Physics Free Fall
Concept and History

From Aristotle to Galileo.- The teachings of the great ancient wise Aristotle stating that heavy objects fall faster than light ones were accepted until the XVI Century. We know that if we drop a hammer and a feather or a sheet of paper from the same height, the hammer will reach first the ground. If we crumple the paper giving it a ball shape it is observed that both objects will reach the ground almost at the same time. It was the famous Italian physicist Galileo Galilei who refuted Aristotle's idea stating that, in absence of air resistance all objects fall with the same uniform acceleration. But Galileo didn't have a machine to create vacuum for sucking the air; the first pneumatic machine able to do this was invented afterwards, by the year 1650. He did not have watches exactly enough nor high speed photo cameras either. However, he cleverly proved his hypothesis using inclined planes getting a slower movement which could be measured with the rudimentary watches of that age. The slope of the planes could be increased gradually until reaching almost a vertical position allowing him to predict behavior of objects in free fall.

Galileo's Free Fall Hypothesis Proved in the Moon.- In the year 1971 an astronaut carried out in the Moon, where there is no atmosphere, the experiment of dropping from the same height and at the same time a hammer and a feather. Both objects hit the lunar ground at the same time.

Theory of Free Fall and
the Acceleration of Gravity.-

When the term object in free fall is used, this term includes the dropping as well as the upward or downward throwing. Any object that falls freely experiences an acceleration directed to the center of the Earth or downward, no matter the initial object movement.

The magnitude of this free fall acceleration is denoted by the symbol g, whose value slightly varies with the altitude and the latitude.

Near the surface of the Earth the g value is approximately 9.8 m/s2.

Now, the cause of this acceleration was found by Newton, who established in his Law of Universal Gravitation that objects attract each other in direct proportion to the product of their masses and inversely to their separation elevated to the square exponent. It is the Earth mass what causes this acceleration of 9.8 m/s2 on its surface and g is named as gravity acceleration.

The free fall is a known example of uniformly accelerated movement, with an acceleration a = -9.8m/s2 (vertical axis pointing vertically upward). If you choose the vertical axis pointing vertically downward, the acceleration is taken as + 9.8m/s2. The kinematic equations for a rectilinear movement under the acceleration of gravity are the same as any movement with constant acceleration:

v = vi - gt velocity as function of time.
y - yi = ˝(vi + v)t displacement as function of time
y - yi = vit - ˝gt2 displacement as function of time
v2 = vi2 -2g(x - xi)velocity as function of displacement

The sub index i denotes initial quantities, g the gravity acceleration and t, the time.

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