http://www.neatorama.com/2008/05/12/...s-behind-them/

The Law: According to Archimedes’ principle, a body wholly or partially submerged in liquid is buoyed up by a force equal to the weight of the displaced liquid. This buoyant force depends on the density of the liquid and the volume of the object, but not its shape.

The law seems simple, but it is actually not intuitive that objects with equal volume experience the same buoyant force when held under water: cubes made of cork and lead would experience the same buoyant force, yet would have completely different behavior. This is because the different ratios of buoyant force to object weights.

Archimedes’ Principle of Buoyancy has many applications, including determining the pressure of a liquid as a function of depth. It helps us understand how floatation works and is one of the founding principles of hydrostatics.

The Famous Legend Behind the Law: One day, King Hieron II of Syracuse, Sicily, wanted to find out whether his wreath-shaped crown was actually made from pure gold. He called upon Archimedes to find out (without damaging the crown, say by melting it down). Roman architect and engineer Marcus Vitruvius wrote:

While Archimedes was turning the problem over, he chanced to come to the place of bathing, and there, as he was sitting down in the tub, he noticed that the amount of water which flowed over the tub was equal to the amount by which his body was immersed. This showed him means of solving the problem … In his joy, he leapt out of the tub and, rushing naked toward his home, he cried out with a loud voice that he had found what he sought.

Archimedes was able to obtain the exact volume of the crown by dunking it in water and measuring the displaced water. He then took the weight of the crown and divided it by its volume to get the density of the crown, which turned out to be between that of gold and silver. Archimedes was thus able to show that the wreath was not made out of pure gold (and the royal goldsmith was executed).

Modern scholars suggest that this story was bogus, as it would be unlikely that Archimedes had measuring equipment with sufficient accuracy to detect the difference (plus, he hated to bathe - see below).
There is more on Hooke's Law, Bernoulli's principle, Dalton's Law of Partial Pressures, Fourier's Law of Heat Conduction...

The Law: According to Archimedes’ principle, a body wholly or partially submerged in liquid is buoyed up by a force equal to the weight of the displaced liquid. This buoyant force depends on the density of the liquid and the volume of the object, but not its shape.

The law seems simple, but it is actually not intuitive that objects with equal volume experience the same buoyant force when held under water: cubes made of cork and lead would experience the same buoyant force, yet would have completely different behavior. This is because the different ratios of buoyant force to object weights.

Archimedes’ Principle of Buoyancy has many applications, including determining the pressure of a liquid as a function of depth. It helps us understand how floatation works and is one of the founding principles of hydrostatics.

The Famous Legend Behind the Law: One day, King Hieron II of Syracuse, Sicily, wanted to find out whether his wreath-shaped crown was actually made from pure gold. He called upon Archimedes to find out (without damaging the crown, say by melting it down). Roman architect and engineer Marcus Vitruvius wrote:

While Archimedes was turning the problem over, he chanced to come to the place of bathing, and there, as he was sitting down in the tub, he noticed that the amount of water which flowed over the tub was equal to the amount by which his body was immersed. This showed him means of solving the problem … In his joy, he leapt out of the tub and, rushing naked toward his home, he cried out with a loud voice that he had found what he sought.

Archimedes was able to obtain the exact volume of the crown by dunking it in water and measuring the displaced water. He then took the weight of the crown and divided it by its volume to get the density of the crown, which turned out to be between that of gold and silver. Archimedes was thus able to show that the wreath was not made out of pure gold (and the royal goldsmith was executed).

Modern scholars suggest that this story was bogus, as it would be unlikely that Archimedes had measuring equipment with sufficient accuracy to detect the difference (plus, he hated to bathe - see below).

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