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Math Help - Lamina Workouts

  1. #1
    Junior Member Selim's Avatar
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    Lamina Workouts

    Given a lamina of uniform density \rho, bounded by y = \sqrt{x} , y=0 ,  x=4.

    1. Set up an integral to find m, the mass of the lamina.
    2. Find m, the mass of the lamina
    3. Set up Integral to find Mx
    4. Find Mx
    5. Set up integral to find My
    6. Find My
    7. Find the center of mass.
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  2. #2
    Junior Member Selim's Avatar
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    m = \rho \int_0^4 \sqrt{x} * dx = \frac{16}{3}

    Mx = \rho \int_0^4 \frac{\sqrt{x}}{2} * \sqrt{x}  * dx = 4

    y = \frac{.25}{3} = \frac{1}{12}

    Center: (x, \frac{1}{12})

    My = ?
    Last edited by Selim; February 25th 2010 at 04:11 PM.
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  3. #3
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    Quote Originally Posted by Selim View Post
    m = \rho \int_0^4 \sqrt{x} * dx = \frac{16}{3}

    Mx = \rho \int_0^4 \frac{\sqrt{x}}{2} * \sqrt{x} * dx = 4

    y = \frac{.25}{3} = \frac{1}{12}

    Center: (x, \frac{1}{12})

    My = ?
    m= \frac{16}{3}\rho

    M_x=4\rho

    y = \frac{M_x}{m} = \frac{3}{4}

    M_y=\rho\int_0^4x\sqrt{x}\,dx

    x=\frac{M_y}{m}
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