Posted by Ethan at Starts With a Bang busts two Galileo myths.
1) That Galileo actually dropped weights off the Leaning Tower of Pisa. He almost certainly didn’t. Like the story of George Washington and the cherry tree, it’s an instructive parable not at variance with the character of the man – but not an event that actually happened.
2) That the experiment would have worked even if Galileo had done it. It wouldn’t have. Air resistance would mean that otherwise identical objects of the same mass wouldn’t have hit the ground at the same time.
Those are the two points that Ethan makes. They’re both quite correct.
Nonetheless, ol’ Galileo’s (fictitious) Pisa experiment deserves a lot of credit. At the dawn of the 17th century our knowledge of physics was terrible. Aristotle’s millennium-old ideas were still quite dominant, and though Aristotle was a brilliant man who at least got the ball rolling (or falling), he was in fact very wrong about a great many things in physics. Gravity was one of those things – Aristotle thought that the acceleration of a falling object was proportional to its mass. A lump of rock weighing 10 mina should fall ten times faster than a 1 mina rock.
But it doesn’t. Not even close. Sure if you carried out the experiment the odds are the 10 mina rock would make it to the ground a little before the 1 mina rock. But would it make it down more than three* times faster? Not a chance. Though the experiment doesn’t quite match Galileo’s “they fall at the same rate” theory, it matches his theory a lot closer than Aristotle’s “they fall in proportion to their mass” theory. What’s more, Galileo actually covered air resistance in his theory. He predicted that in a vacuum the experiment actually would result in the rocks hitting at exactly the same time. Though Galileo never lived to see the moon landing or even a vacuum pump, he was right. In a vacuum we really do observe the objects falling at the same rate. So even if the Pisa experiment didn’t quite illustrate the point perfectly, it still would have served the purpose of eliminating Aristotle and supporting Galileo just fine.
As usual our knowledge has improved over the centuries but the general concept keeps repeating itself. Many times experiments are done at the bleeding edge of experimental and theoretical capability. Sometimes the data is not clear enough to tell you what is happening, but it’s plenty good enough to tell you what isn’t happening. Almost every field of physics has experienced this, so to pick an example at random we might take Bose-Einstein condensation. The theory predicted that very cold helium-4 would undergo a phase transition to a quantum condensate at a particular temperature. When it was first tested it was found that helium-4 did possess very unusual properties, but not quite at the temperature predicted and not quite the properties that the theory predicted. But did it prove that Bose and Einstein were right that bosons didn’t conduct business as usual at low temperatures? Absolutely. Later on corrections along the lines of air resistance in mechanics were made to the original theory and now theory and experiment match very well. The experiment taught us something important and thoroughly smashed the old ideas even if it wasn’t the exact first-shot perfection we might have preferred.
In concluding the whole matter: should you ever find yourself at the top of that perilously leaning tower in Pisa holding two unequal weights, don’t worry that there’s a small difference in the times they reach the ground below. Even with the slight variance with the naive theory of uniform acceleration the experiment is still more than enough to shatter the Aristotelian physics into another Greek ruin.
*Three because distance covered in uniform acceleration is proportional to the time of fall squared. Inverting, the time is proportional to the square root of the distance. Thus ten times the acceleration reduces the time required to cover a given distance by a factor of the square root of 10, or a little above 3.
June 9, 2009
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