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Density of Earth's Mantle w/o knowing radius

  1. Feb 22, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the average density of rock in the mantle? The earth's average density is 5500 kg/m^3; the radius of the core is 3490 km; ratio of core density to mantle density is 2.34

    2. Relevant equations

    Pc = density core
    Pm = density mantle
    Pe = density earth
    Mm = mass mantle
    Mc = mass core
    Rm = radius mantle

    Pc/Pm = 2.34 so Pc/2.34=Pm

    Pm = Mm/(4/3)*pi*Rm^3

    Pc = Mc/(4/3)*pi*(3.49E6)^3

    Rm = Re - Rc

    Assume only the core and mantle compose the earth.

    Mc/Vc + Mm/Vm = Me/Ve = Pe = 5500 (?)

    3. The attempt at a solution

    Pc/2.34 = Pm = (Mc/(4/3)*pi*(3.49E6)^3)/2.34


    I'm not sure what equation would give me Mc, the mass of the core. My other equation had the radius of the earth as a variable. I think I'm just missing one equation, but I can't seem to find another relationship.
     
    Last edited: Feb 22, 2009
  2. jcsd
  3. Feb 23, 2009 #2

    Delphi51

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    Suggest you use m = DV (mass is density * volume).
    If you write Dc*Vc + Dm*Vm = Me (mass of core + mass of mantle = mass of Earth)
    you know or can figure out everything except Dc and Dm = Dc/2.34
    so only one unknown.
     
  4. Feb 23, 2009 #3
    I'm totally lost in a page of equations...there's some simple relationship I'm missing.

    After following your suggestion, I came up with the following:

    Me/Ve = Pc*Vc + Pm*Vm/(Vm+Vc) = 5500 kg/m^3

    Pm = 5500(Vc+Vm)/2.34Vc+Vm

    I try and cancel terms so I'm not putting stuff in terms of earth's radius or volume, but no luck.
     
  5. Feb 23, 2009 #4
    I think you need to be given the earth's radius. (Or volume or mass)
     
  6. Feb 23, 2009 #5

    Delphi51

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    Just some little details to figure out. The volume of the mantle can be figured out - just subtract the volume of the core (found from its given R) from the volume of the Earth (look up its radius in the back of your physics text). Look up the mass of the Earth.
    That's all you need to use
    DcVc + Dc/2.34*Vm = Me
    I get about 10 000 kg/m^3
     
  7. Feb 23, 2009 #6
    This sort of crap is what pisses me of about this Forum.

    A well stated problem needs to include assumed data.

    For example g

    David
     
  8. Feb 23, 2009 #7

    Delphi51

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    I'm coming at this from the other side of the desk - retired high school teacher.
    No teacher wants to write the value of g, G, radius of the Earth, etc. into every question. This isn't laziness or a cost of paper issue - we want our students to understand physics well enough so they don't have to be told when g or G is needed in a problem. Our provincial exams do not have these values written in, either. Rather, we have a standard sheet of formulas and values that all students in the province (Alberta, Canada) use throughout the school year and on the exam. That is the proper solution - each course should have a list of common constants and measurements that students know they can refer to.

    Most students have the really common ones like g and the charge on an electron stored in their calculators and they simply type g instead of 9.81 when doing a calculation.
     
  9. Feb 23, 2009 #8
    I hope there is a teacher's "Common Room" where we can discuss this
    sort of thing privately. In case you hadn't guessed I am a retired teacher myself.

    No doubt no smoking would be allowed.

    But how the **** do you ask someone to calculate something
    without assuming something? (e.g. the density of the earth's mantle)

    Respect,
    David
     
  10. Feb 23, 2009 #9

    Delphi51

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    I thought I saw a staff room when I first saw this forum, but I don't see it now. We can send private messages - just click on a poster's name.

    Not sure what you mean by assuming something like the density of the mantle. You wouldn't find that density in the list at the back of the book. But you can find it from the information given in the problem plus some very common numbers like the mass of the Earth.
     
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