How High do they Float

Consider these cubes made of different material (densities shown in picture). How high will they float in water (density 1 g/cm3)

Answer

It’s all about weight of the block (W=ρoVg) vs the maximum upthrust (Umax=ρfVg)

  • If ρρ, then W > Umax.
    • The object will sink all the way down (where NCF comes to the rescue)
  • If ρρf, then W = Umax.
    • The object will neither sink nor float.
    • It can hover at equilibrium at any depth in the fluid as long as it is fully submerged.
  • If ρρf, then W < Umax.
    • The object will float partially submerged.
    • It will displace just enough fluid to generate the amount of upthrust exactly equal to its weight.
    • The lower the object’s density, the higher it will float.
    • In fact, the fraction of volume submerged is equal to the relative density. So cork, wood and ice float with 1/4, 2/3 and 9/10 of their volume below the water surface respectively.

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