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    A rope is wrapped around a pole so that a force of 75 lbs acts on one end and a force of 53 lbs acts on the other end. If the angle between the two forces is 114 degrees what is the resultant force? What angle does the resultant force make with the 53 lbs force?

    © BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/resultant-force-example-problem-31033

    SOLUTION This solution is FREE courtesy of BrainMass!

    Let the direction of the 53 LBS force be the x axis
    Angle between the two forces = 114 degrees

    x component of the 75 LBS force= 75 Cos 114 = -30.51 LBS
    y component of the 75 LBS force= 75 Sin 114 = 68.52 LBS

    Total force in the x direction= 22.49 LBS =53-30.51
    Total force in the y direction= 68.52 LBS

    Resultant force = square root of {(x component)^2 + (y component)^2}= 72.12 LBS

    Angle between the resultant and direction of 53 LBS force ( x axis) = tan inverse ( y component / x component)
    = tan inverse (68.52/22.49)= 71.82 degrees

    Answer:
    Magnitude of resultant force= 72.12 LBS
    angle between resultant and 53 LBS force= 71.82 degrees

    This can also be solved taking the direction of 75 LBS force as the x axis

    Let the direction of the 75 LBS force be the x axis
    Angle between the two forces = 114 degrees

    x component of the 53 LBS force= 53 Cos 114 = -21.56 LBS
    y component of the 53 LBS force= 53 Sin 114 = 48.42 LBS

    Total force in the x direction= 53.44 LBS =75-21.56
    Total force in the y direction= 48.42 LBS

    Resultant force = square root of {(x component)^2 + (y component)^2}= 72.11 LBS

    Angle between the resultant and direction of 75 LBS force ( x axis) = tan inverse ( y component / x component)
    = tan inverse (48.42/53.44)= 42.18 degrees
    Therefore angle between 53 LBS force and resultant = 114-42.18 =71.82

    Answer:
    Magnitude of resultant force= 72.11 LBS
    angle between resultant and 53 LBS force= 71.82 degrees

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

    © BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf>
    https://brainmass.com/math/vector-calculus/resultant-force-example-problem-31033

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