Question

The density of seawater is approximately 1.027g / cm^3 and the ice density 0.93g / cm^3. An iceberg typically has a mass of 150,000 metric tons (1 metric ton = 1000kg). Calculate:

(a) The buoyant force exerted by the water on the "iceberg"

(b) the volume of the iceberg above sea level,

(c) the volume fraction above sea level.

Answer 1

Volume of the iceberg

V = mass / density

V = 150000000 / 930

V = 161290.32 m³

Now,

fraction of icerberg which is above the surface is given as

f = 1027 - 930 / 1027 = 0.09444 ( answer to part (c) )

so,

volume above the water surface

V_above = V * f

V_above = 15233.85 m³ ( answer to part (b)

Now, to find the buoyant force, we can easily find volume displaced of water

V = 161290.32 - 15233.85 = 146056.5 m³

so

F = 1027 * 146056.5 * 9.8

F = 1.469e9 N ( answer to part (a)