Question

This problem set will allow us to investigate why the plates have the sizes and shapes they do. Your final submission may be typed or handwritten, but it must be legible. Be sure to show all of your calculations and be careful to keep track of your units.

Isostasy and Elevation:
For this exercise you will access to the internet for the Isostasy 2.0 Model. The URL is here: http://www.geo.cornell.edu/hawaii/220/PRI/isostasy.html as well as on blackboard. You will need to have access to this website in order to complete the following problems.

For the following exercises, we will assume the following: Density of Continental Lithosphere = 2.7 g/cm3
Density of Oceanic Lithosphere = 3.0 g/cm3
Density of Asthenosphere (liquid density in model) = 3.3 g/cm3

What is isostasy?

We will start with the continents. If we assume the densities listed above and a crustal

thickness (block height) of 75 km, how thick would the continental root be?

What percentage of total height is the root?

What would happen if the continent had the same density, but was 100 km thick? How

thick is the root?

Is this the same percentage of total height as in question 3? Did you expect this result?

Why or why not?

Now for the oceans, using the densities listed above and assuming a crustal thickness

(block height) of 5 km, how thick is the root under oceanic lithosphere?

What percentage of total height is the root?

What would happen if the oceanic crust was 100 km thick? How does the root

compare to the root under 100 km of continental crust?

Using the data you collected for questions 1 – 8, describe (using isostasy) why the

surface of the planet has the shape it does (100 words). Some prompts to think about and include... Why do the oceans occur over oceanic crust? Why is it very difficult for continental crust to subduct?

Answer 1

Isostasy is the state of equilibrium between the buoyancy force raised in Earth's layer Lithosphere (due to the fluid behavior of Asthenosphere ) and the gravitational force acting on lithosphere.

From model 2, we can apply easily the block hight and get hight of the continental root.

since

from the above equation, if block hight is 75 km then -

which will be of total hight.

For, 100 km continent the root hight will be -

which will be of the total hight. This is same percentage as we got in previous question. This is because the hight is increasing the same proportion as well as the gravitational force and bouyancy for is increasing in same proportion.

For Oceanic crusts the density increases to 3.0 g/cm3, this result for 5km oceanic crust the root hight will be -

  

which is 90.91% of total height of the crust.

For 100 km thick oceanic crust the root hight will come to -