Unit 2, lesson 10. About 15 minutes.

Air resistance and terminal velocity

Why does a leaf drift down gently while a stone drops fast?

Play

Getting the experiment ready…

Explain

Air pushes on things that fall.

Big wide things fall slowly.

Air pushes against anything that moves through it. This is called air resistance.

The faster you go, the harder the air pushes. Soon it pushes up as hard as gravity pulls down.

Then you stop speeding up and fall at a steady top speed. This is terminal velocity. Press the parachute button and see what happens.

Air resistance grows with the square of speed, so we write it as k × v². The drag number k depends on the size and shape of the object.

At terminal velocity, drag equals weight, so the net force is zero. By the first law, the velocity then stays constant.

Worked example: an 80 kg skydiver has k = 0.25. So v = √(80 × 9.8 / 0.25) ≈ 56 m/s.

Gravity pulls down
Speed grows, air pushes back
Forces balance at top speed

Want the full story?

The k value also depends on air density, which changes with height, so real terminal velocity falls as a skydiver descends. The sim keeps k fixed. It runs four times faster than real life, so that you don't wait minutes. The drag numbers are typical values, not exact ones.

The Formula

top falling speed = square root of (weight ÷ drag number)

v_t = \sqrt{\frac{m \times g}{k}}

$v_t$: the terminal velocity, measured in metres per second (m/s)
$m$: the mass falling, measured in kilograms (kg)
$g$: the strength of gravity, 9.8 on Earth, measured in newtons per kilogram (N/kg)
$k$: the drag number, bigger for a wider shape, measured in kilograms per metre (kg/m)

Try the numbers

Mass: 80 kgDrag number: 0.25 kg/m

Terminal velocity: 56.03 m/s

Try it at home

You need two sheets of paper.

You need: two sheets of paper.

Drop paper flat. Now scrunch it up and drop it.

Hold two sheets of paper at the same height.
Scrunch one into a ball.
Drop them together.

What's happening: both have the same weight, but the flat sheet meets much more air resistance.

Physics is life

Your body

You feel air push when you run.

Cyclists crouch low to reduce air resistance, and it lets them go much faster.

Daily life

Cars have smooth shapes.

Smooth shapes let cars use less fuel, because they push less air out of the way.

Nature

Seeds float on the wind.

Dandelion seeds use air resistance to float far from the parent plant.

Space

Parachutes slow space capsules.

Spacecraft use the air of Earth or Mars to slow down, then parachutes to land.

Quick check

Question 1 of 3

When does air resistance get bigger?

Words to know

Air resistance: The force from air pushing against something moving through it.

Air resistance: The force from air pushing against something moving through it.
Terminal velocity: The steady top speed of a falling object, when air resistance balances weight.
Friction: A force between surfaces that rub together. It resists sliding.

Next up

Balanced and unbalanced forces