Mechanics

# The tip of an iceberg

About 90% of the total volume of an iceberg lies below the sea surface.

We know that physics is a science that is interested in several areas of nature, studying from the movement of bodies to how electricity reaches our homes. A very interesting subject that physics studies is Hydrostatics, which is interested in the behavior of fluids.

In the study of hydrostatics, several physicists stood out, but one that we will always remember is Archimedes. Archimedes was a brilliant physicist and mathematician who was born in Syracuse, a small town in Sicily. Archimedes was well known for solving and inventing various instruments that facilitated everyday tasks. The quest to find out if the king’s crown was really made entirely of gold was one of the feats responsible for making him well known.

In the midst of studies on hydrostatics we have something very interesting, which appears in icy waters. They are the Icebergs , which are nothing more than gigantic pieces of ice that float without a defined direction in icy waters. The most interesting thing that we can see, according to the figure above, is that most of an iceberg is submerged, that is, below the surface of the sea water. Therefore, we can say that of the total mass that makes up an iceberg, only 10% of it emerges to the surface.

Icebergs are primarily made up of fresh water, therefore, the floating of an iceberg occurs because it is formed of polar ice, that is, formed by fresh water ice. Thus, the physical principle that explains the fluctuation of an iceberg is Archimedes’ Principle. Therefore, the dimensions of an iceberg, such as height, mass, submerged and emerged volume, are calculated according to the laws of Hydrostatics.

The fluctuation of an iceberg can be understood through the following equation:

In the above equation we have:

am is the volume of seawater displaced
g is the total volume of the iceberg.

Since the density of sea water ρ am = 1.03 g/cm 3 and the density of ice ρ g = 0.917 g/cm 3 , at 0º C, the ratio between the volume of the iceberg (V i = V am ) and its total volume (V g ) can be obtained by the following equation:

This means that 89% of an iceberg’s volume is below the sea surface. Therefore, what we see in iceberg illustrations and figures represents only 11% of its total volume.