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Math Help - Statics of Rigid Bodies.

  1. #1
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    Statics of Rigid Bodies.

    Mechanics module from Maths alevel. Three questions from the Statics of Rigid Bodies topic.







    Any help would be appreciated. I've gathered that you have to use those horrible integral formulars and rho. xx
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  2. #2
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    I suggest that you have gathered correctly. Feel free to demonstrate it. Well, you have one thing not quite right. The formulas aren't that bad. Just do it.

    Let's see what you get.
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  3. #3
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    If you want to see some horrible maths...

    7.

    Mx = Intergal between r and 0 of x root(r^2 -x^2) dx

    = -2/6 (r^2 - x^2)^3/2 = -2/6
    -
    =(r^2)^3/2 = -2/6 r^4/3

    / 1/4 pi r^2


    Am I on the right lines?
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  4. #4
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    I did 11 actually for my last math homework. Here are the basic integrals:

    Centroid: (\overline{x}, \overline{y})

    \overline{x} = \frac{\int_0^1 x(x - x^2)dx}{\int_0^1 (x-x^2)dx}

    \overline{y} = \frac{\int_0^1 y(\sqrt{y} - y)dy}{\int_0^1 (x-x^2)dx}

    I'm not going to tell you the answer though. But they should be clean decimals.
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    I suggest that you have gathered correctly. Feel free to demonstrate it. Well, you have one thing not quite right. The formulas aren't that bad. Just do it.

    Let's see what you get.
    I suppose this was more like moral support than anything but thanks all the same. I managed to solve them. x
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  6. #6
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    You didn't do ALL the integrals for the middle one, did you? I hope you exploited the symmetry in the horizontal direction.
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