Didn't do the research?

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airplanespaceship3
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Didn't do the research?

Postby airplanespaceship3 » Tue Apr 21, 2009 7:58 am UTC

I've heard often about how Aristotle thought a heavier object falls faster than a lighter object. Today, this idea is looked upon (rightfully so) as really, really dumb. As silly as this sounds, could it have actually been empirically observed? Isn't terminal velocity related to the mass of an object? If you were dropping your test objects off a really high tower or ledge (assuming they have about the same cross-sectional area and drag coefficient), such that the objects reached terminal velocity before colliding with the ground, would you not observe that the heavier object hits first? I'm not sure what exact relationship Aristotle proposed (if any) between mass and speed, but I'm just wondering if maybe this is how he got the idea. (Just a little thought experiment to see if maybe Aristotle wasn't as clueless as you'd think.)
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Re: Didn't do the research?

Postby Certhas » Tue Apr 21, 2009 8:33 am UTC

Yep, terminal velocity depends on speed:

mg = D(v)

where D(v) is the drag at speed (v). This is indeed what underlies our intuition about heavy objects falling faster, if terminal velocity is much greater then what is attainable through, say, a two meter drop we have almost free fall. This is more likely to occur for heavier objects.

Aristotle wasn't an idiot, but he didn't do his research in the sense of thorough experimental verification of what he was talking about. That concept was only fully established a few millenia later when Francis Bacon wrote his Novum Organum in reply to Aristotles "Organon".
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Re: Didn't do the research?

Postby Mr_Rose » Tue Apr 21, 2009 9:36 am UTC

Well the simple solution to that is to use two objects and a ledge arranged such that they are still accelerating towards their terminal velocity at the point where they intersect with the ground.

Galileo's solution was a tower, an orange and a cannonball, IIRC; Aristotle certainly had access to oranges and could probably have gotten an iron ball, though he might have had an easier time with bronze, so what Aristotle's problem would have been was finding two points of sufficient vertical distance that human perception could adjudicate the matter conclusively; the ancient Greeks weren't much into tall towers as I recall (though they did have a number of suitable cliffs).

Of course that also means that you have to have realised that air could be affecting your results...
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Re: Didn't do the research?

Postby airplanespaceship3 » Tue Apr 21, 2009 3:15 pm UTC

Certhas wrote:Aristotle wasn't an idiot, but he didn't do his research in the sense of thorough experimental verification of what he was talking about.


Ok, thanks. That's the impression I was under.
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Re: Didn't do the research?

Postby ATCG » Tue Apr 21, 2009 3:38 pm UTC

Bertrand Russell wrote:Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
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Re: Didn't do the research?

Postby gmalivuk » Tue Apr 21, 2009 4:15 pm UTC

Yeah, a lot of the Greeks weren't so into dirtying their hands with actual research. That was menial work best left to servants and women, probably.

The Aristotelian (and thence through the middle ages) notions of physics do closely match the way we conceptualize things, though. They may no longer be "common sense" to anyone with a high school education, but they do match up pretty well with the most common experience of anyone who wasn't actually setting out to check abstract statements.

Inertia is the same way, because in our actual experience, things don't tend to keep moving. They only move as long as they are acted on by an obvious force, after which they slow down rather quickly. So it makes sense that before actually running systematic experiments, people would suppose that the slowing down period was simply the force running out or leaking away. And from this understandable misunderstanding we can also see how natural it was to conclude, from observations of permanent motion in the heavens, that there was some Prime Mover exerting force on those things. Otherwise, why would they keep moving?
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