The principle of objects submerged in fluids was discovered by Greek mathematician Archimedes. It depends on force of buoyancy. This force is not a mysterious force that exists in fluids but exists due to the pressure difference. Let study more about the buoyant force and how this force is responsible for the principle.
Archimedes Principle of BuoyancyBack to Top
Any object completely or partially
submerged in a fluid experiences upward thrust with the magnitude
equal to the weight of the fluid displaced by the immersed part of object. This upward
thrust is the force of buoyancy.
It is given as
Buoyant force acting on an object = Weight of the fluid displaced by the object.
If the density of the object is greater than the fluid the object will sink.
If the density of the object is equal to that of the fluid the object will sink or float.
If the density of the object is less than the fluid the object will float.
Archimedes Principle FormulaBack to Top
The buoyant force in fluids is a physical cause due to the pressure difference between the lower and upper sides of the object that is equal to the weight of the displaced fluid. If P2A acts upwards on the bottom of the surface and P1A and gravitational force due to object Mg acts on fluid in down ward direction then the buoyancy force B is given by,
The density in terms of buoyancy is defined as,
$\rho$ is density of fluid
V is volume of fluid
g is the gravitational force.
Archimedes Principle ExperimentBack to Top
Wdifference is the weight of displaced fluid
Wfluid is the weight of the metal piece immersed in fluid
Wair is weight of the metal piece in air.
Example of Archimedes PrincipleBack to Top
How steel ship floats?
Lighter toys float in water
How Parachute works?
The parachute is made of thin material that traps the air and hence makes it spreads out over larger area. That give out the upward thrust to parachute to fly in air.
Weight of stone in air = 500 N
Weight of stone in water = 450 N
Therefore, Loss of weight in water = (500 - 450)N
But upthrust = Loss of weight = 50 N
A body displaces 2 Litres of water. Since the mass of 1 Litre of water is 1 kg, the mass of 2 kg of water = 2 kg.
Loss in the weight of body in water = Weight of water displaced = Weight of 2 kg of water
= 2 kg $\times$ g = 2 $\times$ 9.8 ms-2 = 19.6 N
Therefore, Weight of body in water = Wt of body in air - loss of weight
= 70 N - 19.6 N = 50.6 N