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What is the relationship between the amount of water and object displaces and the weight of the object? Who discovered this theory?

This is called the law of bouyancy, discovered by Archimedes, and basically says:
any material or object immersed in a fluid will tend to rise through the fluid if the fluid density is greater than the material density. The force associated with buoyancy is the difference between the weight of the displaced fluid and the weight of the immersed material.

Density is the amount of and object (weight or mass) there is an a given volume (the amount of water the object displaces).

So objects which weigh a lot and don't displace much water (have a low volume) will sink, while objects which are light and displace a lot of water will float.

The relationship, then is how well the object will float. If it floats, it is less dense than water, and if it sinks it is more dense than water.

You might think something like a ship is more dense than water, after all, it is made of metal which is certainly more dense than water, but, the ship is filled with air, which is much less dense than water, and makes up the difference. That is why, when a ship gets a hole in it, it sinks. The water pushes out all the air and makes the total density of the ship greater. When the water, metal, and air inside the ship become more dense than the water outside the ship, the ship will sink.


Eric Tolman

You are probably thinking of Archimedes' principle. Archimedes was a Greek philosopher. The story goes that the king of the day wanted a new crown made entirely of gold. After the goldsmith made it, the king was suspicious that the goldsmith made it of iron and coated it with gold. The king did not want to destroy the crown if in fact it were gold, so he asked Archimedes to figure out if it was pure gold or not without destroying the crown. Archimedes pondered this day in and day out until one day while getting into his bath he discovered the principle that bears his name. The tub was full to the rim, and when he sat down in it, he noticed that the more he sank himself into the water, the more water that spilled over the side of the tub. He was supposedly so happy to make this discovery that he ran out into the streets naked shouting "I found it!" What he discovered is that the amount of water displaced by an object depends on the mass of that object (not the weight). If he knew the mass of that object, and the volume of fluid it displaces, he could determine its density. Since the densities of iron and gold are different, he did a test. He determined the density of the crown and compared it to the density of pure gold to see if they were the same. Legend says they were not the same, so the king was tricked.

C. Murphy

An object that FLOATS displaces the amount of water that has the same weight as the object. If it sinks, it displaces an amount of water that has less weight than the object. This is generally attributed to an ancient Greek known as Archimedes.

Greg Bradburn

If the object is less dense than water (if it floats on water), it displaces a weight of water equal to the weight of the object. If the object sinks in water, it simply displaces a volume of water equal to the volume of the object.

This is known as the Principle of Archimedes.

Richard Barrans Jr., Ph.D.

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