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Math Help - moments-with forces applied at an angle.

  1. #1
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    moments-with forces applied at an angle.

    The bar shown is hinged at H and it is in equilibrium. Find the angle  \theta


    I really don't know were to start, how do I find the angle when i don't know the value of any other sides except for the hypotenuse?
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  2. #2
    MHF Contributor
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    Hi

    The 20N force can be separated into 2 parts : 20 cos(theta) i + 20 sin(theta)j
    The projection on x axis (20 cos(theta)) gives no momentum with respect to H
    The projection on y axis (20 sin(theta)) gives a momentum with respect to H equal to 20 sin(theta) x 5
    The bar being at equilibrium, this momentum must be equal to the one generated by the 15N force, which is 15 x 1
    20 sin(theta) x 5 = 15 x 1
    sin(theta) = 3/20 = 0.15
    theta = 8.6 deg
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  3. #3
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    Let pivot be at H. Therefore:
    \tau_{\text{clockwise}}=\tau_{\text{anticlockwise}  }

    You may have forgotten this if you dealt with perpendicular forces mostly, so recall that \tau = F\cdot d\sin{\theta}. Therefore:
    15 = (20)(5)\sin{\theta}

    Edit: running beat me to it. Although with simple problems like these, I think it's better to deal with torques as scalars.
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