When an iceberg floats in the ocean, what fraction of it is visible?( The relative density of ice is 0.92, and the relative density of sea water is 1.03)
Use Archimedes' Principle.
Let the volume of the iceberg be V. The amount below water (V') must displace a weight of sea water equal to the weight of the iceberg.
seawater density x V' = ice density * V
1.03*V' = 0.92*V
V'/V = fraction below water = 0.89
Fraction above water = 1 - V'/V = 0.11
To determine the fraction of an iceberg that is visible when it floats in the ocean, we can compare the densities of ice and seawater.
The relative density of a substance is the ratio of its density to the density of another substance. In this case, the relative density of ice is 0.92, and the relative density of seawater is 1.03.
Since the relative density of ice is less than the relative density of seawater, we know that a certain portion of the iceberg must be submerged in water.
To calculate the fraction of the iceberg that is visible, we can use the following formula:
Fraction visible = 1 - Fraction submerged
Next, we need to find the fraction submerged, which is equal to the ratio of the density difference to the density difference between ice and seawater.
Density difference = density of seawater - density of ice
Density difference = 1.03 - 0.92
Density difference = 0.11
Now we can calculate the fraction submerged:
Fraction submerged = Density difference / Density difference between ice and seawater
Fraction submerged = 0.11 / 0.11
Fraction submerged = 1
Since the fraction submerged is equal to 1, it means that the entire iceberg is submerged in water. Therefore, the fraction of the iceberg that is visible is 0.
In summary, when an iceberg floats in the ocean, the fraction of it that is visible is 0, as the entire iceberg is submerged in the water.
To determine the fraction of an iceberg that is visible when it floats in the ocean, we need to understand the concept of buoyancy and relative densities.
Buoyancy is the force that allows an object to float in a fluid. Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of another substance (usually water for solids and liquids). In this case, we need the relative densities of ice and sea water.
Given:
Relative density of ice (iceberg) = 0.92
Relative density of sea water = 1.03
To determine the fraction of the iceberg that is visible, we need to compare the densities of ice and sea water.
The principle behind buoyancy is that an object will float in a fluid if its density is less than the density of the fluid. In other words, the object will displace a volume of fluid equal to its own weight. If the density of the object is greater than the density of the fluid, it will sink.
Since the relative density of sea water (1.03) is greater than the relative density of ice (0.92), it means that ice is less dense than sea water. This difference in densities allows the iceberg to float.
When an object floats, a part of it is above the fluid surface and part of it is submerged. The portion above the surface is called the "visible fraction," and the portion below the surface is called the "submerged fraction."
To determine the fraction of the iceberg that is visible, we can use Archimedes' principle, which states that the weight of the fluid displaced by a floating object is equal to the weight of the object.
1. Calculate the ratio of the densities: 1.03 (density of sea water) / 0.92 (density of ice) = 1.120
This ratio tells us that the density of sea water is 1.120 times greater than the density of ice.
2. Since the weight of the iceberg is equal to the weight of the water it displaces, the fraction of the iceberg that is submerged is given by the inverse of the density ratio: 1 / 1.120 = 0.892
This means that approximately 89.2% of the iceberg is submerged below the surface of the water.
Therefore, the fraction of the iceberg that is visible is approximately 1 - 0.892 = 0.108, or 10.8%.
So, when an iceberg floats in the ocean, about 10.8% of it is visible above the water's surface.