52 experiments found
Clear filtersEvery atom is made of protons and neutrons in a tiny nucleus with electrons around it; the number of protons decides which element it is
Add protons, neutrons and electrons one by one and see the atom you make: its name, its mass and how its electrons sit in shells. Then turn carbon into nitrogen with a single proton.
NaHCO₃ + CH₃COOH → CH₃COONa + H₂O + CO₂: one mole (84 g) of baking soda gives one mole (44 g, about 24 L) of carbon dioxide and needs one mole (60 g) of acetic acid
Drop 2 to 20 g of baking soda into vinegar and blow up a balloon with the carbon dioxide. Use the equation and moles to find the mass and volume of the gas and how much vinegar the soda needs.
Solubility is the most of a substance that dissolves in 100 g of water at a given temperature; sugar's solubility rises steeply with temperature, but salt's hardly changes
Stir sugar or salt into water at different temperatures until no more dissolves. See how hot water dissolves far more sugar, while salt hardly changes, and why syrup for sweets is made hot.
Food spoils when microbes grow in it; microbes need water, warmth and time, so food keeps longer when we take the water out, keep it cold, heat it to kill the germs, or pickle it in acid or oil
Look at twelve kitchen foods, from sun-dried fish to mango achar, find out how long each keeps and what stops the microbes, and sort them by the way they are preserved: drying, cold, heat or pickling.
Dissolving salt makes water denser; an object floats when the liquid is denser than the object, so an egg floats once the salty water is denser than the egg
Drop an egg into a glass of water and stir in salt, a spoonful at a time, until the egg floats. Then try an old egg, which floats in plain water, and find out why cooks use this to test eggs.
Water boils when its vapour pushes as hard as the air above it; higher up the air pressure is lower, so water boils at a lower temperature (about 1 °C lower for every 300 m) and food cooks more slowly
Boil a pot of water at the seaside, in Kathmandu, Shimla, Leh and at Everest base camp. See how the boiling point falls as you climb, and why dal takes so much longer to cook up high.
A battery's capacity in mAh is the charge it holds: hours to charge = capacity ÷ charger current (plus about 20% losses), and energy in Wh = capacity (Ah) × voltage
Pick a phone battery of 3000, 4000 or 5000 mAh and a 1 A, 2 A or 3 A charger. Work out how long it takes to charge from empty, how much energy it stores and how many hours the screen can stay on.
An LED takes a fixed forward voltage (about 2 V for red, 3.2 V for blue and white); a resistor in series takes the rest, so by Ohm's law R = (supply − LED voltage) ÷ current
Light a red, green, blue or white LED from a 5 V, 9 V or 12 V supply. Work out the resistor that lets just the right current flow, and how much power the resistor turns into heat.
Electricity and fuel cost money and resources, and making them often pollutes the air; small habits, such as switching off, using LED bulbs and covering pots, save energy, while leaving things on or open wastes it
Look at twelve everyday habits, from switching off lights and cooking with a lid to leaving the TV on standby. Find out why each one saves or wastes energy, and sort them.
Energy = power × time: a 0.4 kW panel in 5 hours of sun gives about 0.4 × 5 × 0.8 = 1.6 kWh, after the losses of heat, dust and wiring
Put 2 to 10 solar panels on a roof and choose how many sunny hours a day it gets. See how many kilowatt-hours they make a day and a month, how many LED bulbs that lights for an evening, and how much CO₂ it saves against coal power.
Each fuel gives a fixed heat per gram, its calorific value, but a stove passes only part of it to the pot; grams burnt = heat needed ÷ (calorific value × efficiency), so a good fuel in a good stove burns far less
Boil 1, 2 or 5 litres of water on an LPG stove, a kerosene stove, a coal stove, an open wood fire or a dung-cake chulo. See the heat the water needs and how many grams of each fuel burn to give it.
On a spinner with equal sectors, P(colour) = sectors of that colour ÷ all sectors; the probabilities add up to 1, and the expected number of times = probability × number of spins
Colour the equal sectors of a spinner red, blue and green, and work out the chance of landing on each colour and how many reds to expect in 60 spins. Then make the game fair.
Batting average = runs ÷ times out (runs per dismissal); strike rate = runs ÷ balls faced × 100 (runs per 100 balls)
Change a batter's runs, balls faced and times out, and work out the batting average and the strike rate. Find out why one tells you how reliable a batter is and the other how fast they score.
Amounts in a recipe are in direct proportion to the number of people: each amount × (new number of people ÷ 4), so doubling the people doubles everything
A dal-bhat recipe feeds 4 people. Cook it for 2, 6, 8 or 10 people instead, and see how the rice, dal, water and salt all change by the same ratio.
In the Fibonacci sequence each number is the sum of the two before it (Fₙ₊₁ = Fₙ + Fₙ₋₁); the ratio of neighbours Fₙ₊₁ ÷ Fₙ gets closer and closer to the golden ratio φ = (1 + √5) ÷ 2 ≈ 1.618
Build the Fibonacci numbers 1, 1, 2, 3, 5, 8, … as a spiral of squares, and divide each by the one before. Watch the ratio swing above and below and settle on 1.618, the golden ratio found in sunflowers, pine cones and shells.
In a group of n people each person shakes n − 1 hands, but every handshake is shared by two people, so there are n(n − 1) ÷ 2 handshakes: the number grows much faster than the group
At a party everyone shakes hands with everyone else once. Change the number of people from 2 to 12 and count the handshakes, then find the rule that works for any group.
Each number in Pascal's triangle is the sum of the two above it; the k-th number of row n is C(n, k), the number of ways to choose k things from n, and row n adds up to 2ⁿ
Pick a row n and a place k in Pascal's triangle. Read the number C(n, k), see that it is the sum of the two above it, and find that every row adds up to a power of 2: the ways of choosing, of tossing coins and of walking a grid.
A loan is repaid in equal monthly instalments, EMI = P r (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), with r the monthly rate and n the months; a longer loan has a smaller EMI but much more interest
Borrow Rs 1 lakh to Rs 10 lakh at 8% to 12% a year and choose to pay it back in 1, 3 or 5 years. See the equal monthly instalment (EMI), the total you pay back and how much of it is interest.
A line of symmetry folds a shape into two halves that match exactly; some shapes have one, some have many, and some have none, even if they look balanced when turned
Look at twelve shapes from nature and daily life, from a butterfly and a snowflake to a shoe and a swirl. Find how many lines of symmetry each has, and sort them into one line, more than one, or none.
The minute hand turns 6° a minute and the hour hand 30° an hour plus 0.5° a minute, so the angle between them is |30h − 5.5m|, or 360° minus that if it is bigger than 180°
Set a clock to any time and work out the angle between its hands. Find the times when the hands make a right angle or a straight line, and see why the hour hand is never exactly on the number at half past.
With n people there are n(n − 1)/2 pairs, each with a 1 in 365 chance of sharing a birthday; the pairs grow so fast that the chance of a shared birthday passes 50% at 23 people: P ≈ 1 − e^(−n(n − 1)/730)
Fill a room with 5 to 70 people and find the chance that at least two of them share a birthday. See why a class of 23 already has an even chance, and why the number of pairs, not people, is the secret.
The nth triangular number is 1 + 2 + … + n = n(n + 1) ÷ 2, and a triangle with the one before it makes a square: Tₙ + Tₙ₋₁ = n²
Stack dots in rows of 1, 2, 3, 4 and more to build triangles. Count the dots in each triangle, find the rule n(n + 1) ÷ 2, and see how two neighbouring triangles fit together into a square.
Every measurement has a quantity (length, mass, volume or time) and a unit; we choose a unit that suits the size, so the number is neither huge nor tiny: kilometres for roads, millimetres for an ant
From the distance between two cities to a spoon of cough syrup, decide what each of twelve everyday things measures, length, mass, volume or time, and choose a unit that suits its size.
Body mass index compares mass with height: BMI = mass (kg) ÷ height² (m²); for adults 18.5 to under 25 is a healthy range, but children are still growing, so their BMI is checked on charts for their age and sex
Choose a mass and a height and work out the body mass index, BMI = mass ÷ height². See which adult band it falls in, and learn why doctors use age charts, not these bands, for growing children.
Energy used (kcal) ≈ MET × body mass (kg) × time (hours), where the MET says how many times harder than resting an activity is; harder play, a heavier body and longer play all use more energy
Choose a game or exercise, your body mass and how long you play, and work out how much food energy your body uses, in kilocalories and in rotis.
First aid is the help given before a doctor arrives: it keeps the person safe, stops things getting worse and gets them to proper care; some common habits, like ice on burns or sucking snake venom, harm or waste precious time
Twelve things people do for burns, cuts, nosebleeds, snake and dog bites, diarrhoea and someone who has fainted. Find out why each helps or harms, and sort the good first aid from the old habits that do damage.
Each case of a disease infects R₀ people when no one is immune; when more than 1 − 1/R₀ of people are vaccinated, each case infects fewer than one other and the disease dies out, protecting even those who cannot be vaccinated
Choose a disease, from flu to measles, and how many people in a town are vaccinated. See how many people each case infects now, how many must be vaccinated for herd immunity, and whether the disease dies out or keeps spreading.
Bacteria multiply by splitting in two; in warm food they can double every 20 minutes, so after n doublings one germ becomes 2ⁿ, which grows faster and faster
Start with one germ on a plate of food left out in the warm. Choose how often it doubles and how many hours pass, and watch one germ become thousands, then millions, which is why cooked food should not sit out for long.
The body loses water in sweat, breath and urine, so a child needs about 35 mL of water for every kg of body mass each day, more when playing hard and on hot days
Choose a body mass, the minutes of hard play and whether it is a hot day, and work out how much water a child needs in a day, in millilitres and in glasses.
Inherited traits are set by genes passed from parents to children; acquired traits are learnt or gained during life, from practice, injury or the surroundings, and are not passed on in the genes
Look at twelve traits, from eye colour and dimples to a scar, a suntan and the language you speak. Find where each comes from and whether your children could get it from you, then sort them into inherited and acquired traits.
A lack of one nutrient causes a deficiency disease: vitamin A night blindness, vitamin C scurvy, vitamin D rickets, vitamin B1 beriberi, iron anaemia and iodine goitre; foods rich in that nutrient prevent it
Twelve cards show a sign of poor diet, such as night blindness or a swollen neck, or a food that prevents one, such as carrots or iodised salt. Find out what each tells you, then sort them by the vitamin or mineral they are about.
Red cells may carry A, B and Rh antigens; a patient's blood attacks any A or B it lacks, and an Rh-negative patient reacts to Rh, so O− can give to everyone and AB+ can take from everyone
Check twelve donor and patient pairs, from O− to A+ and AB+ to O−. Find the antigens on the donor's red cells and the antibodies in the patient's blood, and sort each transfusion as safe or not safe.
Magnitude is a logarithmic scale: each step of 1 means 10 times the shaking on a seismograph and about 32 times (10^1.5) the energy
Pick two earthquakes by their magnitude, from a small 3 to a great 8, and see how many times more the ground shakes and how many times more energy the bigger one lets out. Find why the 7.8 Gorkha earthquake of 2015 was so much worse than a 5.
1 mm of rain on 1 m² of roof is 1 litre of water, so a roof collects area × rain × 0.8 litres (some splashes or soaks away): even a small roof can store a lot of water in the monsoon
Choose the size of a roof and the rain in a month, and work out how many litres of rainwater a family could collect in a tank, and for how many days it would give a family of five their water.
Gravity pulls a satellite towards the Earth and keeps it moving in a circle; in an orbit of radius r its speed is v = √(GM ÷ r), so higher satellites move slower and take longer to go round
Put a satellite in a low orbit like the International Space Station, in a GPS orbit, or in a geostationary orbit used for TV. See how far it is from the Earth's centre, how fast gravity makes it go and how long one trip round the Earth takes.
Light travels at about 299 792 km every second, so the time it takes is distance ÷ speed: a fraction of a second from a satellite, 8 minutes from the Sun and more than 4 years from the nearest star
Send light to us from a GPS satellite, the Moon, the Sun, Mars and the nearest star, and work out how long each journey takes. Find out why we see the Sun as it was eight minutes ago.
Light travels in straight lines, so a stick's shadow is its height ÷ tan(the sun's height): the lower the sun, the longer the shadow, and with the sun straight overhead there is no shadow at all
Stand a stick in the sun and move the sun from low in the morning sky to straight overhead. See how long the shadow is each time, and why shadows are long in the morning and evening and shortest at noon.
Trees take carbon dioxide from the air by photosynthesis and store the carbon in their wood: a grown tree takes about 21 kg of CO₂ a year, while a car gives out about 0.17 kg every kilometre
Plant 1, 10 or 100 trees and let them grow for 1 to 20 years. Find how much carbon dioxide they take from the air, and how many kilometres a car could drive to give out the same amount.
A scale model divides every size and distance by the same number: if the Earth were a 22 cm football, the Moon would be a 6 cm ball 6.6 m away and the Sun a 24 m ball 2.6 km away, so space is mostly empty
Shrink the Earth to a football, a cricket ball or a marble, and shrink everything else by the same scale. See how big the Moon and the Sun would be, and how far away they would sit.
Burning petrol and diesel gives carbon dioxide, a greenhouse gas: kg of CO₂ = km travelled × kg per km per person, so walking or cycling gives none, a shared bus gives little, and a car gives the most for each student
Choose how you get to school, how far it is, and for how many days. See how many kilograms of carbon dioxide the trips put into the air, and how many trees it would take a year to soak it up.
The Earth turns 360° in 24 hours, so 15° of longitude is 1 hour: places to the east see the sun first and their clocks are ahead; each country sets its standard time from a longitude near its middle
It is noon in Kathmandu. What time is it in London, Delhi, Tokyo or New York? Pick two cities and see how the turning Earth gives every country its own clock time, and why Nepal is 5 hours 45 minutes ahead of London.
Force = pressure difference × area: a fan that lowers the pressure under a car presses it onto the road
Switch on a fan that sucks the air out from under a sports car, and see how a small pressure difference over the car's floor gives a huge downforce, more grip and faster cornering. Then blow air in to make the car float, and fire thrusters to see when thrust beats weight and the car flies.
A stretched band stores elastic potential energy E = ½kx²; on release it becomes kinetic energy ½mv², so v = √(2E ÷ m), and at 45° the pellet flies about v² ÷ g: twice the stretch gives four times the energy and twice the speed
Stretch a rubber band and fire a paper pellet. Change the band, how far you stretch it and the pellet's mass, and see the energy stored in the band, the launch speed and how far the pellet flies.
A falling object speeds up until air drag equals its weight; then it falls at a steady (terminal) speed v = √(2mg ÷ (ρCA)), so a bigger canopy falls slower
Hang a 20 g, 50 g or 100 g toy under a canopy of 0.1 to 1 m², and find how fast it falls once air drag balances its weight, and how long it takes to drop 10 m.
Gear ratio = front teeth ÷ rear teeth: the back wheel turns that many times for each turn of the pedals, so a big ratio goes far and fast but is hard to push, and a small ratio is easy to push but slow
Change the front and rear gears of a bicycle and see how far one turn of the pedals takes you, and how fast you go at the same pedalling. Find the easy gear for a hill and the fast gear for a flat road.
Radioactive atoms decay at random, but in each half-life half of those left decay: after n half-lives 100% × (½)ⁿ remain, whether the half-life is hours or thousands of years
Watch a crowd of radioactive atoms decay. Choose an isotope used in hospitals or for dating old bones, let half-lives go by, and see what share of the atoms is left and how long that took.
Plants cannot move, so they spread their seeds away from the parent plant by wind, water, animals or bursting pods, and each seed or fruit has a shape that suits its way of travelling
Look closely at twelve seeds and fruits, from the dandelion's parachute to the coconut's husk and the burr's hooks, and sort them by how they travel: by wind, by water, by animals or by bursting pods.
Light arrives almost at once but sound travels only about 343 m a second, so the distance to lightning in km is the seconds from flash to thunder × 0.343
Count the seconds between a lightning flash and its thunder, and work out how far away the lightning struck. Find out why a short gap means you must go indoors at once.
Loudness is measured in decibels (dB): every 10 dB is ten times the sound energy; the level falls about 6 dB each time the distance doubles, and above 85 dB the safe listening time halves for every 3 dB more
Stand near a whisper, a conversation, busy traffic, a pressure horn or a firecracker. See the sound level in decibels, how it drops as you move away, and how long your ears can safely take it each day.
Hot things cool faster the hotter they are than the room: T = room + (start − room) × e^(−kt); a lid and a vacuum flask cut heat loss, giving a much smaller k
Pour tea at 90 °C into an open cup, a covered cup or a vacuum flask in a 25 °C room, and follow its temperature for an hour to see which keeps it hot and why.
Stopping distance = thinking distance (speed × reaction time) + braking distance (v² ÷ 2μg): doubling the speed doubles the first but four-times the second
A child steps onto the road 30 m ahead. Change the vehicle's speed, the driver's reaction time and the road, and find the thinking distance, the braking distance and whether it stops in time.
A scale shows how hard it pushes up on you: N = m(g + a), so you seem heavier when the lift speeds up upward, lighter when it speeds up downward, and weightless in free fall
Stand on a bathroom scale in a lift. See what it reads as the lift starts going up, moves steadily, starts going down, and, if the cable snapped, falls freely.