Galileo's Law of Fall

	What is the law of fall?
	What is the formula for the law of fall?
	How does the law work?
	Innovations of the law of fall...

What is the law of fall?

The law deals with the falling of bodies. The law of parabolic fall claims that the distance traveled by a falling body is directly proportional to the square of the time it takes to fall.

For example: A stone falling for twice as long as another stone will travel four times the distance.

A ball falling for three seconds will travel nine times the distance traveled by a ball falling for one second.

	What is the formula for the law of fall?

How does the law work?

In order to convince yourself that the law is correct, you are invited to conduct a series of laboratory tests. In the laboratory you may determine the angle of the inclined plane, the distance to be traveled by the ball, etc.

LABORATORY

A reminder - the law of fall states that the distance traveled by a falling body is directly proportional to the square of the time it takes to fall. This law leads to the conclusion that the speed of a body increases in direct proportion to the passage of time.

Innovations of the law of fall...

In the period before Galileo, scientists thought that force causes speed, as claimed by Aristotle. Galileo showed that force causes acceleration. On the basis of the law of parabolic fall, Galileo reached the conclusion that bodies fall on the surface of the earth at a constant acceleration, and that the force of gravity which causes all bodies to move downward is a constant force. In other words, a constant force does not lead to constant speed but to constant acceleration.

Galileo's claim that force causes acceleration is inseparable from his claim that bodies do not require a cause to continue their movement. This latter claim states that a body in motion will continue its motion so long as no factor disturbs that motion. This principle is called the principle of inertia.

The law of parabolic fall was an innovation in that it claimed that the speed of a body will continue to increase endlessly. Contrary to the claims of the natural philosophers of his period, Galileo claimed that a body will not attain a certain speed which will remain constant but will continue accelerating until it comes into contact with the ground. This claim is of course true so long as one ignores air resistance, which can be very significant for certain bodies and at high speeds.

it is important to remember that Galileo's law of fall claims that bodies fall at a constant acceleration, i.e., that their speed increases by equal increments within equal time periods, and that the distance traveled by them in equal time periods is not equal.

For example: A falling ball, in the second second of its fall, will travel a distance three times as great as the distance it traveled during the first second; in the third second it will travel a distance five times that of the first second; in the fourth second it will travel a distance seven times that of the first second.

If during the first second, the ball traveled a distance of 10 cm, it will travel a distance of 30 cm during the second second, of 50 cm during the third second, 70 cm during the fourth second, and so on...

Mathematically: