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But first, a few important words about the reformation.
Galileo
In the context of this class, we will characterize Galileo as a strict empiricist (what you see nature do, is what nature does).
The "breakthourgh" that Galileo was able to provide was in his recognition of what aspects of motion (physics) were universal. This ultimately led to his idea of frames of reference.
But, first we begin with the major limitation that Galileo faced and that is the difficult of accurately timing certain phenomenon.
Summarizing Aristotle's View
For the natural motion of heavy objects falling to earth, Aristotle asserted that the speed of fall was proportional to the weight, and inversely proportional to the density of the medium the body was falling through. He did also mention that there was some acceleration, as the body approached more closely its own element, its weight increased and it speeded up. However, these remarks in Aristotle are very brief and vague, and certainly not quantitative.
Actually, these views of Aristotle did not go unchallenged even in ancient Athens. Thirty years or so after Aristotle's death, Strato pointed out that a stone dropped from a greater height had a greater impact on the ground, suggesting that the stone picked up more speed as it fell from the greater height.
Two New Sciences
The ideas are presented in lively fashion as a dialogue involving three characters, Salviati, Sagredo and Simplicio. The official Church point of view, that is, Aristotelianism, is put forward by the character called Simplicio, and usually demolished by the others. Galileo's defense when accused of heresy in a similar book was that he was just setting out all points of view, but this is somewhat disingenuous---Simplicio is almost invariably portrayed as simpleminded.
I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.
This then marks the beginning of the modern era in science---the attitude that assertions about the physical world by authorities, no matter how wise or revered, stand or fall by experimental test.
Galileo Experiements:
Galilean Satellites - observe them for yourself (you don't have to actually do the assignment)
Class Discussion: How can Galileo "slow down gravity" so he can accurately time it?
Translated Quote from one of Galileo's Journals:
For the measurement of time, we employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.