Results 1 to 4 of 4

Thread: Find the center of mass of a thin plate of density

  1. #1
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    679
    Thanks
    1

    Find the center of mass of a thin plate of density

    $\textsf{Find the center of mass of a thin plate of density
    $\delta=3$ bounded by the lines $x=0, y=x$, and the parabola
    $y=2-x^2$ in the $Q1$}\\$
    \begin{align*}\displaystyle
    M&=\int_{0}^{\sqrt{2}}\int_{2-x^2}^{1}3 \, dy \, dx\\
    &=3\int_{0}^{\sqrt{2}}\biggr[y\biggr]_{y=2-x^2}^{y=1}\, dx
    =3\int_{0}^{\sqrt{2}}(x^2-1) \, dx
    =3\biggr[\frac{x^3}{3}-x\biggr]_0^{\sqrt{2}}=\sqrt{2}\\
    M_y&=\int_{0}^{\sqrt{2}}\int_{2-x^2}^{1} \, dy \, dx
    =\int_{0}^{\sqrt{2}}\biggr[y\biggr]_{y=2-x^2}^{y=1}\, dx\\
    &=\int_{0}^{\sqrt{2}}(x^2-1) \, dx = -\sqrt{2}\\
    &\color{red}{\, \bar{x}=\frac{5}{14},\bar{y}=\frac{38}{35}}
    \end{align*}

    ok not doing something right
    red is answer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    819
    Thanks
    374

    Re: Find the center of mass of a thin plate of density

    try

    $\int _0^1\int _x^{2-x^2}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,110
    Thanks
    2595

    Re: Find the center of mass of a thin plate of density

    Find the center of mass of a thin plate of density-clipboard01.jpg
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    679
    Thanks
    1

    Cool Re: Find the center of mass of a thin plate of density

    here is eventually what I did

    Find the center of mass of a thin plate of density-capture.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Center of Mass and Density
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jul 5th 2012, 12:53 PM
  2. Thin plate splines and Radial Basis Function
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: Dec 13th 2010, 12:55 PM
  3. center of mass with varying density
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Apr 21st 2010, 05:55 PM
  4. Replies: 3
    Last Post: Jan 5th 2010, 08:42 PM
  5. Center of Mass through density
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Dec 28th 2008, 06:34 PM

/mathhelpforum @mathhelpforum