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    Three forces act through the point O in the directions shown in the figure in the attachment. The magnitudes of the forces are 15kN, 10kN and P. The resultant R acts at an angle of 10 degrees to Ox. Find the magnitudes of P and R.

    © BrainMass Inc. brainmass.com December 24, 2021, 9:44 pm ad1c9bdddf
    https://brainmass.com/physics/scalar-and-vector-operations/directions-magnitudes-resultant-vectors-408266

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Three forces act through the point O in the directions shown in the figure below. The magnitudes of the forces are 15kN, 10kN and P. The resultant R acts at an angle of 10 degrees to Ox. Find the magnitudes of P and R.

    y

    Solution: Resolving 15 kN, 10 kN and P into x and y components and adding them to get the net x and y components of the three forces:

    Fx = 15cos75O + 10cos30O + Pcos60O = 3.88 + 8.66 + 0.5P = 12.54 + 0.5P .......(1)

    Fy = 15sin75O + 10sin30O - Psin60O = 14.49 + 5 + 0.87P = 19.49 - 0.87P .......(2)

    Fx
    α = 10O
    R
    Fy

    Fy/Fx = tan α

    (19.49 - 0.87P)/(12.54 + 0.5P) = tan10O = 0.176

    19.49 - 0.87P = 2.2 + 0.088P

    P = 18 kN

    ____________________________
    Magnitude of R = √(12.54 + 0.5P)2 + (19.49 - 0.87P)2

    Substituting for P in the above, we get:
    ________________________________
    R = √(12.54 + 0.5x18)2 + (19.49 - 0.87x18)2 = 21.88 kN

    R = 21.88 kN

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

    © BrainMass Inc. brainmass.com December 24, 2021, 9:44 pm ad1c9bdddf>
    https://brainmass.com/physics/scalar-and-vector-operations/directions-magnitudes-resultant-vectors-408266

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