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Assume that the density of the ice and water are constant.
Let V=total volume of the ice
V'=volume of the ice in the water
Di=density of the ice
Dw=density of the water
g=gravitational constant
Since the ice is not bobbing, the net force on it is 0. Let's consider the forces in the direction of gravity.
There are two forces acting on the ice in opposite directions.
Gravity acts "downward" and has a magnitude of Di*g*V.
The force acting up on it is the buoyant force exerted by the water. By Archimede's principle, that force has a magnitude of Dw*g*V'.
Balancing those forces we get Dw*g*V'=Di*g*V.
So V'/V=Di/Dw. The density of ice is about 0.9 g/cm^3 and the density of water is about 1.0 g/cm^3. So the fraction of the volume in the water is V'/V = 0.9.
So the fraction of the water above the water line is about 0.1 or 10% give or take a percent or two. |
