Archimedes' Principle Formula

The Formula

F_b = W_{\text{displaced fluid}} = \rho_{\text{fluid}} g V_{\text{displaced}}

When to use: A fluid pushes up exactly as much as the displaced fluid would weigh.

Quick Example

If a submerged block displaces 2 kg of water, the water pushes up on it with the same force as the weight of 2 kg of water.

Notation

F_b is buoyant force, W is weight, \rho is fluid density, and V is the displaced volume.

What This Formula Means

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

A fluid pushes up exactly as much as the displaced fluid would weigh.

Formal View

Archimedes' principle gives F_b = \rho_{\text{fluid}} g V_{\text{displaced}}, which follows from the pressure difference between the top and bottom of an immersed object.

Common Mistakes

  • Using the object's mass instead of the displaced fluid's mass.
  • Forgetting that only the submerged volume contributes to displaced fluid.

Why This Formula Matters

This principle is the standard way to calculate floating and sinking behavior in liquids and gases and is taught throughout secondary-school fluids units.

Frequently Asked Questions

What is the Archimedes' Principle formula?

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

How do you use the Archimedes' Principle formula?

A fluid pushes up exactly as much as the displaced fluid would weigh.

What do the symbols mean in the Archimedes' Principle formula?

F_b is buoyant force, W is weight, \rho is fluid density, and V is the displaced volume.

Why is the Archimedes' Principle formula important in Physics?

This principle is the standard way to calculate floating and sinking behavior in liquids and gases and is taught throughout secondary-school fluids units.

What do students get wrong about Archimedes' Principle?

The displaced fluid's weight matters, not the object's own weight.

What should I learn before the Archimedes' Principle formula?

Before studying the Archimedes' Principle formula, you should understand: buoyancy.