Les cours

Membres

• Liste membres
• Nos Dossiers

Let’s have a critical mind!

Take a piece of paper and a pen. Drop it in the air from your balcony or from a certain height. Which one comes first?... Easy answer at first look. However, what if you remove air? The two objects will be acted on by only one force: the gravitational force of the Earth and will no longer experience air resistance. In other words, they will keep on accelerating at the same rate instead of reaching different terminal velocities…

A perfect example studying motion

Free-fall motion is a perfect example of the type of motion that can be consider in IB and for which equations in the data booklet WILL work… After a few assumptions!

And don't forget: to use the equations of motion, the acceleration must be CONSTANT.

In fact, for objects dropped from a relatively small distance above ground (i.e from the top of a cliff or a building), the acceleration felt due to gravity stays constant… or it changes so little that it is assumed to be constant! The force of gravity acts on large scale distances and it doesn't change through small distances. As a result, the acceleration it produces doesn't vary either.

However, in real life, another force plays on the objects while they are experiencing free-fall : air resistance. As the velocity of the object increases downwards, air resistance also increases up to the point where it balances the weight of the object.

At the point where air resistance being equal to the gravitational force, the overall acceleration of the object is zero. The object is said to be in dynamic equilibrium and has reached its terminal velocity.

If acceleration is considered constant and air resistance ignored, motion can be analyzed by the following equations:

`F = mg`

`v = u + 2gs`

`s = ut + g t^2`

As you have probably realized, these equations are only the equations of motion and the Newton’s second Law (see course Forces) adapted to free-fall with the acceleration a being change to the symbol of gravitational acceleration g.

An interesting outcome

On earth, objects are falling with a constant acceleration of g = 9.8 m/s². It was Galileo that predicted that when allowed to fall, two different objects will touch ground at the same time if air resistance is ignored.

How did he show it ? Galileo built in 1638 an inclined plane with a channel perfectly polished and smooth. He let balls of different weights roll in it and measure the times for different distances down the incline. He declared in his published work to have used water clocks to measure time and he repeated his experiment for different angles of inclination. He came to the conclusion that for a given incline the ratio of the distance to (the time taken to travel it) squared was always the same. He then thought that free-fall is only one of the cases of an inclined plane, only that it cannot be measured since it involves objects moving at higher speeds. If you want, you can read about a modern reproduction of his experiment in the following link : http://www.ihpst2005.leeds.ac.uk/papers/Riess_Heering_Nawrath.pdf

Oh... And I forgot to mention, he didn't perform the tower of Pisa experiment...

It proved that free-fall is independent of mass and it is also known that it is also independent of shape.

Both of these facts explain that two different objects will fall down in a vacuum at the same velocity.

Considering air resistance

The IB will not ask you to use equations considering air resistance.  However, you should be able to draw graphs for an object in free-fall undergoing air resistance. After the object has reached its terminal velocity, acceleration comes down to zero, velocity stays constant (horizontal line on your graphs) and displacement loses its exponential form to become a straight line with a constant slope (its slope being the terminal velocity).

Use these graphs as a way to test you successfully understood the link between acceleration, velocity and displacement.

Graphs of free-fall motion considering there is air resistance

This page cannot be used to calculate the velocity or predict the motion of a spaceship falling toward Earth because as it moves further from the planet, it experiences a lesser and lesser force of gravity. The distances are too big for the gravitational force to be considered constant.

Now that you have read the course, please respond to the QCM to check your understanding !