Two-forces-F1-and-F2-of-magnitude-3-and-4-Newtons-are-inclined-at-angles-150-and-60-to-the-positive-x-axis-respectively-Find-the-resultant-force-

Question Number 178877 by Tawa11 last updated on 22/Oct/22

Two forces F1 and F2 of magnitude 3 and 4 Newtons are inclined at angles 150° and 60° to the positive x-axis respectively . Find the resultant force?

Answered by ARUNG_Brandon_MBU last updated on 22/Oct/22

Σ F_{x} : F_{2} \cos 60 ° - F_{1} \cos 30 ° = 2 - \frac{3 \sqrt{3}}{2}

Σ F_{y} : F_{2} \sin 60 ° + F_{1} \sin 30 ° = 2 \sqrt{3} + \frac{3}{2}

F = \sqrt{F_{x}^{2} + F_{y}^{2}}

= \sqrt{4 - 6 \sqrt{3} + \frac{27}{4} + 12 + 6 \sqrt{3} + \frac{9}{4}}

= \sqrt{16 + 9} = 5 units

\tan θ = \frac{F_{y}}{F_{x}} = \frac{4 \sqrt{3} + 3}{4 - 3 \sqrt{3}} = \frac{(4 \sqrt{3} + 3) (4 + 3 \sqrt{3})}{16 - 27}

= \frac{12 + 25 \sqrt{3} + 108}{- 11} = - \frac{120 + 25 \sqrt{3}}{11}

θ = 180 ° - \arctan (\frac{120 + 25 \sqrt{3}}{11})

Resultant force is of magnitude 5 units inclined

at angle θ from positive x - axis .

Commented by Tawa11 last updated on 22/Oct/22

God bless you sir . I appreciate .

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