Gravitation

09 Archimedes’ Principle

ARCHIMEDES’ PRINCIPLE

  • The value of thrust force is given by Archimedes principle.
  • It was discovered by Archimedes of Syracuse of Greece.
  • Archimedes’ principle states that when a body is immersed fully or partially in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it.
  • Thus, Buoyant force (or Upthrust) acting on an object = Weight of liquid displaced by that object.
  • The magnitude of buoyant force acting on an object immersed in a liquid is equal to the weight of liquid displaced by the immersed object.
  • Even gases (like air) exert an upward force (or buoyant force) on the objects placed in them.
  • It is the buoyant force (or upthrust) due to displaced air which makes a balloon rise in air.

Apparent weight:

  • Consider a body submerged in water as shown in figure.
  • The weight of the body due to gravity is opposed by the thrust provided by the fluid.
  • The object inside the liquid only feels the total force acting on it as the weight.
  • Since the actual gravitational force is decreased by the liquid’s upthrust, the object feels as though its weight is reduced.
  • The apparent weight is thus given by:

Archimedes principle equation/ Law of buoyancy:

The mass of the liquid displaced is

Mass = Density × Volume = ρ × V[since, ρ = Mass/Volume = M/V]

Thus the weight of that displaced liquid is:

Weight = Mass x Acceleration due to fravity

W = M × g  = ρ × V × g

Thus from Archimedes principle, we can write:

Apparent loss of weight = weight of water displaced =

ρ × V × g

 

Thus the Thrust force is,

Thrust = ρ × V × g

Where,

ρ = density of liquidV= volume of liquid displaced

The thrust force is also called the buoyant force because it is responsible for objects to float. Thus, this equation is also called the law of buoyancy.

Experiment to Prove Archimedes Principle:

  • Take a mug filled with water to the brim and place it in an empty bowl.
  • Now take any solid object and note its weight by measuring using a spring balance.
  • Keep the object attached to the spring balance and submerge the object in the water making sure the spring balance is not submerged.
  • Now, note down the weight shown by the spring balance.
  • You will notice that it is less.
  • Collect the water displaced into the bowl and weigh it.
  • You will find that the weight of water will be exactly equal to the loss of weight of the object. This proves Archimedes’ principle.

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