Forces (F_{1} = (10 N, 090°), F_{2} = (20 N, 210°)) and (F_{3} = (4 N, 330°)) act on a body at rest on a smooth table. Find, correct to one decimal place, the magnitude of the resultant force.
Explanation
(F_{R} = F_{1} + F_{2} + F_{3})
(F_{1} = (10 N, 090°) = begin{pmatrix} 10 cos 90 \ 10 sin 90 end{pmatrix} = begin{pmatrix} 0 \ 10 end{pmatrix})
(F_{2} = (20 N, 210°) = begin{pmatrix} 20 cos 210 \ 20 sin 210 end{pmatrix} = begin{pmatrix} -10sqrt{3} \ – 10 end{pmatrix})
(F_{3} = (4 N, 330°) = begin{pmatrix} 4 cos 330 \ 4 sin 330 end{pmatrix} = begin{pmatrix} 2sqrt{3} \ -2 end{pmatrix})
(F_{R} = begin{pmatrix} 0 \ 10 end{pmatrix} + begin{pmatrix} -10sqrt{3} \ -10 end{pmatrix} + begin{pmatrix} 2sqrt{3} \ -2 end{pmatrix})
= (begin{pmatrix} -8sqrt{3} \ -2 end{pmatrix})
(|F_{R}| = sqrt{(8sqrt{3})^{2} + (-2)^{2}})
= (sqrt{192 + 4} )
= (sqrt{196} = 14 N)