Archimede's Principle

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Archimedes

Archimedes (298 BC- 212 BC) was the greatest mathematician of ancient times. A native of Syracuse, Sicily, he was killed during its capture by the Romans in the Second Punic War. Stories from Plutarch, Livy, and Polybius describe machines including the catapult, the compound pulley, and a burning-mirror invented by Archimedes for the defense of Syracuse.

He spent some time in Egypt, where he invented a device now known as Archimedes' screw. This simple device could bring water from a lower to a high level. To accomplish this, Archimedes designed a helix. As the spiral rotated inside a cylinder, it carried water upward.

Archimedes is also remembered for demonstrating the principle of the lever. He developed formal mathematical principles, then applied them to show that with a bar and fulcrum - or fixed support - and only a slight effort, a person could, as he put it, " move the world." From some stories, he was able to single-handedly move a ship from the harbor onto the sand by applying his principle with a series of pulleys. Archimedes showed how and why the principle of the lever worked, whether used on a small or large scale.

Archimedes was a mathematician, scientist, mechanic, and he will forever be remembered as one of the greatest scholars.

The Story Behind the Science

Hieron, the king of Syracuse and Archimedes' friend, wanted to know whether his crown was made of solid gold. The king suspected that the gold had been mixed with silver, which is worth less than gold. So he asked Archimedes to try to resolve the question. The solution would have been easy if the king had allowed the crown to be melted down. Since that was no possible, Archimedes had to find another solution to determine the metal content of the crown. Archimedes discovered the answer while at a public bath. He noticed that when he got into the water, it overflowed the tub. By measuring the overflow, he found that the volume-the amount of space a thing occupies-of the spilled water was equal to the volume of his body under water. He realized he could determine the gold content of the crown by measuring the water it would displace against the amount of water displaced by a lump of gold weighing the same as the crown. The crown and lump of gold would each displace the same amount of water if the crown were solid gold. If the crown contained silver, it would displace more water, since the volume of a weight of silver is greater than the volume of the same weight of gold. With this discovery, Archimedes leaped from his bath and in his excitement raced naked down the street toward his home, shouting "EUREKA! I have found it!"

Archimedes was the first to develop the physical law that is now known as Archimedes' law. The law explains buoyancy, or why objects seem to lose weight in water or other liquids. This principle has been applied ever since to test precious metals.

Archimedes' Principle

Archimedes' principle is the fundamental natural law of buoyancy, first identified by the Greek mathematician and inventor Archimedes in the 3d century BC. It states that any object floating upon or submerged in a fluid is buoyed upward by a force equal to the weight of the displaced fluid.

This buoyant force is caused by the weight of the fluid, which causes the fluid pressure to increase steadily with increasing depth from the surface. Any submerged object is subject to a greater pressure force on its lower surface than on its upper surface, creating a tendency for the object to rise. This tendency is counteracted by the weight of the object, which will sink if it is heavier than the surrounding fluid and will rise if it is lighter. If the object weighs the same as an equivalent volume of the fluid, it will be in equilibrium and remain motionless. Buoyancy may be thought of as the density of a fluid relative to the densities of objects submerged in it

From this we find two equations: