Calculating Ice Density: Buoyant Force Problem Explained

[Twilit_Truth]

It's me again. This time I actually understand the material, I just need help with figuring this one out.


The tallest iceberg ever measured stood 167 m above the water. Suppose that both the top and bottom of this iceberg were flat and the thickness of the submerged part was estimated to be 1.50 km. Calculate the density of the ice. The density of sea water equals 1.025E7 kg/m^3.


Thank you for your time.

 

[Mindscrape]

What are you initial thoughts so far? How much water does the iceberg displace when it sinks 1.5km? What kind of volumes do we care about? What about the cross section of the iceberg, can that help at all?

This problem doesn't really have do much to do with bouyancy, only in principle, more so density and algebra if that helps at all.

 

[Moetasim]

It's great to hear that you understand the material. Let's dive into solving this problem together. To calculate the density of the ice, we can use the formula: density = mass/volume. In this case, we know the volume of the submerged part of the iceberg (1.50 km or 1,500 m) and the density of sea water (1.025E7 kg/m^3). However, we still need to find the mass of the iceberg. To do this, we can use the information given about its height (167 m) and the fact that both the top and bottom are flat. This means that the volume of the entire iceberg is equal to the volume of the submerged part (1,500 m) plus the volume of the part above water (167 m x 1,500 m = 250,500 m^3). So, the total volume of the iceberg is 252,000 m^3.

Now, we can plug in the values into the formula: density = mass/volume. Rearranging the formula, we get mass = density x volume. Substituting the values, we get mass = (1.025E7 kg/m^3) x (252,000 m^3) = 2.586E12 kg. Therefore, the mass of the iceberg is 2.586 trillion kilograms.

Now, we can finally calculate the density of the ice. Using the formula, density = mass/volume, and substituting the values, we get density = (2.586E12 kg)/(1,500 m) = 1.724E9 kg/m^3. This is the density of the ice, which is significantly less than the density of sea water.

I hope this explanation helped you understand how to solve this problem. Keep up the good work!