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Unformatted text preview: Buoyancy and Archimedes Principle (Pre Lab Assignment Included) Archimedes, the mathematician, physicist and engineer was born around 287 BC in Syracuse, the son of Phidias, an astronomer. Archimedes studied in Alexandria, before returning to his native Sicily. The picture shown here, usually thought to be Archimedes, isn't even him though it is used in coins and stamps. His experiments yielded "Archimedes' Principle" that a body immersed in fluid loses as much weight as the weight of the liquid it displaces. Using water displacement in this way, Archimedes demonstrated that the king's crown was not made of solid gold. Realising his discovery's validity but forgetting to dress before leaving the pool where he was experimenting, he ran down the streets, naked, shouting the now famous phrase "Eureka!" ("I've found it."). Archimedes is also credited with many other notable achievements in physics and mathematics such as the principle of the lever, the discovery of etc. He also probably believed the Earth to be round, a theory expressed in medieval Arab-Norman Sicily, in China and elsewhere. Archimedes was killed during the siege of Syracuse in 212 BC. mg F bottom F top h 1 h 2 Figure 1: Free body diagram of a rectangular object immersed in a fluid. A is the area of the top and bottom. When we jump into the swimming pool we all feel lighter; this is due to the buoyant force. It is not a new force, but is a consequence of the fact that our body is taking up the space that was formerly water. When an object is completely submerged in a fluid (liquids and gases), all parts of the object experience fluid pressure. The fluid pressure increases with the depth of the fluid. The top surface of the object shown supports all the liquid above it and thus F top = ( fluid g h 1 ) A , where fluid is the density of the fluid, g is the acceleration due to gravity, h 1 is the depth in the fluid of the top surface and A is the area of the top surface. The pressure is greater at the bottom of the object and is fluid g h 2 . The total force acting on the bottom surface is F bottom = ( fluid g h 2 ) A . (In the absence of the object, this volume would be filled with the fluid and the pressure along the line marking the bottom surface of the object would be upwards, supporting the fluid above it). Given that would be upwards, supporting the fluid above it)....
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- Fall '07