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What is the Archimedes Principle?

By William Springer

Why is it easier to float in salt water than fresh water? Why don't steel ships sink? And what does all this have to do with a naked greek?


Who is Archimedes, and what is the Archimedes' Principle? Archimedies was a mathematician, physicist, engineer, astronomer, and inventor in ancient Greece; he is perhaps best known for running around naked, screaming "Eureka!" (I have done it! or I have found it!), although that story (see next section) is of doubtful authenticity.

Archimedes' Principle can be simply stated: any floating object displaces its own weight in fluid. Archimedes also stated the principle in terms of force:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

What is Archimedes Principle? The Eureka Story

The following story is, very likely, not true. However, it is very well known, and entertaining.

The king had a new golden crown made, but he suspected that perhaps the manufacturer had left out some gold, replacing it with cheaper silver; he commissioned Archimedes to determine whether that was the case. While pondering the problem at the public baths, he observed how his body displaced an equal amount of water from the bath. Realizing that he could use this to measure the volume of the crown, weigh it, and compare the result to the known weight of gold, he sprang out of the bath; too excited to bother dressing, he ran home naked screaming "Eureka!".

The story was likely invented or embellished by Vitruvius, a Roman writer who first told the tale in the first century BC, several hundred years after Achimedes' discoveries.

Practical Applications and Examples of the Archimedes Principle

One example of Archimedes' Principle in action is seen in the tendency of steel ships to float, while a lump of steel will sink. Because the ship is buoyed up by a force equal to the weight of the water it displaces, distributed over a sufficiently large area, the ship floats. The key insight here is that the amount of water displaced depends on the volume of the displacing object, while the upward force depends on the weight of that water; as such, while a solid mass weighing the same as the ship would sink, the ship isn't a solid mass; the steel thus occupies a greater volume, allowing it to displace enough water to equal the weight of the ship.

Simply stated: the empty space inside the ship results in the average density of that ship being lower than the density of the surrounding water, allowing the ship to float.

The principle applies to other mediums as well. For example, air can be considered as a fluid; an unfilled balloon will sit on the ground, but a balloon filled with helium such that the average density of the balloon is less than the average density of the surrounding air will float.

As a side note, all water is not created equal! It is easier to float in salt water than fresh water, for example, because salt water is heavier than fresh water and thus the same volume of displaced water will provide a greater upward force.