Centroid of cylindrical cone

  1. 1. The problem statement, all variables and given/known data

    Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm.

    2. Relevant equations

    I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be zero and therefore I only need to find the z coordinate of the centroid.

    The equation I am using is

    [tex]z_c = \frac{1}{M} \int_{body} z dm[/tex]

    where M is the total mass and [tex]dm = \rho dV[/tex]

    3. The attempt at a solution

    I am trying to use cylindrical coordinates but I think my limits of integration are incorrect. I have tried to solve the integral above with the following limits.

    [tex]0<\theta<2\pi [/tex]

    [tex]0<r<50 [/tex]

    [tex]0<z<(200-r/4)[/tex]

    I'm not sure if the limits for the z coordinate is correct. Am I on the right path?
     
  2. jcsd
  3. LowlyPion

    LowlyPion 5,338
    Homework Helper

    Well, I wouldn't worry with polar coordinates, because you are dealing with basically a stack of disks aren't you?

    They are each have a weight of ρ*πr²

    Exploit then the fact that r is a function of z, and your integral should be pretty straight forward shouldn't it?
     
  4. Thank you. I was essentially doing the right thing on my first try before I changed everything, but I made an algebra mistake when trying to use cylindrical coordinates. Thanks for the short cut ... less room for stupid mistakes.
     
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