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Homework Help: Mass of the atmosphere

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the total mass of the earth's atmosphere? The radius of the earth is 6.4 x 10^6 m, and 1 ATM = 10^5 N/m^2


    2. Relevant equations
    [tex]F=PA=ma[/tex]


    3. The attempt at a solution
    [tex]F_{g}=P_{atm}A_{earth}=m_{atm}g[/tex]

    [tex]m_{atm}=\frac{P_{atm}A_{earth}}{g}=\frac{P_{atm}\pi r^{2}}{g}=\frac{\left(1\times10^{5}Pa\right)\pi\left(6.4\times10^{6}m\right)^{2}}{9.80\frac{m}{s^{2}}}=1\times10^{18}kg[/tex]

    I think I'm supposed to account for decreasing gravitational acceleration, but how would I do that? I dunno about the height of the atmosphere. The only thing that saved me from getting this problem wrong was my remembering that the mass of the atmosphere was 5x10^18 kg or something
     
  2. jcsd
  3. Jan 21, 2010 #2

    D H

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    Staff Emeritus
    Science Advisor

    Almost right. What is the surface area of a sphere?
     
  4. Jan 21, 2010 #3
    Oh! So I forgot the 4 in front of the pi r2. Thank you!
     
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