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NAME Instructor Course Date The Works of Archimedes Eureka! Eureka! This is the now famous word uttered by Archimedes in the (possibly apocryphal) story of how he discovered the concept of mass while taking a bath and noting that the water level rose as he descended into it and that the mass of his body displaced an equal amount that could be measured…
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The works of Archimedes
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Download file to see previous pages Codex C, of Byzantine origin in the tenth century, retains the only existing copies of On the Method of Mechanical Theorems, On the Measurement of the Circle, On the Sphere and Cylinder, On Spiral Lines, On the Equilibrium of Planes and his most famous work On Floating Bodies. However, the authors of "Infinite Possibilities: Ten Years of Study of the Archimedes Palimpsest" believe that On the Method of Mechanical Theorems “…is arguably the most significant, as it outlines Archimedes' thinking process for proving mathematical conjectures based upon mechanical analogies” (Easton and Noel 55). On Floating Bodies is the first known work on the science of hydrostatics and Archimedes is generally accepted as the father of that discipline. His bathtub Aha! moment became forever known as Archimedes’ Principle, which is generally stated as, "A body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced" (Luhr 73). This principle also states that there is another force that takes place on the surface of liquids that acts on the floating body and is called buoyancy. “…there is a buoyancy force on a floating object equal to the weight of the displaced liquid" (Potter and Wiggert 26). ...
When Archimedes realized that his own body displaced the water in his bath the same way that crown would if immersed, “He thus was able to measure the volume of the crown, calculate its density, and thereby prove that it was not pure gold—to the misfortune of the dishonest goldsmith” (Marshall Cavendish 385). Density is the mass per unit volume of a substance. Several instruments and methods have been developed from Archimedes original ideas here. This includes measuring the density of the liquid itself. A graduated hydrometer is one such instrument. This is usually made out of a long glass tube that has a scale inside it and a weighted bulb on the end. The liquid to be tested is put into a tall graduated cylinder and the hydrometer is lowered in until it floats freely, and the density, or specific gravity, of the fluid can be seen in the scale. These devises have many applications from testing battery acid, to the level of cream in a container of milk (Marshall Cavendish). Another is the Mohr-Westphal balance which can measure the weight of a solid object both in air and as well as in a liquid. “In a typical measurement, the apparent weight of the sinker in air, in water, and in the liquid of interest is measured. The ratio of the apparent change of weight in the—liquid to that in water, when multiplied by the density of water, is the density of the liquid” (Marshall Cavendish 386). A third is the pycnometer, which consists of a vessel that holds a precise amount of a volume of liquid. The volume that It hold is determined by filling it with a liquid of known density, it is then emptied and a solid is placed inside and the weight of the combination is measured. “From the weight of the liquid that is added, the volume not occupied by the solid ...Download file to see next pagesRead More
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