Archimedes' principle explains why objects float or sink in fluids. It's all about the upward force created by fluid pressure differences. This force, called buoyancy, equals the weight of fluid pushed aside by the object.
Floating or sinking depends on an object's density compared to the fluid's density. If it's less dense, it floats. If it's more dense, it sinks. This principle helps us design ships, submarines, and even hot air balloons.
Archimedes' Principle and Buoyancy
Physical basis of Archimedes' principle
- Archimedes' principle states body immersed in fluid experiences upward buoyant force equal to weight of displaced fluid
- Pressure difference between top and bottom of object in fluid creates net upward force
- Fluid pressure increases with depth due to weight of fluid above
- Discovered by ancient Greek scientist Archimedes (287-212 BCE)
- Legend describes Archimedes' eureka moment in bathtub while solving golden crown problem
Calculation of buoyant force
- Buoyant force formula $F_b = \rho g V$ calculates upward force on immersed object
- $F_b$ represents buoyant force (N), $\rho$ fluid density (kg/m³), $g$ gravitational acceleration (m/s²), $V$ displaced fluid volume (m³)
- Buoyant force equals weight of displaced fluid
- Factors affecting buoyant force include fluid density (saltwater vs freshwater), displaced fluid volume (ship hull shape), gravitational field strength (Earth vs Moon)
Floating and Sinking
Floating vs sinking in fluids
- Object floats when its density < fluid density (wood in water)
- Object sinks when its density > fluid density (rock in water)
- Object remains neutrally buoyant when densities equal (scuba diver adjusting buoyancy)
- Fraction of volume submerged for floating objects determined by density ratio
- Specific gravity compares object density to water density indicates float/sink behavior
Problem-solving for fluid systems
- Apply density formula $\rho = m / V$ to find object or fluid densities
- Use buoyant force equation $F_b = \rho g V$ to calculate upward force
- For floating objects, buoyant force equals object weight $F_b = mg$
- Calculate submerged volume fraction: $\text{Fraction submerged} = \rho_{\text{object}} / \rho_{\text{fluid}}$
- Problem-solving steps:
- Identify known and unknown quantities
- Select appropriate equations
- Solve for desired variables
- Real-world applications include ship design (cargo capacity), submarine depth control (ballast tanks), hot air balloons (heated air density)