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AP Physics - Free Fall

Aristotle (384 – 322 BC), one of your basic ancient Greek philosophers, said that things fall because they want to regain their natural state - earth with earth, water with water, and so on. Thus a rock will fall back to the earth to be with the other rocks. Since a big rock possesses more "earth", it will fall faster than would, say, a feather (which is woefullyinadequate in the earth amount category compared with your basic rock). Aristotle’s idea appears to be true because a rock certainly falls faster than a feather. In fact it made so much sense, that Aristotle's ideas on the subject were the accepted truth for around 2 000 years until the Renaissance.

The first scientific study of gravity was done by Galileo Galilei (1564 - 1642). He was trainedas a mathematician and was a university professor. In the late 1500's Galileo conducted a series of experiments on gravity. He is supposed to have demonstrated that heavy objects and light objects fall at the same speed. The act of doing experiments to find out what would happen – this was a very daring idea.

Here is Galileo's account of the experiment from his book, Dialogues of two NewSciences.

"But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits...the larger outstrips the smaller by two finger-breadths, that is, when the larger has reached the ground,the other is short of it by two finger-breadths.

Galileo did not, as is popularly believed, state that the objects would hit the ground at the same time – he understood air resistance. He did understand that without air resistance, the objects would fall at exactly the same rate.

Galileo wrote about doing the experiment as if he had done it several times, but it is not clear where or whenhe did it. The story that he dropped cannon balls from the Leaning Tower of Pisa has only one source, his last pupil and biographer, Vincenzo Vivani. He describes a very public event -- the entire university in attendance to witness the thing. But no one at the university ever mentioned witnessing the event. So whether Galileo did or did not do the experiment is sort of up in the air.Galileo's idea that things fall at the same rate flies in the face of common sense. It seems reasonable that heavy things ought to fall faster than light ones

To study gravity, Galileo found that he had to slow it down. This was because he couldn’t measure the time it took an object to fall with the crude instruments of the time. Gravity was “slowed down” by having balls roll down inclinedplanes (ramps). Gravity still caused the motion, but its effect was decreased to the point where Galileo could gather useful data. Galileo found that the distance that accelerated objects would travel was proportional to the square of the time. More on this later.

Acceleration of Gravity: On the earth, gravity exerts a force on everything with mass. (A force is a push or pull.) The force makesall objects accelerate downwards, towards the center of the earth. This acceleration varies a tiny little bit depending on where you are - at the North Pole this acceleration is 9.83217 m/s2 and at the Equator it has a value of 9.78039 m/s2. This is because the earth is not a perfect sphere. Fortunately we can safely ignore the tiny differences in the acceleration of gravity. The value whichis commonly used for this acceleration is 9.80 m/s2 . In English units it is 32.0 ft/s2. Gravity's acceleration is kind of special so it is given its very own little symbol, g.

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Drop a rock from the top of a cliff and, in one second, it will reach a speed of 9.80 m/s, after two seconds it will be traveling at 19.6 m/s, in three seconds it’s going 29.4 m/s, at four seconds...
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