Question

What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the iceberg floats in (a) the ocean (salt water, density 1024 kg/m3) and (b) in a river (fresh water, density 1000 kg/m3)? (When salt water freezes to form ice, the salt is excluded. So, an iceberg could provide fresh water to a community.)

Answer 1

The fraction of the volume of an iceberg that is visible when it floats in saltwater or freshwater can be calculated using Archimedes' principle. For the given densities, the iceberg would sink in both saltwater and freshwater.

Step-by-step explanation:

When an iceberg floats in water, a fraction of its volume is submerged, which is determined by the density of water and the density of the iceberg. To calculate the fraction of the iceberg that is submerged, you can use Archimedes' principle. Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

In this case, the density of the iceberg is given as 917 kg/m³. Let's calculate the fraction of the volume of the iceberg that would be visible when floating in (a) the ocean (salt water, density 1024 kg/m³) and (b) a river (fresh water, density 1000 kg/m³).

1. (a) For the iceberg floating in saltwater, the fraction of the volume submerged can be calculated as:

Fraction submerged = (density of iceberg - density of seawater) / density of iceberg

Using the given densities:

(917 kg/m³ - 1024 kg/m³) / 917 kg/m³ = -0.1166

The negative value indicates that the iceberg would not float in saltwater. In other words, it would sink.

1. (b) For the iceberg floating in freshwater, the fraction of the volume submerged can be calculated as:

Fraction submerged = (density of iceberg - density of fresh water) / density of iceberg

Using the given densities:

(917 kg/m³ - 1000 kg/m³) / 917 kg/m³ = -0.0902

Again, the negative value indicates that the iceberg would sink in freshwater as well.