Calculating Density & Mass of 10cm Crust Block

[cgarr017]

A block of lithospheric crust that is 10 cm (height) by 10cm (width) by 10cm (depth) is "floating" on the athenosphere. 4 cm of the block protrudes up above the interface with the athenosphere and 6 cm is submerged. a) if the density of the athenosphere is 4.5 g/cm^3, what is the mass of the block of crust? b) what is the density of the crust? c) Do you think that it is continental or oceanic crust? d) Would you get the same density if the block of crust was 100km by 100km by 100km and 40km was protruding above the interface?

Remember an object will displace a volume equal to the weight of the object and that density=mass/volume.

__________________
4 l l
cml l
-l--------------------l----------------
6 l crust l
c l l
m l_________________l asthenosphere
10cm

My thoughts are that the density of the block is 60% of the value of the asthenosphere. If that's true, then the density of the block of crust would be 2.7 g/cm^3 and with a volume of 10x10x10. then the mass would be 2700g. The density of continental crust is 2.7 g/cm^3 and oceanic crust is 2.9 g/cm^3, so if my calculation methods are correct that would make this continental crust. And then I'm guessing raising the values while keeping the same proportions wouldn't change the answer correct?
What are yall's thoughts?

 

[jbsteele]

Yes, your thoughts are correct. The density of the block of crust is 2.7 g/cm^3, and its mass is 2700g. This would make it continental crust. Increasing the size of the block while keeping the same proportions would not change the answer.

 

[thomate1]

I would like to clarify a few things in your response. Firstly, the statement "an object will displace a volume equal to the weight of the object" is not completely accurate. Objects will displace a volume equal to their own volume, regardless of their weight. This is known as the Archimedes' principle.

Now, let's move on to the calculations. You are correct in using the formula density=mass/volume to find the density of the block of crust. However, in order to find the mass, we need to use the formula mass=density x volume. So, for part a), the mass of the block of crust would be 2.7 g/cm^3 x 1000 cm^3 = 2700 g. This is the same answer you got, but it's important to use the correct formula.

For part b), you are correct in finding that the density of the crust is 2.7 g/cm^3.

For part c), it is likely that this block of crust is continental crust, based on the density. However, the density of continental crust can vary and can range from 2.6-2.9 g/cm^3, so we cannot say for certain without further information.

For part d), the density would remain the same as the proportions of the block are the same. However, the mass would increase significantly to 2.7 g/cm^3 x 1,000,000,000 cm^3 = 2.7 x 10^9 g. This is because the volume has increased by 100 times, so the mass would also increase by 100 times.

Overall, your calculations and reasoning are correct. It is important to use the correct formulas and units when solving scientific problems. Good job!