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Archimedes

Archimedes is probably best known for the story, which has him sitting in the bathtub, shouting “Heureka” – “I found it”. This apparently happened after he lowered himself into said tub and figured out that objects displace their volume. This in my mind, however, does not warrant such fame. I am sure you could ask a five-year old, what would happen to the water level if you lower something into a glass filled with water. He or she would probably correctly answer that the water level rises. In fact, I just tested this and my six-year old son predicted correctly that the water level would rise. My little daughter just wanted to have a sip of water.

This story is told in connection to the one with the crown that was believed to be made of “fake” gold – some of the gold was substituted with silver. Archimedes knew that the fake crown would have more volume because silver is less dense then gold and the same mass of silver would have more volume than the same mass of gold. Archimedes then knew that the water level could rise more for the fake crown then for the same amount of pure gold.

 

In class we figured out how the difference would not have been measurable by water displacement since the crown is fairly big and would have had to be put into a bucket filled with water. In such bucket the water level would not rise to a level distinguishable form the real gold.

There is, however, a cleverer method in figuring this out, one that uses the more brilliant Archimedes’ Principle as well as Archimedes own law of levers. You put both the fake crown and the lump of gold on a balance beam. The beam should be level since both have the same weight. But put the whole thing in water, the fake crown, because it is more voluminous, will displace more water and therefore have a bigger buoyant force. With this buoyant force the crown will appear lighter under water and the balance beam will no longer be even.

 

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This is at the much more elegant and worthy of a legend. It uses Archimedes’ Principle and the law of levers rather than something a six-year old could have figured out.

 

 

 

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