Section 6.4: Archimedes' Principle
Archimedes’ Principle states that a body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body.
Formula
\[
F_B = \rho_{\text{fluid}} g V_{\text{sub}}
\]
where:
\( F_B \) = buoyant force (N)
\( \rho_{\text{fluid}} \) = density of fluid (kg/m³)
\( g \) = acceleration due to gravity (m/s²)
\( V_{\text{sub}} \) = volume of fluid displaced (m³)
Example 1: Floating Block
A wooden block of volume 0.02 m³ is placed in water (density = 1000 kg/m³). Find the buoyant force acting on the block.
\( F_B = \rho g V = 1000 \times 9.8 \times 0.02 = 196 \, \text{N} \)
The buoyant force on the block is 196 N.
Example 2: Submerged Sphere
A metal sphere of volume 0.005 m³ is submerged in water. Calculate the buoyant force.
\( F_B = 1000 \times 9.8 \times 0.005 = 49 \, \text{N} \)
The upward buoyant force is 49 N.
Practice Problems
- A cube of volume 0.01 m³ is fully submerged in oil (density = 800 kg/m³). Find the buoyant force.
- A metal cylinder of volume 0.002 m³ is submerged in water. Determine the buoyant force.
- A floating object displaces 0.03 m³ of water. Calculate the buoyant force.
- A sphere of volume 0.004 m³ is submerged in a fluid of density 1200 kg/m³. Find the upward force acting on it.
- A wooden plank of volume 0.05 m³ floats in water. Calculate the buoyant force on it.