Does the air matter?

The idea

Building a model means making assumptions and deliberately ignoring details that matter little for the question; these choices are not mistakes, and more complex models add extra details for greater accuracy.

A 20 m drop

A stone, a tennis ball and a feather are dropped from a 20 m tower. First imagine there is no air at all.

Which one hits the ground first?

• The stone
• The feather
• All three together

Two models, one drop

Model A ignores air. Model B adds air. Drop each object and compare when they land.

An assumption is a choice

Building a model means making assumptions and deliberately ignoring details that matter little for the question. These choices are not mistakes. A more complex model adds extra details for greater accuracy.

The same assumption can be good for one object and poor for another. So we choose it for the question we are asking. (The times use top speeds in air of about 65 m/s, 20 m/s and 1 m/s.)

• Object | A: no air | B: with air | Ignoring air
• Stone | 2.02 s | 2.04 s | fine (under 1% off)
• Tennis ball | 2.02 s | 2.19 s | rough (8% off)
• Feather | 2.02 s | 20 s | poor (10 times off)

Notes

Building a model means making assumptions and ignoring details that matter little. These choices are not mistakes. More complex models add details for greater accuracy.

Check yourself

Scientists often ignore air resistance when studying a falling object. Why?

For a cricket ball hit for a six, which detail is very important for deciding if it clears the boundary?

Later we add air resistance and spin to the cricket model. What do we gain?

For a tennis ball, the no-air model gives 2.02 s and the air model 2.19 s. What is the best conclusion?

• To see the basic effect of gravity in a simple model — correct. Yes. Start simple, then add details if needed.
• Because there is no air on Earth. Air is there. It is left out on purpose, when it matters little.
• Because they forgot about it. It is a deliberate choice, not a mistake.
• The colour of the ball. It makes no difference to where the ball lands.
• The amount of grass on the field. It makes no difference to the flight.
• The speed and direction of the hit — correct. Yes. They decide how far the ball goes.
• Greater accuracy — correct. Yes. More complex models add details for greater accuracy.
• The first model becomes a mistake. No. It was fine for a simple answer.
• A model with no assumptions. Every model makes assumptions. Only the details change.
• The no-air model is useless. It is only about 8% off. It is fine for a rough answer.
• No air is fine for a rough answer. Add air for more accuracy — correct. Yes. The question decides how much detail you need.
• Air never matters for a ball. It matters a little here, and a lot for a feather.