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Math Help - Force on one face of a right triangle

  1. #1
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    Force on one face of a right triangle

    Got no idea how to solve this problem. All I know is that it's related to differential calculus and most definitely use vectors.


    Find the force on one face of a right triangle of sides 4 meters and altitude of 3 meters. The altitude is submerged vertically with the 4 meter side in the surface.


    Can anyone show me how ?
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  2. #2
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    The selections by the way are

    a. 58.86 kNewton
    b. 53.22 kNewton
    c. 62.64 kNewton
    d. 66.27 kNewton
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  3. #3
    Senior Member
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    Pressure of water at depth h is:
    P(h) = \rho g h.

    Where \rho is the density of water, and g the acceleration due to gravity.

    Total force on triangle is then

    \displaystyle \int_A P(h) dA = \int_A (\rho g h) dA = \int_0^3 \int_0^{4 - \frac{4}{3}h} (\rho g h) dw dh

    Where dw is along the width of the triangle.

    I get about 58.8 kN.
    Last edited by snowtea; December 18th 2010 at 08:01 AM.
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