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Homework Help: Centre of mass

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Let Ω be a tank whose shape is that of the lower hemisphere of radius R. The tank with a muddy suspension whose density ρ is ρ(x,y,z):=e^-h(x,y,z), where h(x,y,z) is the height of (x,y,z) above the lowest point of the tank. Find the center of mass in the tank


    2. Relevant equations



    3. The attempt at a solution
    First of all, how does one determine the height, h(x,y,z)? I guess it would be R but I am not able to give a reasoning to my guess. I would appreciate if someone could give me a graphical illustration on how to find the limits of integration for this problem as well (ignore this if it will cause too much hassle). Thanks
     
  2. jcsd
  3. Mar 7, 2010 #2
    If z is the vertical coordinate, and z =0 at the bottom of the tank, then h(x,y,z) = z
     
  4. Mar 7, 2010 #3
    I got a feeling its z+R. Could anyone let me know what are the phi limits of integration?
     
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