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J. Perelman
"Entertaining physics". Book 2.
Chapter 2. Power. Work. Friction

COULD ARCHIMEDES TO RAISE THE EARTH?

"Give me a fulcrum and I will raise the Earth!" this exclamation according to the legend, Archimedes, ingenious mechanics of antiquity, who discovered the laws of the lever.


"Archimedes lever raises the Earth."
Engraving from the book of Varignon (1787) about the mechanics.

"Once Archimedes, " we read in Plutarch, wrote Syracuse king Hieron, which he was a relative and friend, that this force can move any cargo. Passionate about the power of evidence, he added that if there were another Earth, he crossed it, would move from place our".

Archimedes knew that no such goods, which it was impossible to raise the weak force, if you use the lever: it is necessary only to apply this effect to a very long lever arm and the short arm to force to act on the load. So he thought, pressing on extremely long lever arm, can arm strength to lift and cargo, the weight of which is equal to the weight of the globe (Under the expression "to lift the Earth" we mean to introduce certainty into the task of raising on the surface of such cargo, the weight of which is equal to the mass of the planet.).

But if the great mechanic of ancient times knew how huge mass of the globe, he probably abstained from their proud exclamations. Imagine for a moment that Archimedes was given that "another Earth", the fulcrum that he was looking for; imagine further that he made a lever to desired length. You know how long it would take him to the load equal to the weight of the globe, to raise at least one centimeter? Not less than thirty thousand billion years!

In fact. The mass of the Earth is known to astronomers; the body with such a mass would weigh on the Earth is round number 6 000 000 000 000 000 000 000 tons.

If people can directly raise only 60 kg, then to lift the Earth, he will need to put their hands to a long lever arm, which is more short 100 000 000 000 000 000 000 000 time!

A simple calculation will convince you that until the end of the short arm rises to 1 cm, the other end will describe in the universe huge arc 1000 000 000 000 000 000 km

Such an incredibly long way was to go hand Archimedes, leaning on the lever to lift the Earth" only one centimeter! How much time will be needed for this? If we assume that Archimedes was able to lift a weight of 60 kg to a height of 1 m in one second (performance almost the whole horsepower!), and then for "lifting the Ground" 1 cm will require 1000 000 000 000 000 000 000 seconds, or thirty thousand billion years! For all his long life of Archimedes, pressing on the lever, not "would raise the Earth even to the thickness of the thinnest hair...

No tricks genius inventor would not have helped him significantly shorten this period. "The Golden rule of mechanics States that on any machine gains in strength inevitably accompanied by a corresponding loss in the length of the displacement, i.e. in time. Even if Archimedes had brought the quickness of his hands to the greatest speed which is possible in nature, up to 300 000 km per second (speed of light), and with such an incredible assumption it "would raise the Earth" 1 cm only after ten million years.

Entertaining physics J. Perelman

 




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