Applications

Many modern inventions today use the principle of Archimedes' without most of the population knowing it. Here are a few examples.


1. Hydrometer

- A hydrometer is an instrument that is used to measure the density of a liquid.

- A hydrometer consists of a glass tube attatched to a glass bulb. At the base of the glass bulb, is placed lead  shots. The purpose of these lead shots is to enable the hydrometer to be in a more vertically upright position. The function of the glass bulb is to increase the buoyancy of the hydrometer.

- The sensitivity of the hydrometer can be increased by using a glass tube with a smaller diameter.


2. Submarine

- A submarine has a large ballast tank, which is used to control its position and depth from the surface of the sea.

- When the ballast tanks are filled with water, the weight of the submarine becomes greater than the buoyant force acting on it. So the submarine dives into the sea.

- To enable the submarine to rise up, compressed air is used to expel the water from the ballast tanks so that the weight of the submarine becomes smaller.


3. Hot-Air Balloons

- 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 is equal to the buoyant force.

- The weight of the hot-air balloon can be controlled by varying the quantity of hot air in the balloon.  


4. Ships

 

    
- 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 constucted 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.

- The density of sea water varies with location. The plimsoll line marked on the body of the ship acts as a guideline to ensure that the ship is loaded within the safety limit.

- A ship submerge 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.
 

 

The Principle & Formula

The Principle 

So, what is Archimedes' principle? Archimedes' principle states that for an object that is partially or completely immersed in a fluid, the buoyant force acting on the object is equal to the weight of the fluid displaced.

              Buoyant Force = Weight of Fluid Displaced

U = W 

Proving the Formula

Alright, there are two ways to prove Archimedes' Principle. The experimental way, as well as the mathematical way. For the experimental way, here it is in the video below.

 Cr: Owner Of This Video

  The mathematical way is a little bit harder to grasp, nonetheless, here it is:

From this picture, we can derive the formula through meticulous work:

 

                                                      Where, F = Surface Area

                                                                 H = Height

                                                                 ρ = Density of Liquid

                                                                 U = Buoyant Force

                                                                W = Weight of Fluid Displaced

From this, we can see that, both ways proved the legitimacy of Archimedes' Principle.

 

The Story

Before he became well known, he was just a mathematician, physicist, engineer and an inventor. But, his discovery has made a remarkable breakthrough for education today. So, this is how it all began,


Archimedes's tale takes place some 2,200 years ago when King Hieron II of Syracuse in Sicily gave a jeweller a bar of gold and ordered him to make it into a crown. The king, however, suspected that the jeweller had substituted some of the gold for cheaper metal like silver, while pocketing the leftover gold.

The king had no way of proving his suspicions, so he asked Archimedes – a Greek mathematician, engineer, inventor, and astronomer – to find a definitive answer. Archimedes had spent a long time trying to figure out the answer, which came to him when he noticed how water would splash out of his bath tub the moment he stepped into it, and the more he stepped into the tub, even more water got displaced.

At the time, Archimedes had known that gold was denser than silver, so if a certain weight of silver had been substituted for the same weight of gold, the crown would occupy a larger space than an identical one of pure gold.

So to find the crown’s volume, all Archimedes had to do was essentially immerse the crown and exact measurement of pure gold in a tub filled with water to the brim, measure the spillage, and compare the volume of spillages – if the jeweller had indeed made a crown of pure gold the volume should be the same.

Archimedes was said to be so thrilled with this discovery that he immediately hopped out of the bath and ran onto the streets naked shouting 'Eureka!' 'Eureka!'.

And in case you were wondering, the jeweller was indeed cheating the king.

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