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Archimedes

287 BC to 212 BC

 

Archimedes's Principle:

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object.

Archimedes was a Greek mathematician, physicist, engineer, inventor, and astronomer.

 

Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics, and the explanation of the principle of the lever.

 

He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

 

He is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi.

 

He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.


Despite his mathematical prowess, Archimedes is perhaps best remembered for an incident involving the crown of King Hiero.

The King's Crown and the Principle of Buoyancy

As the story goes, the king of Syracuse had given a craftsman a certain amount of gold to be made into an exquisite crown. When the project was completed, a rumor surfaced that the craftsman had substituted a quantity of silver for an equivalent amount of gold, thereby devaluing the crown and defrauding the king. Archimedes was tasked with determining if the crown was pure gold or not. The Roman architect Vitruvious relates the story:

While Archimedes was considering the matter, he happened to go to the baths. When he went down into the bathing pool he observed that the amount of water which flowed outside the pool was equal to the amount of his body that was immersed. Since this fact indicated the method of explaining the case, he did not linger, but moved with delight, he leapt out of the pool, and going home naked, cried aloud that he had found exactly what he was seeking. For as he ran he shouted in Greek: Eureka! Eureka! (eureka translated is "I have found it").

Although there is speculation as to the authenticity of this story, it remains famous. Probably no other tale in all of science combines the elements of brilliance quite so effectively. Whether the story is true or not, there is no doubt to the truth of Archimedes understanding of buoyancy.

Here is what Archimedes had found. Since an object immersed in a fluid displaces the same volume of fluid as the volume of the object, it was possible to determine the precise volume of the crown by immersing it in water. After determining the volume of water, a piece of pure gold could easily be made to match the volume of the water, and thus the volume of the crown. In theory, if the volume of the crown and the volume of the gold block are the same, they should also have the same mass. The only reason they would not have the same mass is if one of them was not pure gold. When the two objects were placed in a balance they did not have equal mass. Faced with this evidence the craftsman confessed to his crime.

Extending this idea further, if the mass of the water displaced is greater than the mass of the object, the object will float (Note: this calculation will require that the object be forcibly submerged). If the mass of the water is less than the mass of the object, the object will sink. If by chance the two masses are equal, the object will be suspended in the water at varying depths depending on the initial depth of the object and the water's temperature and turbidity. Every vessel that has ever sailed on water, every submarine that has ever launched, and in short, all objects that come in contact with a body of water, are governed by the principle of buoyancy defined by the great mind of Archimedes.