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 (Triple Integral)

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data

    T is the solid bounded by the cylinder y^2+z^2=4 and the planes x=0 and x=3. The mass density at a point P of T is directly proportional to the distance between P and the yz-plane.

    Find the center of mass of the solid T.

    2. Relevant equations




    3. The attempt at a solution

    I drew the solid and got a cylinder extending from x=0 (yz-plane) all the way to x=3 with a radius of 2.

    I also attempted to set up an integral but I think my main problem is figuring out what the density to integrate is.

    I set up my integral as the integral from x=0 to x=3, the integral from y= -2 to y=2, and the integral from
    z= -√(4-y^2) to z=√(4-y^2) dz dy dx.

    Is that correct? I don't know how to go about determining my p(x,y,x) aka my density.

    Edit: Initially I tried to use x as my density but I couldn't integrate that so I tried y and then z but none of them worked out.
    Last edited: Apr 14, 2013
  2. jcsd
  3. Apr 15, 2013 #2
    No one knows? :confused:
  4. Apr 15, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper

    Hi Reefy! :smile:

    (try using the X2 button just above the Reply box :wink:)
    Yes :smile:

    (but in this case the density is constant over each circular slice, so you could just use πr2, and integrate only over x :wink:)
    You can't integrate ∫ x dx ? :confused:

    (or ∫∫∫ x dxdydz)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Center Mass Triple Date
Finding center of mass of solid Oct 14, 2017
Find center of mass of planar quadrilateral Nov 16, 2016
Center of Mass and Mass Sep 18, 2016
Center of Mass Using Triple Integrals Question Apr 6, 2015