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Why Boats Float: All about Buoyancy

It has been told that the King of Syracuse sent a lump of gold to a goldsmith to have a crown made. When the crown came back it was beautiful, and it weighed just as much as the lump of gold that was sent, but the King didn’t trust that the goldsmith had used all the gold for the crown, and thought that he had replaced some of the gold’s weight with silver instead. The King went to Archimedes, the smartest man in Syracuse, to ask him to determine whether or not he had been swindled by the goldsmith. Archimedes couldn’t exactly melt down the crown to determine this, so he had to think of another way. Deciding that a bath would help him think, Archimedes realized that his body weight displaced the bathwater as he got into the pool. He had an idea and after he tested the King’s crown, some pure silver, and some pure gold to determine the relationship between the weight of the metal and how much water was displaced, he realized that items that weighed the same would have different displacements in water. Archimedes had to tell the King of Syracuse that the goldsmith had, in fact, cheated him out of some of the gold he was given to make the crown. This Article is provided as a public service by Action Donation Services® who handles the boat, yacht and vessel donations for some of America’s favorite charities.

The relationship that Archimedes discovered between weight and displacement was later restated as “the buoyant force acting upward on an object completely or partially immersed in a fluid equals the weight of the fluid displaced by the object” and renamed Archimedes’ Principle. Because gold and silver each weigh different amounts, they have different buoyancy, and the goldsmith had to add a different amount of silver than he removed of gold to make the crown weigh the same. Archimedes was able to determine how much of the crown was actually gold by using the formulas he developed in his research of buoyancy and displacement.

In mathematical terms, F (buoyancy) = -pVg, where p = the density of the fluid, V = the volume of the object being submerged, and g = the standard gravity on Earth (approximately 9.81 N/kg). The buoyant force pushing up on the object in the fluid is what causes it to float. Water has different densities depending on the amount of salt in it and what the temperature is. When building boats, engineers design the bottoms of the boats so that the upward force, or buoyancy, will keep them afloat in varying densities of water. Salt water has more density, so it results in more buoyancy, and the boats will sit up higher in the water.

With the right materials and a few quick experiments, it’s easy to figure out the buoyancy of many objects that we come in contact with every day. Every time we run a bath now, we will know the reason why we’ve learned not to fill it up too high before we get in. And when we see the many shapes and sizes of boats on the ocean, in a lake, or even in our bathtubs, we will know that buoyancy is at work. Archimedes may have put a name to it and used the principle to determine the materials used to make the King’s crown, but displacement and buoyancy have always existed. Now we know how to use them in many ways scientifically to engineer anything to be used on a boat, like storage containers and cranes, or to be used under water, like drills or submarines.

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