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Homework Help: 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

    it is correct.

    ehild
     
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