Calculating Density of Ice from a Buoyant Force Problem - Homework Help

AI Thread Summary
To calculate the density of ice from the buoyant force problem, the key is to use the relationship between the weight of the iceberg and the buoyant force. The iceberg's volume can be expressed in terms of its height, assuming it is a rectangular prism, which simplifies the calculations. The submerged volume can be calculated using the thickness of the submerged part and the height above water. By applying the relevant equations, the length and width of the iceberg can be treated as variables that will cancel out in the calculations. This approach allows for the determination of density without needing to know the specific dimensions of the iceberg.
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Homework Statement



The tallest iceberg ever measured stood 167 m above the water. Suppose that both the top and the bottom of this iceberg were flat and the thickness of the submerged part was estimated to be 1.50 km. Calculate the density of ice. The density of sea water equals 1025 kg/m3.


Homework Equations



Weight of the object / Buoyant Force = Density of the object / Fluid density
V = L x W x H
Density of fluid / density of object = volume of object / volume of fluid

The Attempt at a Solution



I don't want an answer, I just need help figuring out how I'm supposed to find the volume.
I know that I need the volume in order to find the density, and the mass...but how do I find either the density OR volume with just the height and the submerged height? I know that I'm supposed to assume the iceberg is a rectangular prism...but shouldn't I know the mass or volume in order to find the density?
How do you find the volume with only the height?
 
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You don't need to know the mass. You are assuming it is a rectangular box, not a prism. So the length and width are the same for the volumes of the iceberg above and below the water.

The second equation you listed is all that is really needed.
 
But how do you find the volume with only a height? I don't know the length and width...
 
You can still express the volumes you need in terms of L,W,H by just using the variables and put them into the equation. You don't need to know L and W directly. They will be canceled out.
 

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