• Archimedes' Principle

    When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it. Archimedes’ principle has many applications. It is used in designing ships and submarines. Lactometers, which are used to determine the purity of a sample of milk and hydrometers used for determining the density of liquids, are based on this principle.

    B = F2 − F1

    B = P2 A − P1 A

    B = (ρfluid g h2 − ρfluidgh1) A

    B = ρfluid gΔhA = ρfluid gV = mfluid g

    B = Wfluid

    B = ρfluid gVdisplaced

     

    The apparent weight (W ′) of an object immersed in a fluid is given by…

    W ′ = W − B

    W ′ = mobjectg − mfluidg

    W ′ = (ρobjectV − ρfluidV)g

    W ′ = (ρobject − ρfluid)gV

    W ′ = ρ′gV

    where,  ρ′ = ρobject − ρfluid     

    When

    ρobject   >  ρfluid    the apparent weight is positive but less than the actual weight.

    ρobject  =  ρfluid   the apparent weight is zero and the object has neutral buoyancy.

    ρobject  <  ρfluid    the apparent weight is negative and the object is said to be  "lighter than air".

     

    The factors that affect buoyancy are…

    The density of the fluid,
    The volume of the fluid displaced, and
    The local acceleration due to gravity.

     

    The buoyant force is not affected by…

    The mass of the immersed object.
    The density of the immersed object.