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Many think that this experiment was never performed by Galileo and it is only a legend, since there is no in existence an account by Galileo himself of such an experiment conducted by him, and it is accepted by many science historians that this experiment was at most a thought experiment which did not actually take place. To learn more about this dispute see the link section below.
In his Two New Sciences (1634) Galileo discusses the mathematics (first to apply mathematics for physics analysis) of a simple type of motion what we call today uniform acceleration or constant acceleration. Then he proposes that heavy bodies actually fall in just that way and that if it was possible to create a vacuum, any two falling bodies would travel the same distance in the same time. On the basis of this proposal, he predicts about balls rolling down an inclined plane, Finally, he describes some inclined plane experiments corroborating his theory.
Galileo used inclined planes for his experiment to slow the acceleration enough so that the elapsed time could be measured. The ball was allowed to roll a known distance down the ramp, and the time taken for the ball to move the known distance was measured. The time was measured using a water clock.
Galileo showed that the motion on an inclined plane had constant acceleration, dependent only on the angle of the plane and not the mass of the rolling body. Galileo then argued, but couldn’t prove, that free-fall motion behaved in an analogous fashion because it was possible to describe a free-fall motion as an inclined plane motion with an angle of 90°. Using Newton’s laws, we can prove Galileo’s theory by decomposing the gravitational force, acting on the rolling balls, into two vectors, one perpendicular to the inclined plane and one parallel to it. http://www.physics.smu.edu/~ryszard/1313fa98/1313-Incline_.PDF
Following his experiments, Galileo formulated the equation for a falling body or an object moving in uniform acceleration: d=1/2gt2.
The distinguished French historian of science Alexandre Koyré states that the experiments reported in Two New Sciences, to determine the law of acceleration of falling bodies, required accurate measurements of time, which appeared to be impossible with the technology of 1600. According to Koyré, the law was arrived at deductively, and the experiments were merely illustrative thought experiments.
However, Galileo's prominence lay in this that his theoretical (or practical?) work mentioned above established mechanics as a science and paved the way for Newton later in the century especially his mechanics and his law of universal gravitation.
Now, back to our falling bodies experiment. Some evidence shows that such experiments were really performed by various scientists and experimenters preceding Galileo's theoretical work about falling bodies and by this disproving Aristotle's assertion that heavier bodies fall faster than light ones.
As early as 1544, the historian Benedetto Varchi referred to actual tests which refuted Aristotle's assertion.
In 1576, Giuseppe Moletti, Galileo's predecessor in the chair of mathematics at the university of Padua, reported that bodies of the same material but different weight, as well as bodies of the same volume but different material, dropped from a height arrived at the Earth at the same time.
In 1597 Jacopo Mazzoni, of the University of Pisa, reported that he had observed objects falling at the same speed regardless of weight and pieces of an object descending at the same rate as the whole.
The most notorious of those is Simon Stevin that in 1586 (3 years before Galileo) reported that different weights fell a given distance in the same time. His experiments, with the help of his friend Jan Cornetts de Groot, were conducted using two lead balls, one being ten times the weight of the other, which he dropped thirty feet from the church tower in Delft. from the sound of the impacts they concluded that the spheres fell with the same speed, not as stated by Aristotle. Stevin is regarded by many as the first one to perform falling bodies experiments.
Nevertheless, there is some evidence that Stivens preceded Galileo, he didn't perform his experiment scientifically - he did not measure time as Galileo did or proposed, he didn't use mathematics as a tool to establish his theory, and as such no wonder that Galileo's theories were those that paved the way for Newton.
To sum up the debate, we think that Galileo should be credited with the falling bodies and inclined plane experiments since his work led to further scientific development while the contributions of others, that shouldn't be ignored, were if not meaningless then at least aimless.
Warning: We do not recommend dropping lead balls and other objects from high buildings and towers since this activity can be very dangerous.
Instead we suggest a few safe experiments to demonstrate the phenomenon.
1. Hold on the tip of the fingers of different hands a coin and a paper disc about one meter or more above the floor. Drop both of them simultaneously. The coin will reach the floor before the paper disc. From this experiment is possible to conclude mistakenly that heavier objects fall faster.
2. Mount the paper disc on the coin and drop them together. Both objects will reach the ground at the same time. The meaning of this experiment is that not the amount of mass causes falling bodies to fall faster or slower but the resistance/friction of air because air resistance is applied here only to the coin and not to the paper disc and by that we can infer that air resistance and not the amount of mass prevented the paper disc from falling faster - the same as the coin.
To exclude the possibility that the coin and the disc of paper attract each other you can show that they do not stick together in any position.
Experiments 1 and 2 are adopted from:
Weiss Moshe, Physics by Experimental Demonstrations, vol II, Jerusalem: Rubin Mass, 1968, pp. 208-209
3. Repeat experiments 1 and 2 with different combinations of materials, mass or shape in a vacuum chamber (if your school has one). All the dropped objects from the same height will fall at the same rate, whatever their mass because there is no air resistance.
4. Try some experiments with inclined planes and find out if the acceleration is constant? Does the acceleration depend on the mass and diameter of the rolling body, on the angle of inclination of the plane, on the distribution of mass of the body, whether the body is a sphere or a cylinder, solid or hollow? Try to evaluate the effect of friction on your results by using different surfaces for your experiments. http://collegeofsanmateo.edu/physics/docs/physics250/lab03.pdf
5. The falling bodies experiment could be also experimentally demonstrated by the comparison of pendulum motions in air with bobs of lead and of cork which have different weight but which are otherwise similar - the period is independent of the bob weight.
A few links about freely falling bodies physics:
Galileo's Acceleration Experiment - Michael Fowler, University of Virginia
Galileo's Law of Fall
What is Galileo's Explanation? - Carl Martikean
Measuring the Acceleration of Gravity - SMART
Aristotelian Physics - QuarkNet, FSU
Gravity - HyperPhysics
Galileo's Battle for the Heavens - PBS
Did Galileo perform the leaning tower of Pisa experiment?
Galileo's Battle for the Heavens - PBS
On Motion - The Galileo Project
Weights Make Haste: Lighter Linger - Science News
Simon Stevin Links
Simon Stevin (1548—1620), Dutch engineer and mathematician. His experiments in hydrostatics showed that the pressure exerted by a liquid is dependent only on its vertical height and not on the shape of the liquid's container, and demonstrated the principle of the hydraulic press. He probably anticipated Galileo's experiments with falling bodies. Stevin is also credited with the introduction of decimals into common usage.
Simon Stevin - The Galileo Project
Simon Stevin - The Catholic Encyclopedia
Simon Stevin's Introduction of decimals - Phill Schultz, University of Western Australia
Simon Stevin - Wikipedia
Simon Stevin Home Page
The Museum of Unworkable Devices - Donald Simanek's Pages
Simon Stevinus - Britannica 1911