1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Center of mass of infinite cylinder of air

  1. Jul 29, 2012 #1
    1. The problem statement, all variables and given/known data

    The density of air at height z above the Earth’s surface is proportional to e^(−az) , where a is a constant > 0. Find the centre of mass of an infinite cylinder of air above a small flat area on the Earth’s surface. Hint : Consider line density and the identities:



    2. Relevant equations

    Center of mass = [itex]\frac{1}{M}\sum{m_{i}x_{i}}=\frac{1}{M}\int{xdm}[/itex]

    3. The attempt at a solution

    I have no idea how to get started because I don't know how to use the e^(-az) expression. Could I just write that the density of air at height z = be^(-az) where b is some constant of proportionality? Then I think I would try to find M and dm/dx, plug it into the center of mass equation and integrate from 0 to infinity?
  2. jcsd
  3. Jul 29, 2012 #2


    User Avatar
    Homework Helper

    Yes, taking into account that dm=ρ(z)dz, and you integrate with respect to z.

  4. Jul 29, 2012 #3
    Thanks :) I did the calculation and got 1/a, is that correct?
  5. Jul 30, 2012 #4


    User Avatar
    Homework Helper

    It is correct. Well done!

  6. Jul 30, 2012 #5
    Thanks again!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook