Results 1 to 6 of 6

Math Help - center of mass

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    33

    center of mass

    Find the center of mass (x,y) of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2009
    Posts
    166
    Another hint: take a triangular piece of paper. From each corner, draw a line to the middle of the opposite side. Each line will intersect at a particular point. That point is your center of mass.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    First draw the curves



    Then compute the intersects of the 2 curves by solving 4-x^2 = x+2
    Spoiler:

    r \:x=1" alt="(x-1)(x+2)=0 \implies x=-2 \r \:x=1" />


    The coordinates of the center of mass G are given by the formula

    x_G = \frac{\int\int x\:dx\:dy}{\int\int dx\:dy}

    y_G = \frac{\int\int y\:dx\:dy}{\int\int dx\:dy}


    You can see that the area is defined by :
    x between -2 and 1 ; y between (x+2) and 4-x (see green line)

    Therefore

    Spoiler:

    x_G = \frac{\int_{-2}^{1}\int_{x+2}^{4-x^2} x\:dy\:dx}{\int_{-2}^{1}\int_{x+2}^{4-x^2} \:dy\:dx}

    y_G = \frac{\int_{-2}^{1}\int_{x+2}^{4-x^2} y\:dy\:dx}{\int_{-2}^{1}\int_{x+2}^{4-x^2} \:dy\:dx}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    thanks but i dont understand double integers
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by mikegar813 View Post
    thanks but i dont understand double integers
    You mean that you haven't studied double integrals ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    we have not learned double interals sorry
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 15th 2009, 05:04 PM
  2. Replies: 1
    Last Post: November 11th 2009, 04:39 PM
  3. center of mass
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 17th 2009, 07:20 AM
  4. Center of Mass
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 10th 2009, 01:48 PM
  5. center of mass of a rod
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 27th 2007, 12:15 PM

Search Tags


/mathhelpforum @mathhelpforum