Archimedes' Principle

2.5  Archimedes' Principle
  Archimedes' principle  
  An object when partially or completely submerged in a fluid is acted on by a buoyant force equal to the weight of fluid displaced.  
  • Volume of water displaced = Volume of submerged objects
  • Weight of water displaced = Buoyant force
  Buoyant force, \(F\)  

 \(F=\rho v g\), where F = buoyant force, \(\rho \) = density of the liquid, v = volume of liquid displaced, g = gravitational acceleration


Archimedes' principle application

  1. Submarine
    • Dives (move downwards)
      • Ballast tank is filled with water
      • Weight greater than buoyant force (W > F)
      • Submarine dives downwards
    • Rises (move upwards)
      • Water is removed from tank
      • Weight less than buoyant force (W
      • Submarine moves upwards
    • Constant depth @ floats
      • W=F

  2. Hot air balloon
    • Downwards
      • Temperature decrease, volume of balloon decrease
      • Volume of air displaced decrease
      • Buoyant force decreases
      • W>F
    • Upwards
      • Temperature increase, volume increase
      • Volume of air displaced increase
      • Buoyant force increases
      • W
    • Constant depth
      • W=F

  3. Plimsoll line
    • In cooler or denser water, ship floats more.
    • In warmer or less dense water, ship sinks more.
    • Goal: to ensure the ship is loaded within safety limit

  4. Hydrometer
    • In low-density liquid
      • hydrometer sinks deeper
      • give low readings
    • In high-density liquid
      • hydrometer floats higher
      • give high readings