2. A very informative story on the social interaction of science, politics, and
ID: 2073874 • Letter: 2
Question
2. A very informative story on the social interaction of science, politics, and art is the one of how Archimedes came up with his famous principle. Here is some background: Hiero, the king of Archimedes's native town of Syracuse, Sicily had commissioned to an artist a beautiful golden crown for himself. The royal ornament was delivered along with a pretty noticeable check for the acquisition of the necessary gold. When he saw the amount, Hiero wondered how he could be sure that the yellow crown was indeed golden and not an alloy containing the much cheaper silver that would allow the artisan to conveniently pocket the difference. He presented the question to Archimedes, who solved it using his principle. Can you explain how he did it?Explanation / Answer
Archimedes Principle:
When a body is immersed in a fluid either wholly or partially, it is buoyed or lifted up by a force, which is equal to the weight of fluid displaced by the body
Explanation:
First, Archimedes took a lump of gold and a lump of silver, each weighing exactly the same as the crown, and filled a large vessel with water to the brim, precisely measuring how much water was contained in the vessel.
He then gently lowered the lump of silver into it. This caused as much water to spill out over the sides of the vessel as was equal in volume to the lump of silver. Archimedes took the lump of silver out of the water and carefully measured the amount of water left in the vessel, thus arriving at the amount of water that had been displaced by the silver.
He again filled the vessel with water to brim, taking care to fill it with exactly the same amount of water as before. He then lowered the lump of gold into the water, and let the water displaced by it spill out over the sides. Then, doing as he had done with the lump of silver, Archimedes took out the lump of gold from the water, and arrived at the amount of water that had been displaced by the gold.
He found that a smaller quantity of water had been displaced by the gold than the silver, and the difference was equal to the difference in volume between a lump of gold and a lump of silver of the same weight.
He filled the bowl with water to the brim a final time, taking care to fill it with exactly the same amount of water as before. This time he lowered the crown into the water. He knew that if the crown was pure gold, its volume would be the same as that of the lump of gold (which he had made sure weighed the same as the crown), regardless of shape, and that it would displace the same amount of water as the gold. But, if the goldsmith had replaced some of the gold with silver, then the volume of the gold+silver crown would be greater than the volume of the gold, and so the crown would displace more water than the gold.
Archimedes found that the crown did, in fact displace more water than the lump of gold of equal weight. Thus he came to the conclusion that the crown was not pure gold, and that the goldsmith had indeed mixed some silver (or other, lighter metal) into the gold in an attempt to cheat the king.
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