify their place in the spectrum, but waves can differ in other ways too, such as amplitude.

For light of a single visible wavelength, longer wavelengths are associated with red and shorter ones with violet. Orange, yellow, green and blue lie between. Colour is not simply a wavelength label for everything we see. Our eyes also respond to mixtures: white light contains a combination of wavelengths, and different mixtures can look like the same colour.

When straight rays work

In a uniform transparent material, a straight line is a useful model of light's path. Uniform means that the optical properties do not change from place to place. We draw a ray along the path, with an arrow showing the direction of travel. This model works well for mirrors, cups and other objects much larger than light's wavelength.

It has limits. Waves spread around edges, an effect called diffraction. This becomes especially noticeable with very small openings. Light can also follow a curved path where the optical properties change gradually, as in layers of air at different temperatures. So a boundary is not the only place where light's direction can change.

An opaque object blocks direct rays from a source and creates a shadow behind it. A shadow need not be totally black: light from other directions can still reach it. For a ray sketch, choose a small source, draw lines past the object's edges, and shade the region where that source is blocked.

Follow the arrows all the way to the eye. You can see a lamp by light arriving directly from it. You see a book when light from a source reflects from the book into your eye. Vision does not work by sending sight rays out from your eyes. Without visible light entering them, waiting in a dark room will not reveal the book.

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. A ray at 30 degrees to the surface is at 60 degrees to the normal, because those two angles add to 90 degrees. Angles measured from the surface also match each other in reflection, but they are not the angles named in the law.

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 ray segments on the front side of the mirror enclose 25 + 25 = 50 degrees. This angle between the drawn segments is different from the change in the light's travel direction.

Try a different starting point. A ray arrives at 35 degrees to the mirror surface. First subtract from a right angle: 90 - 35 = 55 degrees to the normal. Its reflection angle is therefore 55 degrees, not 35 degrees. To check your sketch, the reflected segment should make 35 degrees with the surface on the other side of the normal.

Two kinds of reflection matter in ordinary life.

• Specular reflection occurs at a surface smooth on the scale of the wavelength. A flat mirror sends parallel incoming rays out parallel and can form a clear image. A smooth curved mirror also gives specular reflection, but its changing surface direction can make the rays converge or spread out.
• Diffuse reflection spreads reflected light over many directions. In a simple rough-surface model, small patches face different ways, each with its own normal. An illuminated wall can send light towards many viewing positions, without forming a clear mirror image of nearby objects.

The point: For a rough surface, draw the normal to the small patch the ray hits. Using one normal for the whole wall would miss why its reflected light spreads out.

Refraction: the bend at the boundary

Light travels at different speeds in air, water and ordinary glass. In water, visible light travels at about three quarters of its vacuum speed; in common glass it travels more slowly still. The bending associated with a change in speed is called refraction.

In a flat diagram, think of a wavefront as a line joining points along the same wave crest. A ray points at right angles to that line. When the wavefront meets water at a slant, one part reaches the water first. Waves there travel a shorter distance in the same time than waves still in air. The new wavefront tilts, and the ray direction changes with it. This describes a wave pattern, not a solid beam with wheels that grip the water.

If a ray arrives along the normal at a flat air-water boundary, the transmitted ray continues along that same line. Its speed changes but its direction does not. The angle of incidence is zero degrees. We call this normal incidence.

Oblique incidence means arriving at a slant, rather than along the normal. Use these rules for the transmitted ray:

• For oblique incidence, going into a slower material, such as air into water, the transmitted ray bends towards the normal.
• For oblique incidence from water into air, a ray that crosses the boundary bends away from the normal.

The second rule says "a ray that crosses" for a reason. At a sufficiently large angle inside water, light can reflect back into the water without a transmitted ray entering the air. This is total internal reflection. It does not occur when light goes from air into water.

The frequency stays the same as light crosses a stationary boundary. Since wave speed equals frequency times wavelength, slowing down means the wavelength becomes shorter in the water. A speed change does not by itself turn red light into blue light.

Worked prediction. A ray meets water from air at 40 degrees to the normal. Will its angle in water be less than, equal to, or greater than 40 degrees? It slows down, so it bends towards the normal: choose less than 40 degrees. The rule gives a direction, not an exact numerical angle. For that, we would need the speed ratio and Snell's law. Now change the incoming angle to zero. The answer becomes zero degrees even though the light still slows down.

For a submerged point seen through a flat water surface, extend the outgoing rays backwards in straight lines on your sketch. They seem to come from a shallower position than the actual point. This explains why a pool bottom can appear raised. It is an image effect, not a change in the pool's depth.

The straw involves the same change of direction. Looking through a cup's side also involves the water-cup and cup-air boundaries. Curved cup walls add distortion, so the exact view depends on the cup, straw and eye positions. A single air-water sketch explains the basic idea without predicting every detail of that view.

Splitting white light

In ordinary glass, visible wavelengths travel at slightly different speeds. A triangular prism can therefore send them out in different directions, with violet deviated more than red. This spreading of white light into a spectrum is an example of dispersion. The spectrum is continuous, even though we give names to several colour bands.

In his 1672 letter to the Royal Society, Isaac Newton described experiments begun in 1666. He used a first prism to spread sunlight, then holes in boards to select different parts of the spectrum for a second prism. Those selected rays bent by different amounts. In a separate recombination setup described near the letter's end, a lens brought the separated colours together on white paper, producing white light again.

These tests answered different questions. The second prism tested differences in how the separated light refracted. Recombination showed that the separated colours could together produce white. The evidence supported Newton's account of sunlight as a mixture, rather than colour being created by the prism.

A primary rainbow also involves dispersion, but a raindrop does more than a prism. Light refracts as it enters, reflects once inside the drop, then refracts again as it leaves. Many drops send different colours towards your eyes. For an ordinary sunlight rainbow, look away from the Sun towards illuminated droplets. They can be in rain, a waterfall or a sprinkler.

Experiment: bend the light and move a coin

Use a stable opaque cup, a coin, a small jug of room-temperature water and a tray for spills. Keep water away from electrical equipment. Ask an adult to help pour while you keep your viewing position fixed.

1. Put a coin flat in the bottom of the cup, near the far edge from you.
2. Lower your head slowly until the rim of the cup just hides the coin. Do not move from that spot.
3. Have someone gently pour water into the cup without moving it or splashing the coin.
4. Keep your eye exactly where it was and watch.
5. Stop pouring before the cup overflows. Record whether the coin reappears and whether anything in the setup moved.
6. As a separate observation, lean a straw in a clear plastic cup of water. Compare views from several positions, then take it out to check its actual shape.

What to look for: The coin may become visible while remaining on the bottom. Light from it can leave the water along a path that reaches your eye over the rim. If it stays hidden, record that first. Then try a position where the dry coin is only just hidden, and repeat with your helper.

Explain the observation: Draw the water surface, a normal and a ray from the coin to that surface. Bend the outgoing ray away from the normal towards the eye. Extend its air segment backwards to show the apparent raised position. Moving your head or the cup can also reveal the coin, which is why keeping both still matters.

A view from above is not a test in which every ray crosses at zero degrees. Light reaches your pupil from many points on the straw, with different paths. Use a single ray drawn along a normal to reason about normal incidence; do not infer it just from where your head is.

Experiment: test the law of reflection

Ask an adult to help secure a small, unbroken mirror upright in a stable holder on a table. Use a battery LED torch, not a laser or sunlight. Keep direct and reflected beams out of eyes. Leave enough room light to move and read safely.

1. Set the supported mirror on a sheet of paper, perpendicular to 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. Shine the torch across the paper towards the point where the normal meets the mirror. Two cards held with a narrow gap in front of the torch can help make a narrow strip of light on the paper. Do not cover the torch or block its ventilation.
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.

Record the result: Make columns for incoming angle, reflected angle and their difference. The model predicts equal angles. Your readings may differ because of beam width, dot placement, the protractor scale, or mirror alignment. A household torch may not make a trace sharp enough to measure. If it does not, use the paper practice below instead of inventing readings.

For example, suppose a practice table contains 30 degrees incoming and 33 degrees reflected. The difference is 3 degrees. That number alone does not tell you which part of the setup caused it. Check the normal and mirror alignment, mark the centres of the strips consistently, and repeat. Keep both sets of readings. Do not adjust them to fit the prediction.

Paper alternative: Draw a mirror line and a normal. Add incoming ray segments at 20, 40 and 60 degrees to the normal. Predict the reflected paths before using a protractor to draw them. Each outgoing segment belongs on the opposite side of the normal, at the same angle. This is practice applying the law, not experimental evidence that the law is correct.

Common misconceptions

"We see by sending rays out of our eyes." Vision depends on visible light arriving at the eye, directly from a source or after reflection or transmission. Staring harder does not supply the missing light.

"A flat mirror swaps the two sides of the room." A mark on the left side of the mirror still appears on that side. The mirror reverses the direction perpendicular to its surface, often described as front and back. Thinking of the image as another person turned to face you creates the familiar left-right comparison.

"Entering water always makes a ray bend." At normal incidence, its speed changes without a change of direction. Check the angle before predicting a bend.

"The prism adds colour to white light." A prism separates wavelengths already in the incoming light. Newton's tests of separated colours and his lens recombination experiment supported this explanation.

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 band of the electromagnetic spectrum. Single wavelengths and mixtures both contribute to perceived colour.
• Straight rays work well in uniform materials for objects large compared with the wavelength. They help explain shadows and images.
• In reflection, the angle of incidence equals the angle of reflection, both measured from the normal.
• A flat smooth mirror preserves orderly ray directions; a rough wall spreads reflected light over many directions.
• For an oblique transmitted ray at an air-water boundary, slowing bends it towards the normal and speeding up bends it away. Normal incidence causes no directional bend.
• White light is a mixture, and a prism separates it because each colour bends by a slightly different amount.

Before leaving, sketch one reflected ray and one ray entering water straight on. Label each normal and explain why the second ray can change speed without turning. Tomorrow, try the same sketches without looking back, using a different mirror angle, then check your reasoning here.

Sources

1. NASA, Science Mission Directorate. (2010). Anatomy of an electromagnetic wave. NASA Science. Fields, vacuum travel and wave properties. NASA
2. Ling, S. J., Sanny, J., and Moebs, W. (2016). University Physics, Volume 3, sections 1.1, 1.2 and 1.3. OpenStax. Ray model, speed, reflection and refraction. Propagation; Reflection; Refraction
3. Ling, S. J., Sanny, J., and Moebs, W. (2016). University Physics, Volume 3, sections 1.5, 1.6 and 2.1. OpenStax. Dispersion, wavefronts, diffraction and mirror images. Dispersion; Wavefronts; Mirror images
4. Urone, P. P., and Hinrichs, R. (2020). Refraction. Physics, section 16.2. OpenStax. Apparent displacement and total internal reflection. OpenStax
5. Urone, P. P., and Hinrichs, R. (2022). Color and color vision. College Physics 2e, section 26.3. OpenStax. Single wavelengths and mixtures. OpenStax
6. Newton, I. (1672). A letter containing his new theory about light and colors. Philosophical Transactions, no. 80, pp. 3075-3087. The Newton Project, University of Oxford, normalized transcription. Selected-colour tests at pp. 3078-3079 and lens recombination at pp. 3085-3086. Newton's letter

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.

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.

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.

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