The Eureka Moment

There is a legend about Archimedes being asked to uncover a fraud that was being perpetrated against the Greek tyrant King Hieron II of Syracuse.  The king suspected that a goldsmith was cheating him when he ordered a solid gold crown, thinking that it was partly made of silver, so the local tyrant contracted the ancient Greek polymath Archimedes to detect any fraud in the manufacture of this golden crown.  Archimedes accepted the challenge, but he didn’t have any idea how he was going to resolve this, till he came up with Archimedes’ Principle.

Archimedes’ Principle says that when a body is partially or completely immersed in a liquid, the buoyant force acting on it is equal to the weight of the displaced liquid and it acts in the upward direction at the center of gravity of the displaced liquid.  This is the basis of why things float on water and such weight measurements can be used to determine the average density of irregular objects, and also to estimate body fat in people.  There is a story which says that Archimedes discovered the law of buoyancy while he was taking a bath, realizing that the water that ran over equaled in volume the submerged part of his body.  As he leaped out of the tub more water splashed on the floor, and he was so excited that he didn’t even stop to grab a towel, dashing out of his house running through the streets naked to announce his discovery, but in reality, he did further experiments.

Water has a specific gravity of 1, and the densities of all other materials are relative to that of water.  Gold has a higher density than silver, which results in gold objects feeling like they are heavier than silver.  Archimedes took two pieces of pure gold and two of pure silver that had identical weights to the weight of the king’s crown.  He then successively immersed the gold, the silver, and the crown in a container filled to the brim with water and measured the volume of water that overflowed with each material.  He found that the crown displaced more water than the gold but less than the silver, thereby proving that the crown contained some other metal which was less dense than gold.  The goldsmith had to make the crown larger when he substituted silver for some of the gold, so that it would weigh the same as a pure gold crown.  However, the silver-gold crown took up more space in the bowl and made the water rise higher.

Written FOWC with Fandango – Buoyant.

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