Forces · System
Air and water resistance
A skydiver falls for a minute and stops getting any faster. Nothing has caught them, and their weight has not changed by a single newton.
Start here
Falling for a minute, and no longer speeding up.
Ten seconds after stepping out of the aircraft a skydiver is falling at about 55 metres per second. Twenty seconds later, still falling, still nothing underneath them: 55 metres per second. It does not go up any further.
Why does the falling stop getting faster?
Air resistance is not a fixed force. The faster you go, the more air you have to shove out of the way every second, so the harder it pushes back — and it keeps growing until it matches the weight exactly. At that point the resultant is 0 N, and with nothing left over nothing changes. The weight was the same 750 N the whole way down.
Air resistance and water resistance are the same idea: moving through a fluid means pushing it out of the way, and it pushes back. Both act against the motion, both grow as you go faster, and both grow when you present a bigger area to the flow. Together with friction they are called drag.
At the bench · the fall
Watch the two arrows close the gap
Change a control to begin
Pick something falling, then set how fast it is going as a share of its own steady speed. The weight arrow never changes. The resistance arrow does.
Commit first. A skydiver has just stepped out and is barely moving. What is the air resistance at that instant?
What is falling
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Weight, down
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Resistance, up
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Resultant
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What happens next
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One jump, four stages
The weight arrow is the same in all four.
Step out
Barely moving, so almost no air is being pushed aside and the resistance is close to 0 N. The whole weight is left over, and the fall speeds up fastest right here.
Speeding up
Faster means more air shoved aside every second, so the resistance grows. Something is still left over downwards, so the speed is still rising — but more slowly each second.
Terminal velocity
The resistance has grown until it matches the weight exactly. Resultant 0 N, nothing changes, and the fall continues at a steady speed of about 55 metres per second.
Parachute opens
A far bigger area facing the flow, so the resistance jumps well above the weight. The resultant now points upwards, which slows the fall — down to a new steady speed of about 6 metres per second.
Water does the same job with far more force behind it, because a cubic metre of water has around eight hundred times the mass of a cubic metre of air. That is why a swimmer at two metres per second feels more resistance than a runner at four, and why boats are shaped the way they are.
Key fact
Air and water resistance act against the motion and grow as the object goes faster. When the resistance has grown to match the weight, the resultant is 0 N and the falling speed stops changing — a steady speed called terminal velocity.
Think again
“Heavier things always fall faster.”
Drop a golf ball and a table-tennis ball together and the golf ball wins, so the belief has good evidence behind it. But look at what is actually different. The two balls are almost the same size, so at any given speed the air pushes back on them by about the same amount — and that push is a small fraction of the golf ball's weight and a large fraction of the table-tennis ball's. The light one runs out of gap between weight and resistance almost immediately and settles to a slow steady speed; the heavy one is still speeding up when it lands. Take the air away and the difference goes with it: on Apollo 15 an astronaut dropped a hammer and a feather on the Moon, and they hit the dust together. Weight is not what decides how fast something falls — the balance between weight and resistance is.
“When the parachute opens, you get pushed back up.”
The resultant force does point upwards for a few seconds — the bench above will show you that — and it is a violent few seconds. But an upward resultant does not mean upward motion. It means the downward motion is changing, which here means slowing: from about 55 metres per second to about 6, in the space of a couple of seconds. The skydiver is going downwards the whole time. As soon as the speed has dropped far enough, the resistance falls back to 750 N, the resultant returns to 0 N, and the rest of the descent is at a new steady speed. Nobody goes up.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Apply
A hailstone with a weight of 1 N is falling at a steady speed. What is the air resistance on it?
Rung 2 · The one that catches people
A lead ball and a plastic ball are the same size. Both are dropped from a tall tower. Which lands first, and why?
Rung 3 · Explain
A racing cyclist crouches low over the handlebars and wears tight clothing instead of a loose jacket. Explain, in terms of forces, why both of these make her faster.
Rung 4 · Take it somewhere new
A car with the accelerator held flat to the floor speeds up, then settles at a top speed and goes no faster, even though the engine is still working just as hard. Explain why a car has a top speed at all.
Key note
Moving through air or water means pushing it out of the way, and it pushes back against the motion. That resistance grows with speed and with the area facing the flow, so a falling object speeds up until the resistance has grown to match its weight — after which the resultant is 0 N and the speed stays the same. Streamlining reduces the resistance; a parachute is designed to maximise it.
Going further
At the speeds a car or a cyclist travels, air resistance does not simply double when the speed doubles — it roughly quadruples, because you are hitting twice as much air per second and hitting each bit of it twice as hard. The bench above uses exactly that rule, which is why the resistance arrow grows so slowly at first and then so fast. It also explains a fact drivers notice and rarely explain: fuel economy falls off a cliff above about 60 miles per hour, and driving at 80 rather than 70 costs far more than the extra tenth of the speed suggests. For a racing cyclist, most of the effort at speed goes into air, not into the road, which is why the shape of a helmet earns more than the weight of a frame.
Water resistance is the same physics in a much heavier fluid, and it sets the shape of everything that swims. Fish, dolphins, submarines and torpedoes converge on the same long, rounded-nose, tapering-tail form, because water separating cleanly from a tapered tail leaves far less of a churned-up wake than water tearing away from a blunt one. Engineers call that shape streamlined, and the test of it is the wake: the less mess left behind, the less energy has been thrown away. It is also why competitive swimmers shave, wear full-body suits and spend a fortune on the moment their fingers enter the water.
Before this lesson
Connects to
At GCSE this becomes
- Drag, terminal velocity as a balance of forces, velocity–time graphs of a falling object, and streamlining.
Where to next
Ask Mr Badmus AI
Want to work out the terminal velocity of something of your own?
The fall bench is a teaching model. Resistance is calculated as growing with the square of the speed, fitted so that each object reaches the steady speed quoted for it, and the speeds and weights are typical values rather than measurements. The slider is a share of that object's own steady speed, so 125 per cent is a state only reached for a few seconds — right after a parachute opens. Real resistance also depends on air density, which falls with altitude, and only the vertical forces are drawn.
Lesson content © MrBadmusAI.