Question

The density of ice is ρice = 920 Kg/m3, and the average density of seawater is ρw = 1.025 g/cm3. What fraction of the total volume of an iceberg is exposed, and what fraction is immersed?
(Hints: The iceberg is in equilibrium)

Answer 1

The problem indicates that the iceberg is in equilibrium, that is, it floats, and by theory it is known that this condition is achieved by the iceberg when its weight is equal to the volume of water displaced.

Expressed in formula:

Fw = Vw x ρw x g

Fi = Vi x ρi x g

So that they are in equilibrium they are equal,

Fw = Fi

Vw x ρw x g = Vi x ρi x g

Grouping similar terms:

Vw / Vi = ρi / ρw

The volume of water displaced by the iceberg is equal to the volume of the part of the iceberg that is under water.

So the volume of the iceberg on the surface of the water (Vexp) is:

Vexpuesto = Volume of ice - Submerged volume

Vexp = Vi - Vsub = Vi - Vw

Thus, the portion or fraction of the exposed ice is:

Vexp / Vi = 1 - Vw / Vi = 1 - ρw / ρi

The density of the water must be converted to values of Kg / m³

ρw = 1,025 g / cm³ = 1025 Kg / m³

Substituting the values:

Vexp = 1 - 920 Kg / m³ / 1025 Kg / m³ = 1 - 0.8975 = 0.1024

V exp = 0.1024 = 10.24 %