Archimedes Law

You remember Archimedes. He was a Greek mathematician, famous for all kinds of things, but among the most oft-repeated tales is how he came to the aid of his friend, Hiero, king of the Greek city of Syracuse. Hiero suspected that a goldsmith charged with making him a royal crown -- one assumes he needed a spare -- had kept some of the gold provided for himself, and mixed in silver to ensure the weight of the final crown matched that of the original lump of gold provided. He didn't want to melt the crown down to discover the truth, but the thought just nagged at him, and he asked Archimedes to help. Inspiration hit one day as Archimedes lowered himself into one of the public baths in the city and noticed displaced water flowing over the sides of the tub. Legend has it that he was so excited with his insight, he leapt out of the tub and ran (naked?) through the streets of Syracuse yelling, "Eureka! Eureka!" ("I found it! I found it!")

A theoretical insight must be backed up by experiment, so Archimedes took a lump of gold and of silver, each weighing the same as the king's crown, although the lump of silver was much larger because silver is lighter than gold. He put each lump in a vessel filled to the rim with water, and noted that the larger amount of silver caused more water to overflow than the lump of gold, because there was more material, even though both weighed the same. He concluded that a solid material will push away an amount of water equal to its own bulkiness (volume). So if the king's crown were indeed made of pure gold, it would have to displace the same amount of water as the lump of pure gold that weighed the same. Unfortunately for the dishonest goldsmith, the crown made more water overflow than the pure lump of gold, proving that the goldsmith had added silver to the crown to make it bulkier. The goldsmith's fate was probably not a happy one.

This property is known as buoyancy: an object will float if its buoyancy is greater than its weight, and will sink if its weight is greater than its buoyancy. It must be said that the shape and position of a given object plays a vital role here: a concrete canoe placed on end in water will sink because the weight of the concrete is greater than that of the displaced water. But in its normal position, the weight of the canoe depends on its total volume, and this includes all the air inside it. So the average weight is less than that of the water displaced, and the canoe floats. It's weird, but true, like many counter-intuitive concepts in physics. And let's face it -- it's also pretty cool. (According to Wikipedia, the competition rules allow teams to insert concrete-covered, non-structural foam pieces in their canoes so that the canoes float after being submerged. Hmmm. Seems like a bit of cheat to me.)

Concrete in some form or another dates back to 5600 BC Serbia (Bora! would be so proud), evidenced by the discovery of remnants of a hut with a floor made of red lime, sand and gravel. In China, the pyramids of Shaanxi (thousands of years old) contain a mixture of lime and volcanic ash or clay, and the Assyrians and Babylonians also used clay as cement in their concrete. Builders in the Roman Empire preferred concrete made from quicklime, pozzolanic ash, and an aggregate mad from pumice (similar to modern Portland cement concrete). They also figured out that adding horse hair made concrete less likely to shrink, while adding blood -- you heard me: blood -- made the concrete more frost-resistant. The Egyptians liked to different and opted for lime and gypsum cement -- although in all seriousness, the variations probably had as much to do with available materials in the different regions as anything else.