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

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

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

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

earth!“earth!“

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

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

From the equation mg = GMm/RFrom the equation mg = GMm/R2, M = mass of Earth

R = Radius of Earth = about 6400km G = Gravitational constant = about 6.67 x 10Gravitational constant = about 6.67 x 101111

g = gravity = 9.8m/s2

∴ M = mass of Earth = about 6 x 1024kg

Supposing a man could lift only 60 kg directly Supposing a man could lift only 60 kg directly and the distance between the pivot and Earth and the distance between the pivot and Earth be 1m :be 1m :

clockwise moment = anticlockwise momentclockwise moment = anticlockwise moment FF11 x D x D11 = F = F22 x D x D22

6 x 1024kg x 1m = 60kg x D22

D2 2 = 10= 1023 23 mm

The distance between the Sun and the Earth is The distance between the Sun and the Earth is about 1.5 x 10about 1.5 x 101111m.m.

D2 2 = 6.7 x 10= 6.7 x 101111 x Distance between Sun and Earth x Distance between Sun and Earth

6.7 x 106.7 x 101111 = 6700 hundred million = 6700 hundred million ∴ D2 2 = 6700 hundred million x Distance between = 6700 hundred million x Distance between

Sun and EarthSun and Earth

The diameter of Milky Way is about 9.5 x The diameter of Milky Way is about 9.5 x 10101717km, which means that km, which means that D2 2 is more than 100 is more than 100 times of the diameter of Milky Way !times of the diameter of Milky Way !

Also, even though Archimedes can go beyond Also, even though Archimedes can go beyond Milky Way, he absolutely doesn’t have the Milky Way, he absolutely doesn’t have the ability to “lift” the Earth for 1mm. ability to “lift” the Earth for 1mm.

From the equation :From the equation : SSBKBK / S / SAHAH = D = D22 / D / D11

SSD2D2 / S / SD1D1 = D = D22 / D / D11

1 / S1 / SD2D2 = 1 / 10 = 1 / 102323

SSD2D2 = 10 = 102323mm = 10mm = 101717kmkm

Assume Archimedes could push/run 100km per Assume Archimedes could push/run 100km per day, he should run for about 2.7 x 10day, he should run for about 2.7 x 101212 years ! years !If he could push/run with the speed of light, If he could push/run with the speed of light, 300,000 km per sec, natures fastest possible, he 300,000 km per sec, natures fastest possible, he would have lifted the earth by 1mm after would have lifted the earth by 1mm after three three million yearsmillion years of pushing ! of pushing !

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

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