Archimedes' Principle & Law of Flotation

Archimedes' Principle

Archimedes' principle states that any object, fully or partially submerged in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

This principle helps us understand why objects float or sink and is crucial in calculating the buoyant force acting on an object.

Formula for Buoyant Force

The buoyant force $F_b$ can be calculated using the formula:

$$F_b = \rho \cdot V \cdot g$$

• $\rho$ is the density of the fluid
• $V$ is the volume of fluid displaced
• $g$ is the acceleration due to gravity

Example

A metal block with a volume of $0.5 \text{ m}^3$ is submerged in water. If the density of water is $1000 \text{ kg/m}^3$, calculate the buoyant force.

• $F_b = 1000 \times 0.5 \times 9.8 = 4900 \text{ N}$

Law of Flotation

The law of flotation states that a floating object displaces a weight of fluid equal to its own weight.

This principle is essential in understanding how ships and boats float.

Conditions for Flotation

• An object will float if its density is less than the density of the fluid.
• An object will sink if its density is greater than the density of the fluid.
• An object will remain suspended if its density is equal to the density of the fluid.

Example

A wooden block with a density of $600 \text{ kg/m}^3$ is placed in water. Will it float or sink?

• Since the density of the block is less than the density of water, it will float.