Section 1.3: Buoyancy
This section covers buoyant force, which is the upward force exerted by a fluid on an object submerged or partially submerged in it. This principle explains why objects float or sink.
Key Equations & Concepts:
- Buoyant Force: \( F_b = \rho_{fluid} V_{displaced} g \)
- Weight of object: \( W = mg \)
- Floating condition: \( F_b = W \)
- Submerged fraction: \( \text{fraction submerged} = \frac{\rho_{object}}{\rho_{fluid}} \)
Example 1
A 5 kg block is fully submerged in water. Find the buoyant force if the block's volume is 0.002 m³.
\( F_b = \rho_{water} V g = 1000 \cdot 0.002 \cdot 9.8 = 19.6 \text{ N} \)
Example 2
A cube floats in water with 25% of its volume above water. Find the density of the cube.
Submerged fraction = 1 - 0.25 = 0.75
\( \rho_{cube} = 0.75 \cdot \rho_{water} = 0.75 \cdot 1000 = 750 \text{ kg/m³} \)
Practice Problems
- A block of volume 0.01 m³ is submerged in oil (\( \rho = 900 \text{ kg/m³} \)). Find the buoyant force.
- An object of mass 2 kg floats in water. Find its submerged volume.
- A wooden block (density 600 kg/m³) is placed in water. What fraction is submerged?
- A 10 N object is fully submerged in mercury (\( \rho = 13,600 \text{ kg/m³} \)). Find buoyant force.
- A cube floats with 40% above water. Find its density.
- An object weighs 30 N in air, 20 N in water. Find buoyant force.
- A metal sphere of volume 0.003 m³ floats in water. Find mass for neutral buoyancy.
- A rectangular block (0.2x0.1x0.05 m³) floats in oil (\( \rho = 800 \text{ kg/m³} \)). Find maximum mass to float.
- An object submerged in fluid experiences 50 N buoyant force. If \( \rho_{fluid} = 1200 \text{ kg/m³} \), find displaced volume.
- Explain why a ship floats even though it is heavier than water it displaces.