A real system has too many details to handle at once. A model keeps the few quantities that decide the answer to one question and leaves out the rest, on purpose.
Take a cricket ball after it leaves the bat. Gravity pulls it down. Air pushes against it. Wind moves it sideways. Its spin changes how the air flows around it. Its seam and scuff marks change that flow again.
A description that included every one of these would be very hard to calculate with. Most of them also change the answer by only a small amount. So science does not start with every detail.
A model is a simplified description of a real system. It keeps the quantities that decide the answer to a particular question. It leaves out the quantities that do not.
Because the model depends on the question, one object can have several models. The figure shows one car described in two ways.
One car, two models. Neither picture is the car. For travel time, only position and speed matter, so the car becomes a point. For parking, only length and width matter, so it becomes a box.
You have already used many models. An atom drawn as a small sphere is a model; a real atom has no hard surface. The Earth treated as a perfect sphere is a model; the real Earth is about 43 km wider at the equator than from pole to pole. A model is judged by one test: does it give a correct enough answer to the question it was built for?
A batsman hits the ball high. The question is: will it cross the boundary? For a first model, which of these would you keep — the speed it left the bat, the angle it rose at, the colour of the ball, the brand of the bat, the strength of gravity?
Keep: the launch speed, the launch angle and the strength of gravity. Change any one of them and the landing point changes.
Leave out: the colour and the brand. Neither one changes any force on the ball, so neither one changes where it lands.
You have just built a model. It has three quantities. It is enough to estimate where the ball comes down.
The first model of the shot. Three quantities decide the path when air is ignored. Colour and brand exert no force on the ball, so they are left out.
Many students expect a heavier ball to fly a shorter distance. In the first model, it does not. When gravity is the only force, every object falls with the same acceleration, about 9.8 m/s², whatever its mass. So mass drops out of the calculation.
Mass returns when air resistance is added to the model. Air pushes back on the ball with a force that depends on its speed and size. For two balls of the same size, that force slows the lighter ball more, because the same force gives a smaller mass a larger change in speed. The question decides which version of the model you need.
🏏 Test the model › In Will it be a Six?, keep air resistance off and change the ball’s mass. The landing point stays the same. Turn air resistance on and change the mass again.When a scientist ignores air resistance for a falling stone, it is a deliberate choice. It keeps the calculation simple. The cost is a small error in the answer.
The rule for that choice is one question: does leaving this out change the answer by more than I can accept? If the change is small, the detail is left out. If the change is large, it is kept.
In 1920 the Indian physicist Meghnad Saha studied the spectra of stars. A spectrum is the pattern of light a star gives off, split by wavelength. Different stars show different dark lines in their spectra.
Saha modelled the outer layer of a star as a hot gas. He kept only temperature, pressure, and the energy needed to remove an electron from each kind of atom. From these he calculated what fraction of each element is ionised, that is, has lost an electron. His result showed that the line patterns depend mainly on the star’s temperature. Stars that look different in a spectrum need not be made of different elements.
You want to estimate how long your bicycle ride home takes. Which quantities would you keep, and which would you leave out?
Keep: the distance, and your usual average speed. If there is one steep hill or one long traffic signal, keep that too, because each one adds minutes.
Leave out: the colour of the bicycle and what you ate for lunch. They do not change the time.
Time = distance ÷ average speed gives an answer in a few seconds. It will be off by a minute or two. For deciding when to leave, that error is acceptable.
A model that leaves something out stays accurate only while that thing has a small effect. Ignore air resistance for a stone dropped from 2 m and the predicted fall time is correct to about 1%. Ignore it for a feather and the prediction is wrong by a factor of ten or more.
Every model has a boundary. The same assumption — “ignore the air” — is wise on the left and useless on the right. Knowing where your model stops working is part of using it.
When a model stops giving accurate answers, the details that were left out are added back, one at a time. Air resistance is added first for the feather. A model gets more detailed only when a question needs more accuracy.
Answer all of them, then press Check answers.
1A ball is hit high. For a first model of “will it cross the boundary?” with air ignored, sort each detail into Keep or Leave out.
2What is a scientific model?
3With air resistance ignored, a 0.16 kg ball and a 0.32 kg ball are launched with the same speed and angle. Which lands farther?
4A scientist ignores air resistance for a falling stone. The best reason is…
5A simplified description of a real system that keeps only what matters for a given question is called a ____.
6Meghnad Saha explained the different line patterns in star spectra by…
7Which of these are models?
More than one answer is correct.
8Ignoring air resistance gives a good answer for a stone but a poor one for a feather. This shows that…
Next: how science gives ordinary words exact meanings.
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