Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q23P

Expert-verified
Fundamentals Of Physics
Found in: Page 408

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

In analyzing certain geological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the gravitational force on the overlying material. Thus, the pressure on the level of compensation is given by the fluid pressure formula. This model requires, for one thing, that mountains have roots of continental rock extending into the denser mantle (Figure). Consider a mountain of height H=6.0 km km on a continent of thickness T=32 km. The continental rock has a density of2.9 g/cm3 , and beneath this rock the mantle has a density of 3.3 g/cm3 . Calculate the depth of the root. (Hint: Set the pressure at points a and b equal; the depth y of the level of compensation will cancel out.)

The depth of the root is 44km

See the step by step solution

Step by Step Solution

Step 1: The given data

  1. The height of the mountain, H=6.0km or 6000m
  2. Thickness of a continent, T=32 km or 32000m
  3. Density of continental rock, ρc=2.9 g/cm3 or 2.9×103kg/m3
  4. Density of mantle, ρm=3.3 g/cm3 or 3.3×103 kg/m3

Step 2: Understanding the concept of pressure

The pressure at some horizontal level of compression, deep inside the earth, is the same over a large region and is equal to the pressure exerted by the gravitational force on the overlying material. Therefore, using the formula of gauge pressure, we can find the depth of the root.

Formula:

Pressure applied on a body, p=ρgh (i)

Step 3: Calculation of depth of the root

As pa=pb,From equation (i) and the given values, we get But, pa=ρcg(6.0km+32km+D)+ρm(y-D) .......(a) andpb=ρcg(32km)+pmy.........................................(b) Therefore, equating equations (a) and (b), we get ρcg(6.0km+32km+D)+ρm(y-D) =ρcg(32km)+ρmy ρc(38.0km+D)+ρm(y-D) =ρc(32km)+ρmyρc(6.0km)+ρcD+ρmy-ρmD-ρmy=0 ρc(6.0km)+ρcD-ρmD=0 D=ρc(6.0km)ρm-ρc D=(2.9g/cm3)(6.0km)3.3g/cm3-2.9g/cm3 D=43.5km

Therefore, the depth of the root is 43.5km

Most popular questions for Physics Textbooks

Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.