Statics

The two forces shown act in the x-y plane of the T-beam cross section. If it is known that the resultant R of the two forces has a magnitude of 3.8 kN and a line of action that lies 14° above the negative x-axis, determine the magnitude of F1 and the orientation è of F2.

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  1. A description of the accompanying figure is required. Minimally, the directions of F1 and the magnitude of F2 are required.

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  2. The figure shown includes an x, y, and z axis. On the positive x-y plane, force F2 points toward the origin with a magnitude of 3kN and an angle theta between it and the positive x axis. On the negative x-y plane, force F1 points toward the origin with an angle of 27 degrees between it and the negative y axis.

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  3. Do your homework, son.

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  4. So you have three forces, the magnitude and angles of which two are known.

    You will need to first compile a table of known and unknown values.

    To avoid confusion, you need to follow these rules for describing forces:
    1. All angles are to be measured counter-clockwise from the positive x-axis.
    2. All forces should originate from the origin. If the force is towards the origin, add 180 degrees to convert it to originate from the origin.
    3. Unknown magnitude and angles should be given a variable name, so that forces can be summed along the x and y directions.

    So here's a summary table for you to complete (magnitudes are in N, and angles in degrees, measured CCW from +x axis). Remember all forces originate from the origin.

    Force magnitude angle (&alpha)
    F1 x -27
    F2 3 θ+180
    R 3.8 N -14

    Check the above table and draw a diagram to represent the forces.
    We can continue after that.

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