1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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 for a function defined body

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data

    The upper side of a uniform plate of thickness w is given by a function y(x) = 4a+x^2/a. Length of this plate on the x-axis is a . Find x coord of the center of mass of this object, with respect to the origin O . Take density of the plate as p

    3. The attempt at a solution

    Y(x)= 4a+(x^(2))/a

    Can be restated as w.dA=w(4a+(x^(2))/a).dx
    therefore using
    w.dA.p=dm
    w(4a+(x^(2))/a).dx.p=dm

    distance from O to CoM qouted as S
    will be S= 1/M∫x.dm
    S=1/M∫x.w(4a+(x^(2))/a).p.dx
    S=1/M.w.p∫(4ax+(x^3)/a).dx

    therefore finally , integrating from x=0 to x=a

    S=1/M.w.p(2a^3+(a^3)/4)
    Mass M can be substituted by = p.w.∫1.dA = p.w.∫y(x).dx from 0 to a

    Is this is correct ???!!! :) Thanks in advance

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



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 29, 2011 #2
    You have roughly a rectangle of width a and height 4a. The center of mass you get should be close to (a/2,2a)? Did you get an answer close to this?
     
  4. Nov 30, 2011 #3
    I did it for the x distance from the origin , i got 27/52*a which is about o.519a i.e nearly 1/2a
     
  5. Nov 30, 2011 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    it is correct.

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook