Archimedes principle4/15/2023 ![]() ![]() As a ship is lowered into the water it will displace more and more water until the weight of the displaced water equals the weight of the ship. ![]() How then does that explain why a ship floats? For flotation, the upward force exerted by the water, that is the buoyant force, must equal the downward force exerted by the ship’s weight. And here we have Archimedes principle, namely that the upward force on a body immersed in a fluid is equal to the weight of the fluid displaced. But since that downward force is exerted by the weight of the water occupying the same volume as your body had, the conclusion is that the buoyant force must equal the weight of the water that was displaced by your body. Since you are now stationary, the downward force must equal the upward force, or the buoyancy. But the volume of water that has replaced your body has a certain weight, pushing downwards. However, this replacement water experiences the same pressure from below, that is, the same buoyant force, as your body did, since water pressure is dependent solely on depth. This water has the same volume as your body had occupied, but not the same weight. Now imagine that we can hit the pause button on the dive at some point and somehow magically remove your body and replace it with water. This means that the downward force due to your weight plus the pressure of the water on top of you is less than the force exerted by the water on the bottom of your body pushing you up, which is referred to as the “buoyant force.” But the deeper you go, the greater the force you feel pushing you up towards the surface. You see some pretty coral at a depth of some twenty feet and decide to dive down for a closer look. Let’s begin with an imaginary snorkeling adventure. While that narrative may be somewhat fanciful, there is no doubt that Archimedes really did formulate the principle of buoyancy which explains, among other phenomena, why ships float. How much reliance we can place on this account is questionable since we first hear of it from the Roman architect and engineer Vitruvius in the 1st century B.C., some two hundred years after the eureka moment supposedly happened. When it came to the crown, Archimedes suggested that whether it had been adulterated with another metal could be determined by comparing its density to that of pure gold. Then dividing the weight of that object by its volume allows its density to be calculated. This led him to conclude that a body immersed in water displaces a volume of water equal to its own volume, meaning that the volume of any irregularly shaped object that sinks in water can be determined from the volume of the water displaced. How could one determine if the crown was pure gold, wondered the king?Īs the story goes, the answer came to Archimedes as he noted that the level of the water in a tub rose as he immersed himself in it. it was not the discovery of the principle named after him that sent the Greek mathematician, physicist and inventor running naked through the street yelling “Eureka,” meaning “I have found it.” What he supposedly found was a solution to a problem posed to him by King Hiero of Syracuse who had suspected that a goldsmith tasked with making him a gold crown had substituted some of the gold with silver. Archimedes’ principle states that any object, totally or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
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