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.

Answer 1

261∠36° Newtons

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°.

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