Archimedes Principle

The notorious Archimedes Principle, popularly known as the Physical Law of Buoyancy was discovered by the ancient Greek mathematician Archimedes of Syracuse.   

The principle states that any object completely or partially submerged in a fluid (gas or liquid) at rest is acted upon or governed by an upward, or buoyant force. The magnitude of that force is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface for an object partially submerged in a liquid. The weight of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. The buoyant force on a body floating in a liquid or gas is also equivalent in magnitude to the weight of the floating object and is opposite in direction; the object neither rises nor sinks.

So in simple sense: Buoyant force = Water displaced by the body

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Why Do Ships Float?

We’ve all wondered this at least once in our lives. The answer lies with the Archimedes principle.

The propositions to explain this are:

A ship that is launched sinks into the ocean until the weight of the water it displaces is just equal to its own weight. When the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously balances the weight of the ship and its cargo.

Other Applications Of This Principle

The reasoning behind the Archimedes principle is that the buoyancy force on an object depends on the pressure exerted by the fluid on its submerged surface. The Archimedes principle is easiest to understand and apply in the case of entirely submersed objects.

Floatation And Density

Now let’s study the phenomenon of floatation and density. Density plays a substantial role in Archimedes’ principle. The average density of an object ultimately determines whether the object floats or not. If suppose its average density is less than that of the surrounding fluid, the object will float. The sole reason for this is because the fluid, having a higher density, contains more mass and thus more weight in the same volume. The buoyant force, which is equivalent to the weight of the fluid displaced, is greater than the weight of the object. Likewise, an object denser than the fluid will sink. The extent to which a floating object is submerged depends on how the object’s density is related to that of the fluid. For example, an unloaded ship has a lower density, and less of it is submerged compared with the same ship loaded with cargo. We can derive a quantitative expression for the fraction submerged by considering density. The fraction submerged is the ratio of the volume submerged to the volume of the object.