What is Archimedes’ principle?

Short Answer:

Archimedes’ principle states that when a body is completely or partially immersed in a fluid, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by it. This upward force acts opposite to gravity and is responsible for the floating or sinking of objects.

In simple words, Archimedes’ principle explains why objects like ships and balloons can float. If the weight of the object is equal to the weight of the fluid displaced, the object will float; if greater, it will sink. This principle is widely used in fluid mechanics and engineering applications.

Detailed Explanation :

Archimedes’ Principle

Archimedes’ principle is a fundamental law in fluid mechanics discovered by the Greek scientist Archimedes of Syracuse around 250 BC. It explains the relationship between a body immersed in a fluid and the fluid displaced by it. The principle states that “any body, wholly or partially immersed in a fluid, experiences an upward thrust (buoyant force) equal to the weight of the fluid displaced by the body.”

This principle is the foundation of buoyancy and is essential in understanding how and why objects float or sink. It applies to both liquids and gases, as both are fluids. The upward thrust experienced by a submerged object is known as the buoyant force.

Statement and Mathematical Expression

According to Archimedes’ principle:

When a body is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by it.

Mathematically,

Where,

  •  = Buoyant force (N)
  •  = Density of the fluid (kg/m³)
  •  = Acceleration due to gravity (9.81 m/s²)
  •  = Volume of fluid displaced by the body (m³)

The buoyant force acts vertically upward through the center of buoyancy, which is the centroid of the displaced volume of fluid.

Explanation of Archimedes’ Principle

When a body is placed in a fluid, the fluid exerts pressure on all sides of the body. The pressure at the bottom of the body is greater than at the top because pressure in a fluid increases with depth.

Due to this pressure difference:

  • The fluid exerts an upward force on the bottom surface.
  • The difference between the upward and downward forces results in a net upward force, known as the buoyant force.

The magnitude of this buoyant force depends on the density of the fluid and the volume of the displaced fluid.

Example:
If a stone is immersed in water, it appears lighter than its actual weight. The loss in weight equals the weight of the water displaced by the stone, which is the buoyant force acting on it.

Conditions of Floatation

Archimedes’ principle helps explain three conditions for an object placed in a fluid:

  1. Floating Condition:
    If the weight of the object (W) equals the buoyant force (FB), the object floats in equilibrium.

Example: A ship floats because its design allows it to displace water equal in weight to its own weight.

  1. Sinking Condition:
    If the weight of the object (W) is greater than the buoyant force (FB), the object sinks.

Example: A solid metal ball sinks in water.

  1. Rising Condition:
    If the weight of the object (W) is less than the buoyant force (FB), the object rises and floats on the surface.

Example: A wooden block or cork floats on water.

Experimental Verification

To verify Archimedes’ principle, perform the following experiment:

  1. Take a solid object and weigh it in air — let this weight be  .
  2. Now, immerse the object completely in water and measure its apparent weight — let this be  .
  3. The loss of weight of the object in water is  .
  4. Measure the weight of the water displaced by the object — it is found to be equal to  .

Thus,

This verifies Archimedes’ principle experimentally.

Applications of Archimedes’ Principle

  1. Design of Ships and Submarines:
    • Ships are designed with hollow hulls to displace enough water to balance their weight.
    • Submarines use ballast tanks to control buoyancy — by taking in water to sink and releasing it to rise.
  2. Hydrometer:
    • A hydrometer is an instrument that measures the density or specific gravity of liquids.
    • It floats deeper in a lighter liquid and less in a denser liquid based on Archimedes’ principle.
  3. Hot Air Balloons:
    • The balloon rises because the weight of the air displaced is greater than the weight of the balloon system.
  4. Floating of Icebergs:
    • Ice floats on water because the density of ice is lower than that of water, and it displaces water equal to its own weight.
  5. Measurement of Volume and Density of Irregular Solids:
    • When an irregular object is submerged in water, the volume of displaced water equals the object’s volume.
    • This helps calculate density using  .

Example Calculation

A wooden block of volume   floats in water. Find the buoyant force acting on it.
Given:

 

Hence, the buoyant force acting on the block is 490.5 N.

Importance of Archimedes’ Principle

  1. Explains why objects float or sink.
  2. Helps determine density and specific gravity of materials.
  3. Useful in the design of floating and submerged bodies.
  4. Applied in the working of hydraulic instruments and airships.
  5. Provides the basis for fluid statics and buoyancy calculations.
Conclusion

In conclusion, Archimedes’ principle is a vital concept in fluid mechanics that explains the behavior of bodies submerged in fluids. It states that the buoyant force acting on a body equals the weight of the fluid displaced by it. This principle is applied in designing ships, submarines, hydrometers, and other engineering devices. It not only explains the phenomenon of floatation and sinking but also forms the basis of many practical engineering and scientific applications related to fluids.