Topic 7 of 7
Falling with air resistance
A falling object can speed up while its acceleration gets smaller. Increasing air resistance reduces the downward resultant force.
Weight is mg, and acceleration comes from resultant force / mass. Take downwards as positive in the examples on this page.
Without significant air resistance
For a body of constant mass in a uniform gravitational field, weight is constant. If air resistance is negligible, weight is the only force, so:
The mass cancels, which explains why objects of different masses have the same free-fall acceleration in this model. Gravity has not disappeared: it is the force causing the acceleration. With no air resistance, this model does not produce a terminal speed.
As a body falls through still air
Consider the same body released from rest, with its shape and orientation unchanged. At release its speed relative to the air is zero, so air resistance is zero. As its downward speed increases, upward air resistance grows, while its weight remains the same.
Same object and same weight throughout. Each snapshot uses the same force scale.
1. Released from rest
Selected body: 0.50 kg falling object
Air resistance: 0 N. Resultant: 5.0 N downwards.
2. A later instant
Selected body: 0.50 kg falling object
Resultant: 3.0 N downwards. The object is still speeding up.
3. Terminal motion
Selected body: 0.50 kg falling object
Equal forces. Zero acceleration; non-zero downward velocity.
Worked example
Follow the resultant, not just the weight
The object has mass 0.50 kg and g = 10 N/kg. Its weight is 5.0 N throughout. Subtract the upward air resistance from the downward weight.
| Air resistance / N | Downward resultant / N | Acceleration / (m/s2) |
|---|---|---|
| 0 | 5.0 - 0 = 5.0 | 5.0 / 0.50 = 10 |
| 2.0 | 5.0 - 2.0 = 3.0 | 3.0 / 0.50 = 6.0 |
| 5.0 | 5.0 - 5.0 = 0 | 0 / 0.50 = 0 |
At the middle stage, acceleration is still downwards, so the downward speed is still increasing. It increases less rapidly than at release because the resultant has fallen from 5.0 N to 3.0 N.
Terminal velocity
When air resistance equals weight, the resultant and acceleration are zero. The object continues downwards at a constant, non-zero velocity called its terminal velocity, while these conditions remain unchanged.
Velocity increases while acceleration decreases
Downwards is positive. This is a schematic graph.
The curve approaches a level above zero. The force snapshots do not supply numerical times or speeds.
Read the two features separately: increasing graph height means increasing downward velocity; decreasing gradient means decreasing acceleration. A horizontal line at a positive velocity represents steady downward motion, not rest.
The supplied force values let us calculate acceleration at the three stages. They do not tell us the times of those stages or the numerical terminal velocity. A real falling object may reach the ground before it approaches terminal motion.
What if the air resistance changes?
If an already downward-moving object suddenly experiences air resistance greater than its weight, the resultant is upwards. Its acceleration is then upwards, so it slows while still travelling downwards. Zero acceleration occurs only when the forces balance.
Terminal velocity does not mean zero weight or zero velocity. Both weight and air resistance still act. Their balance gives zero acceleration and a constant downward velocity.