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:I believe the weight dropping is legend, but he did experiment with inclined planes, where the effect can be demonstrated much easier. His thought experiment is not convincing though: it assumes that the force that an object feels does only depend on the object's mass and not on its shape. He forgot to state that assumption, and in fact the assumption is not justified in the presence of air resistance or in a non-homogeneous gravitational field (like the Earth's). --AxelBoldt |
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:I believe the weight dropping is legend, but he did experiment with inclined planes, where the effect can be demonstrated much easier. His thought experiment is not convincing though: it assumes that the force that an object feels does only depend on the object's mass and not on its shape. He forgot to state that assumption, and in fact the assumption is not justified in the presence of air resistance or in a non-homogeneous gravitational field (like the Earth's). --AxelBoldt I don't recall if he physically dropped weights, but I am certain that he did pendulum experiments which are equivalent. His observation that the period of a pendulum only depends on it's length is equivalent to saying that falling objects accelerate at the same rate. His inclined plane experiments may have been part of his observations, but their primary importance was in the idea of inertia. Galileo observed that when a ball rolled down an inclined plane and up a second, the ball will roll up the second plane until it has reached its original height, no matter the angle of the two planes. Galileo then imagined removing the second plane, and postulated that it would not stop since it would never re-achieve its original height. Also, Galileo's assumption that force due to gravity does not depend on shape was a damn good one. How would he know that? Simple, people have been using balances for millenia. Balances measure the relative force due to gravity. Showing that two objects that have different shapes but the same mass experience the same gravitational force is trivial using a balance as long as their size is small compared to the radius of the Earth. The other nice thing about a balance is that it eliminates air resistance entirely. You're point about Earth's gravitational field being non-homogenious is also false in a practical sense. IIRC, the variation to g (9.80665 m/s/s) is in the third decimal place as one travels over the surface of the Earth. Essentially, because the radius of the earth is so tremendous compared to human scales (on order of magnitude of thousands of kilometers IIRC) that treating the proportionality between mass and force due to gravity as a constant is perfectly fine for everyone but geophysicists. Essentially, all he needed to observe would be that traveling around he didn't change weight at all to prove that sufficiently for his purposes. My whole point is that he didn't make these assumptions a priori, he made them based on experimental results. Whether or not people knew they were conducting experiments is another matter, but the results are the same. BlackGriffen |
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