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Archimedes' Principle
of buoyancy



Archimedes' Principle
of buoyancy

A knowledge of Archimedes' Principle is important in the design of ships and submarines because upthrusts must be calculated.

The designer must know how low a ship will lie in the water before it is actually put in the water.

Archimedes discovered that floating objects or objects that are fully or partially submerged in a fluid have a certain amount of upthrust, or buoyancy, acting on them.

The size of this upthrust is equal to the weight of the fluid that the object displaces.

Given that various fluids have differing densities, this upthrust changes accordingly.

An object will seem lighter, for instance, in salt water than fresh. A ship will actually ride higher in the salt water.

'Give me a lever and a place to stand and I shall move the Earth.'

Archimedes was a Greek mathematician and inventor who lived from around 287 to 212 BC.

Born in Syracuse, Sicily, Archimedes discovered the principle of buoyancy.

He also worked out the laws of levers and pulleys showing that heavy loads could be moved with a small force.

Archimedes considered his calculations of the areas of circles and curves as his most important work and much of it is still basic to mathematics.

During a Roman siege of Syracuse, catapults invented by Archimedes were used to hold the enemy off.

Although ordered to be spared, he was killed when the Romans finally broke through and had failed to recognise him.


Archimedes' Principle of Buoyancy:
An object weighs less in water than it does in the air. This loss of weight is due to the upthrust of the water acting upon it and is equal to the weight of the liquid displaced.

Because salt water is more dense than pure water the object displaces a greater weight of salt water and, therefore, weighs less.

The denser the liquid, the easier it is to float in it making it easier to swim in the ocean or a chemical filled pool than a mountain stream.

Object weighed in air is (say) 640 grams.
Object weighed in water is (say) 410 grams.
Object weighed in salt water is (say) 400 grams.
A minimal weight of air is displaced.
Weight of water displaced is 230 grams.
Weight of salt water displaced is 240 grams.

Archimedes' Crowning Glory

The king of Syracuse had sent a lump of gold to the goldsmith to have a new crown made from it.

Although the finished crown weighed exactly as much as the lump of gold had, the king suspected that he had been ripped of by the smith. Believing that he had kept some of the gold and made up the weight with copper and silver, the king asked Archimedes if he could prove his theory.

Archimedes reasoned that a block of gold would weigh more than a block of silver or copper of the same size but thought that the king would probably not be pleased if he melted the crown to test it.

It is believed that, one day in the public bath house, Archimedes jumped into a tub full of water making it overflow. This gave him the idea of how to solve the problem.

He was so excited that, without thinking to get dressed, he ran through the streets of the town yelling 'Eurika' which means 'I have found it'.

He had figured that the crown would displace its own volume of water and so would a lump of gold of the same weight.

During his experiments he found that the water displaced was equal to the apparent loss of weight of a suspended object.

The crown and the gold weighed the same in the air but Archimedes found that, in water, the crown weighed less (displaced more water) showing that it's volume was larger.

This showed that the crown was made of an alloy rather than the pure gold given by the king and that the goldsmith had cheated.

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