Three forces with magnitudes 300 Newtons, 180 Newtons, and 250 Newtons act on an object at angles −30◦ , 45◦ , and 135◦ with the positive x-

Question

Three forces with magnitudes 300 Newtons, 180 Newtons, and 250 Newtons act on an object at angles −30◦ , 45◦ , and 135◦ with the positive x-axis, respectively. Find the direction and magnitude of the resultant of these forces.

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Vivian 3 months 2022-02-16T15:10:30+00:00 1 Answer 0 views 0

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    2022-02-16T15:12:00+00:00

    Answer:

      261∠36° Newtons

    Step-by-step explanation:

    A straightforward way to find the resultant is to add the x- and y-components of the forces:

      r = 300(cos(-30°), sin(-30°)) +180(cos(45°), sin(45°)) +250(cos(135°), sin(135°))

      = (300√3/2 +180√2/2 -250√2/2, -300/2 +180√2/2 +250√2/2)

      = (150√3 -35√2, -150 +215√2)

      ≈ (210.310, 154.056)

      ≈ 260.698∠36.22°

    The resultant is approximately 261 Newtons at an angle of 36°.

    _____

    From components (x, y), the angle is found as arctan(y/x). The magnitude is found as √(x²+y²).

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45:7+7-4:2-5:5*4+35:2 =? ( )