 The Archimedes law states that “If a solid body floats or is submerged in a liquid- the liquid exerts an upward thrust force- a buoyant force- on the body equal to the gravitational force on the liquid displaced by the body.”

## Definition

The Archimedes law also known as the physical law of buoyancy was discovered by the ancient Greek mathematician and scientist, Archimedes and he stated that any particular body that is partially or completely submerged in any sort of fluid be it gaseous or liquid, which is at rest will be acted upon with the help of an upward or floating motion, force the measure of which is equal to the weight that the fluid has and is displaced by its body. The volume of the fluid that is displaced is equal to that of the volume of an object that is fully immersed in the fluid or even to that particular fraction of the entire volume that is below the surface for any object that is partially submerged in the fluid. This is to say that the weight of the portion that has been displaced from the fluid is now equal to the magnitude of that of the buoyant force.

## Other factors governing the law

It must also be mentioned that the buoyant force on a body that is floating in liquid or gas is equal in terms of its magnitude, to the weight of the object that is floating and lies to the opposite direction. This particular object will neither rise nor sink. In explaining this, the instance of a ship that is traversing the ocean may be mentioned. If the weight of water the ship displaces from the surface of the ocean it is traveling on is not equal to its own weight, then chances are that ship will most certainly sink. When you load the same ship further, its weight increases thus sinking deeper and displacing more water. This helps the magnitude of the buoyant force to continuously match with the weight of the vessel and all the goods that are being carried.

### A practical example of Archimedes law

Supposing that a 5 kg object is immersed in water and is being acted upon by an upward buoyant force of about 2kg and this is also equal to the weight of the water displaced by the object that is immersed. It must be noted that the buoyant force lessens the object’s apparent weight by about 2kgs which reduces the net weight of the object from being 5kgs to 3kgs.

## More facts on the Archimedes law

It must be mentioned that if the weight of an object is less than that of the fluid that is displaced, the object will experience a rise as is the case of a bar of wood that is left below the surface of the water. An object that is inherently heavier than the quantity of the fluid it is able to displace, will sink when released but at the same time, will experience a loss in weight that is equal to the weight of the displaced fluid. In fact, when it comes to weighing, a correction is needed to be made so as to be able to compensate for the effect of buoyancy of the air that surrounds it.

## The causal effect

While demonstrating the Archimedes principle, it must be mentioned that gravity has an important role to play in the entire phenomenon. That is to say that the force of buoyancy that always opposes the element of gravity is in fact caused by gravity itself. The pressure within fluids increased as the depth increases because there acts within, a gravitational weight on the fluid at hand, from above. This pressure that is increasing steadily applies a force on an object that is submerged and that increases with the depth of the fluid. The result of such a phenomenon is buoyancy.

## The principle governing levers

It must also be mentioned that the Greek scientist postulated that balancing of a beam using different weights that is distributed along the length of the beam can prove to be a good instance of a situation that is applied in the physical world which is most clearly explained when one treats it using abstract terms that have to do with mathematics. Archimedes traced the footsteps of Euclid in setting up certain axioms which are otherwise simple abstractions of experiences that are present within the real world and it is from therein that he goes on to derive a few of the properties of this phenomenon. He talks at length about the situation wherein the beam that is being used for the experiment is supported at a juncture which can also be termed as the fulcrum through which the distances to all of the weights can be measured. It must also be mentioned that the center of gravity of several of these weights that are placed on the beam concerned is exactly at the fulcrum because of which the beam is placed horizontally and thus remains in equilibrium.

## Where is Archimedes Principle used?

• Submarine: 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. Conversely, it floats by reducing water in the ballast tank.-thus its weight is less than the buoyant force.
• 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’s weight is higher than the buoyant force. It becomes stationary when the weight equals the buoyant force. The weight of the Hot-air balloon can be controlled by varying the quantity of hot air in the balloon.
• 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.
• Fishes: Certain group of fishes uses Archimedes’ principles to go up and down the water. To go up to the surface, the fishes fill its swim bladder (air sacs) with gases.
• Water walking bugs: Archimedes principle explains why some bugs can walk on water.

## How Archimedes Principle works:

• Density is the mass per unit volume of a substance. = M / V
• Specific Gravity is the ratio of the density of the substance to the density of water. SG = S / W.
• In general: SG = S / W = (MS / VS) / (MW / VW) = (MSg / VS) / (MWg / VW) = (WS / VS) / (WW / VW)

In some circumstances, the volume of the substance is equal to the volume of the water. In particular, when a solid object is completely immersed in water, the volume of the water displaced must be equal to the volume of the object. Furthermore, by Archimedes’ Principle, upon immersion the object would receive a buoyant force equal to the weight of the water displaced. Thus, an object weighed in air and then weighed while immersed in water would have an effective weight that was reduced by the weight of the water displaced, if the buoyant force of the air is negligible. When weighed in air, the object receives a buoyant force equal to the weight of the air displaced by the object. However, the density of air is small enough (compared to the density of most solids) to allow this buoyant force to be neglected when weighing most solids in air.

Usually, we assume air = 1.3 x 10-3 grams/cm3

Specific Gravity for an object more dense than water

The formula for specific gravity is given by:

SG = (WS / V) / (WW / V) = WS / WW = WS / (buoyant force) = WS / (loss of weight in water)
= WS / (WS – weight of substance in water)

By Hooke’s law:

F = – k x
Substituting the values, we get:

SG = WS / (WS – weight of substance in water) = (k xA) / (k xA – k xW)

Specific Gravity for an object less dense than water

The equation above is only true if the object is more dense than water. If the object is less dense than water, a lead weight must be attached and three spring elongations must be measured to determine the SG.

There are 3 notations in this situation:

• xA: the object alone, in air
• xB: the object in air with the lead sinker submerged completed in water
• xC: both the object and the sinker completely submerged in water

This was a comprehensive study of Archimedes Law. Also check out our article on Murphy’s Law here.

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