Archimedes Principle

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  • Archimedes Principle
    • Pressure in Fluids
      • Gases and liquids exert pressure on surfaces due to constant bombardment by their molecules
      • Pressure exerted by the Earth varies with altitude
        • The pressure at sea level is 101kPa
        • At the summit of Ben Nevis, the pressure is 87kPa
    • Liquids
      • Pressure exerted by a vertical column of any liquid is calculated using P=hpg
        • h is the height of the liquid
        • p is the desnsity
        • g is the acceleration of freefall (9.81ms-2)
      • p is directly proportional to h, meaning pressure increases with depth
      • The denser the liquid, the more pressure is exerted
    • Upthrust
      • Upthrust is due to pressure differences
      • If the cross sectional area of a block of wood is A and its height is x:
        • The force at the top surface is hpgA
        • The force at the bottom surface is (h+x)pgA
        • the resultant upward force is (h+x)pgA-hpgA
        • This is the equation for upthrust
      • The volume of the block of fluid displaced is Ax, with a mass of (Ax)p
      • Upthrust is equal to the weight of the fluid diplaced
      • Archimedes Principle: the upthrust exerted on a body immersed fully or partially in a fluid, is equal to the weight of the fluid that the body displaces
        • An object will sink if the upthrust is less than the weight
        • For an object to float, the upthrust must be equal to the weight
    • Icebergs
      • 9/10 of an iceberg is under water
      • Densities at 0 degrees C
        • Ice = 900kgm-3
        • Water = 1000kgm-3
      • An ice cube with sides 1m will have a weight of (900x9.81)=8830N
      • When it floats, it will displace water of weight 8830N which has a volume of 0.9m3 (8830/1000x9.81)
      • The ice cube will sink until it displaces 0.9m3 of water
      • This is 9/10 of the volume of the cube

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