# Air Resistance and Terminal Velocity

Demonstration of the 'hammer and feather' principle on Earth by Dr. Prash 'Galilei' Sinnathamby.

## Galileo's Cannonball

Galileo Galilei, the famous Italian scientist, around 1590, proposed that two objects would fall at the same acceleration in the absence of air. He imagined two balls, one a heavy metal cannonball, the other the same size and shape, but made of wood.

If they were dropped from the Tower of Pisa, he mused, would the heavier ball fall faster than the wooden ball?

Most people then (and some today!) believed that an object falls at a constant speed proportional to its weight. Galileo did some experimenting (which in itself was a revolutionary way of approaching scientific questions), and found two things:

• 1. Objects do not fall at constant speeds, but get faster as they fall.
• 2. It makes no difference how heavy an object is!

Test it yourself: take two objects and drop them.

Convinced?

Now, if you had chosen a piece of paper, you may have found that it fell slower than, say, a pen. But why? Is it its weight? You can test this by scrunching the paper into a ball and trying it again.

## Air Resistance

You should have found that the paper, when scrunched up, falls faster than the same paper allowed to float down. This is the first principle of air resistance: an object will have resistance proportional to its surface area and speed as it moves through a gas or liquid. This is because the object is trying to push through more air molecules as it moves. Although air molecules are very small and light, there are a lot of them - enough to cause a piece of paper or feather to slow right down as it falls.

To test if it really is the air slowing the objects down, we need to drop them where there is no air. This can be done in a laboratory, using tubes from which most air has been removed. But to get totally air-free, we need to travel to the Moon.

In case you have not done this, don't worry. In 1971 two Apollo astronauts were able to test the theory on the Moon for us. Of course, Galilei was right all along!

Demonstration of hammer and feather drop on the Moon by David Scott of Apollo 15, Aug 2 1971.

If there were no air on Earth, the acceleration due to gravity would be 9.8 m/s2, and its symbol is 'g'. This means that every second an object falls it is moving 9.8 m/s faster.

On the Moon, the acceleration is 1/6 this: or 1.6 m/s2. Can you see the feather and hammer fall more slowly in the video of David Scott?

## Flight

One of the consequences of air resistance is flight.

An aircraft flies because the forces due to air resistance are not equal on the top and bottom of a wing, creating lift. The aircraft's wings are shaped in just the right way to create a difference in air pressure. As you know, pressure is force, so the aircraft takes off.

This pressure difference only exists if the aircraft is moving. The faster it moves the greater the lift.

In equilibrium, an aircraft's thrust equals drag, and lift equals gravitational force.

To make the aircraft move, the engines create thrust. Because there is air resistance, there is a resistance to this movement forward, called drag. Drag is always in the opposite direction to the thrust.

In the vertical axis, gravity pulls the craft towards the Earth with a force equal to its weight. When the craft is not gaining or losing height, the lift force produced by the wing equals the weight. To go higher, the aircraft's engines push it faster forward. To lose altitude, the pilot eases off the engines, causing the lift to decrease.

## Terminal Velocity

When a parachutist is in freefall, he initially accelerates at g, but as he increases in speed he encounters a resistance to his motion from the air. The faster he goes the greater the air resistance force.

At a certain speed, the air resistance is equal to the force of gravity pulling him through the air. He is in equilibrium, and the net force is zero. If there is no net force, Newton's Second Law of Motion, F = m.a, dictates that he is experiencing no acceleration - therefore his velocity is constant.

The velocity at which a falling object is no longer accelerating due to air resistance is known as terminal velocity.

Demonstration of the effect of air resistance by physics teacher, Paul Greenwood.

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