archimedes discoveries and invention

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Archimedes (c. 287 BC c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the moment.

The catapult is a device that applied the principle of moment. The force is very large and the load is very small. Like putting an elephant on one side of the seesaw and a small child on the other. You can imagine the result.

The sling is the oldest projectile weapon. There is a pouch and two long strings. Then, at the proper moment, one end of the sling is let go with the other end is still held by the hand. The pouch can no longer hold the projectile and the projectile continues on it's way, releasing the projectile.

Archimedes had made a claim to King Hiero. "Give me a place to stand and I will move the earth!

Archimedes knew that by applying moment, one could lift the heaviest of weights even by the weakest of forces. Therefore, He thought that by pressing his hand on the extremely long arm of a lever, he would be able to lift the earth.

But was this really possible? Imagining that he had another planet to stand on and a lever large enough to do so, could he really have moved the earth?

From the equation mg = GMm/R2, M = mass of Earth R = Radius of Earth = about 6400km G = Gravitational constant = about 6.67 x 1011 g = gravity = 9.8m/s2 M = mass of Earth = about 6 x 1024kg

Supposing a man could lift only 60 kg directly and the distance between the pivot and Earth be 1m : clockwise moment = anticlockwise moment F1 x D1 = F2 x D2 6 x 1024kg x 1m = 60kg x D2 D2 = 1023 m

The distance between the Sun and the Earth is about 1.5 x 1011m.

D2 = 6.7 x 1011 x Distance between Sun and Earth 6.7 x 1011 = 6700 hundred million D2 = 6700 hundred million x Distance between Sun and Earth

The diameter of Milky Way is about 9.5 x 1017km, which means that D2 is more than 100 times of the diameter of Milky Way !

Also, even though Archimedes can go beyond Milky Way, he absolutely doesnt have the ability to lift the Earth for 1mm. From the equation : SBK / SAH = D2 / D1

SD2 / SD1 = D2 / D1 1 / SD2 = 1 / 1023 SD2 = 1023mm = 1017km

Assume Archimedes could push/run 100km per day, he should run for about 2.7 x 1012 years ! If he could push/run with the speed of light, 300,000 km per sec, natures fastest possible, he would have lifted the earth by 1mm after three million years of pushing !

In conclusion, the principle of moment can be represented by a sentence:

Archimedes can lift the Earth via the principle of moment theoretically. The force he gain let him can lift the Earth, but the distance he loss make him break his promise.


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