Assume g = 9.808m/s^2 unless stated otherwise. Use MKS units unless stated other

Question

Assume g = 9.808m/s^2 unless stated otherwise. Use MKS units unless stated otherwise.

The phrase, "It's only the tip of the iceberg", comes from the fact that a majority of the volume of the iceberg is below the surface of the water. If the density of ice is 0.92g/cm^3 and the density of seawater is 1.03g/cm^3, determine the ratio of the volume of the iceberg below the water surface to the volume above to the correct number of significant figures (=V below/ V above). Assume that the iceberg is in equilibrium. Hint: the volume of the water displaced is equal to the volume of the submerged portion of the iceberg.

Explanation / Answer

Eureka! weight of object = weight of displaced water vol displaced water = V below vol ice = V below + V above weight is proportional to mass - we could use 9.808m/s^2, but it will divide out. Volume w * density w = tot vol of ice * density of ice V below* 1.03 = (V below + V above) * 0.92 1.03/0.92 = (V below + V above)/ V below = (V below/V below) + (V above/V below) 1.03/0.92 = 1 + (V above/V below) (1.03 - .92)/0.92 = (V above/V below) 0.92/(1.03 - 0.92) = V below/V above 8.36 = V below/Vabove

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