The Archimedes' Principle

Archimedes of Syracuse (Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity.

                Long time ago Archimedes a Greek mathematician, scientist and engineer,   lived in the Greek city-state of Syracuse on the island of Sicily about 200 B.C. He was a good friend of the King Heron. Heron wanted a gold crown. Heron suspected that his crown was not pure gold but the goldsmith has mixed some other cheap metal with gold to make the crown. He asked Archimedes to determine whether the crown was of pure gold or not. Archimedes thought of the problem while he stepped into a full bath. As the water ran over the sides of the tub, he realized the solution. He immediately ran to Heron's house, through the streets of Syracuse, naked, yelling "Eureka", which means "I found it". No doubt normal people find scientists weird.

                First, he weighed the crown. Then, he took a lump of gold and of silver, each weighing the same as the crown. The silver lump was larger because silver is lighter than gold. It takes much more silver to weigh as much as the lump of gold.

                He put each lump in a vessel. The vessels were filled to the rim with water. The larger amount of silver caused more water to overflow than the lump of gold did, although both weighed the same. Archimedes knew then that any solid material will push away an amount of water equal to its own bulkiness, or volume. If the crown were pure gold, it would have to push away, or displace the same amount of water as the lump of pure gold that weighed the same.

                But the crown made more water to overflow than the lump of gold had. Was the goldsmith honest or dishonest? He was dishonest. He had added silver to the crown to make it bulkier. The king found him guilty.

                Archimedes' principle states that an object totally or partially immersed in a fluid (liquid or gas) is buoyed (lifted) up by a force equal to the weight of the fluid that is displaced.

                Everyone must have felt while bathing in swimming pool or bath tub that in water you would be much lighter than you are when standing on land. Thats because we feel some force from the water. This force is called the ' Buoyancy Force'. It is defined as

                The force exerted vertically upward by a fluid on a body wholly or partly immersed in it; its magnitude is equal to the weight of the fluid displaced by the body.

                The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). In simple terms, the principle states that the buoyant force on an object is going to be equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational constant, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.

               

F=(d)(V)(g)

Where,

d=density of liquid

V=volume of solid

g=acceleration due to gravity

                Suppose a rock's weight is measured 10 newton, when suspended by a string with gravity acting upon it.Assume that when the rock is lowered into water, it displaces water of weight 3 newton. The force it then exerts on the string from which it hangs would be 10 newton minus the 3 newton of buoyant force: 10-3 = 7 newton. Buoyancy reduces the apparent weight of objects. Let’s look at some applications of Archimedes' principle.

APPLICATIONS

1. Submarine:submarine is a watercraft capable of independent operation below the surface of the water. It differs from a submersible, which has only limited underwater capability.

The term submarine most commonly refers to large crewed autonomous vessels; however, historically or more casually, submarine can also refer to medium sized or smaller vessels (midget submarines, wet subs), Remotely Operated Vehicles or robots.The word submarine was originally an adjective meaning "under the sea” and so consequently other uses such as "submarine engineering" or "submarine cable" may not actually refer to submarines at all. Submarine was shortened from the term "submarine boat", and is often further shortened to "sub".

A submarine has a large ballast tank, which is used to control its position and depth from the surface of the sea.
A submarine submerges by letting water into the ballast tank so that its weight becomes greater than the buoyant force (and vice versa). It floats by reducing water in the ballast tank. Thus its weight is less than the buoyant force.

2. Hot-air balloon

The atmosphere is filled with air that exerts buoyant force on any object.
A hot air balloon rises and floats due to the buoyant force (when the surrounding air is greater than its weight). It descends when the balloon weight is more than the buoyant force. It becomes stationary when the weight = buoyant force.
The weight of the Hot-air balloon can be controlled by varying the quantity of hot air in the balloon.

3. Hydrometer
A hydrometer is an instrument to measure the relative density of liquids.
It consists of a tube with a bulb at one end. Lead shots are placed in the bulb to weigh it down and enable the hydrometer to float vertically in the liquid.
In a liquid of lesser density, a greater volume of liquid must be displaced for the buoyant force to equal to the weight of the hydrometer so it sinks lower.
Hydrometer floats higher in a liquid of higher density.


4. SHIP
 

A ship floats on the surface of the sea because the volume of water displaced by the ship is enough to have a weight equal to the weight of the ship.
A ship is constructed in a way so that the shape is hollow, to make the overall density of the ship lesser than the sea water. Therefore, the buoyant force acting on the ship is large enough to support its weight.
A ship submerges lower in fresh water as fresh water density is lesser than sea water. Ships will float higher in cold water as cold water has a relatively higher density than warm water.

-         Mayand Dave.