# Archimedes’ Principle of Floatation

Archimedes was one of the greatest mathematicians of all times. He was a Greek mathematician who was also a physicist, scientist and a great inventor. Born in 287 B.C. in Sicily, Archimedes had many great inventions to his credit before his death in 212 B.C. His most famous inventions include the screw propeller and the principle of floatation, among others. His mathematical works include inventing infinitesimals and formulas on measurement of a circle, parabolas, spheres, cylinders and cones. The one theorem that he considered to be his most prized and valuable achievement, is the one that states that if you have a sphere and a cylinder, both of the same height and diameter, then the volume and the surface area of the sphere will be 2/3 of that of the cylinder, with the surface area of the cylinder inclusive of the surface areas of its bases. However, the principle of floatation remains one of his most popular inventions.

**Principle of Floatation by Archimedes**

**The Story Behind the Principle**

Most of the inventions of Archimedes were made to help his country during the time of war. However, the story behind the formulation of the principle of floatation is an interesting one. Briefly put, it goes this way. The king of the land had got a golden crown made to be offered to the deity of a temple. However, he doubted the honesty of the goldsmith, due to which he wanted to make sure that it was only pure gold that was used to make the crown. The great scientist that Archimedes was, he was called by the king and was asked to check the purity of the crown, without causing any damage to it. Now, this was certainly not an easy job and it put him in a fix. However, one day as he stepped into the bathtub, he noticed the water spilling over. Thus, an idea struck him that by measuring the volume of water displaced by the crown, he could easily obtain its density. All he needed to do was divide the mass of the crown by the volume of displaced water. So much was he excited by this discovery that he took to the streets shouting, “Eureka, eureka!” (I found it!)

**Principle of Floatation: Definition**

The Archimedes’ principle states that any object, wholly or partially immersed in a fluid, experiences an upward force equal to the weight of the fluid displaced by it.

Note that, for an object that is completely submerged in a fluid, the volume of the fluid displaced by it, is equal to its own volume. On the other hand, for an object that is floating on the surface of the fluid, the weight of the displaced fluid is equal to the weight of the body. The upward force experienced by the body is termed as the buoyant force. Thus,

Buoyant force = weight of the fluid displaced by the body

Now, the weight of the fluid displaced by the body is directly proportional to the volume of the displaced fluid, since the density of the fluid is constant. This can be illustrated by the following equations.

Weight = Mass x g (where g is the acceleration due to gravity and is a constant)

and

Mass = Density x Volume

Thus, we can say

Weight = Density x Volume x g

Let us take a small example. Suppose an iron ball weighs 20 kg. When a string is tied to the ball and it is submerged in water, the weight of water displaced by the ball is, say, 7 kg. Therefore, the ball would experience an upward force equal to 7 kg. This means that the net downward force experienced by the string would be equal to 13 kg (20 – 7 = 13). Thus, it can be concluded that the weight of the ball decreases when it is immersed in water. This reduced weight is termed as the apparent weight. Hence, the Archimedes’ principle can be restated as follows.

Reduced weight of the body in water (Apparent weight) = Weight of the body – weight of the fluid displaced

This was a brief introduction to the concept behind the Archimedes’ principle of floatation. This principle has a wide range of applications, including the hydrometer, hot air balloons, submarines and water transports such as ships and boats. So, the next time you have a fun time on a cruise, you know whom to thank for!