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    Resultant Force on Eyebolt

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    Determine the resultant force acting on the eyebolt shown in the attached figure, as a result of the four forces shown, both analytically and graphically. Compare and comment on the two results.

    See the attached file.

    © BrainMass Inc. brainmass.com December 24, 2021, 11:08 pm ad1c9bdddf
    https://brainmass.com/business/business-math/resultant-force-eyebolt-541285

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Convention for unit vector
    Upward (+y axis): j; downward (-ve y axis): -j; right side (=ve x axis): i; left side (-ve x axis): -i
    Hence, foces in vector form in cartesian system

    F1 = 800kN (-j)
    F2 = 400 kN (-j)
    F3 = 300kN (-i cos(50) - j sin(50)) = 300 (- 0.643 i - -.766 j) = (- 192.84 i -229.81j)
    F4 = 20 kN (-i cos(45) + j sin(45)) = 20 (- 0.70 i + 0.707 j) = (-14.14 i + 14.14 j)

    Note: Fi == Fi vector; |Fi| == magnitude of Fi vector

    Resultant force,
    R = F1 + F2 + F3 + F4
    = - 800 j - 400 j + (- 192.84 i -229.81j) + (-14.14 i + 14.14 j)
    = - 206.98 i - 1415.77 j

    Magnitude of resultant force,
    |R| = sqrt (206.98^2 + 1415.77^2) = 1430.82 kN --Answer

    Direction:
    theta (-ve x to -ve y direction) = tan-1(1415.77/206.98) = 81.685 degree --Answer

    For graphical part, see attachment.
    Note: Graphical part: Please measure the length of the resultant, and see result. Result should be more or less similar to what we are getting here. There may be a small error in graphical method, because of inaccuracy in drawing exact angle and length.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:08 pm ad1c9bdddf>
    https://brainmass.com/business/business-math/resultant-force-eyebolt-541285

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