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13 December, 20:30

determine the required values of the tension in ac and ad so that the resultant of the three forces applied at A is verticalFigure:A wire is coupled from three sides

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  1. 13 December, 22:42
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    Fac = 21 KN

    Fad = 64.29 KN

    Explanation:

    Step 1: Find the unit vectors in BA, CA, and DA directions

    BA = - 16 i + 48 j - 12 k

    CA = - 16 i + 48 j + 24 k

    DA = 14 i + 48 j

    The following magnitudes

    mag (BA) = sqrt (16 ^2 + 48^2 + 12^2) = 52

    mag (CA) = sqrt (16 ^2 + 48^2 + 24^2) = 56

    mag (DA) = sqrt (14 ^2 + 48^2) = 50

    Now compute unit vectors

    unit (BA) = (-4 / 13) i + (12 / 13) j - (3 / 13) k

    unit (CA) = (-2 / 7) i + (6 / 7) j - (3 / 7) k

    unit (DA) = (7 / 25) i + (24 / 25) j

    Step 2: Compute Force Vectors F (ml) dot unit (ML)

    Fab = (-4*Fab / 13) i + (12*Fab / 13) j - (3*Fab / 13) k

    Fac = (-2*Fac / 7) i + (6*Fac / 7) j - (3*Fac / 7) k

    Fad = (7*Fad / 25) i + (24*Fad / 25) j

    Step 3: Equilibrium force equations in x and z direction

    Fr, x = 0 = 39 * (-4 / 13) - Fac * (2 / 7) + Fad * (7 / 25)

    Fr, z = 0 = 39 * (-3 / 13) + Fad * (3 / 7)

    Step 4: Solve the above equations for Fca and Fda

    Fca = 21 KN

    Fda = 64.29 KN
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