Forces of magnitude 3N, 4N and 2N act along the vectors (j ; -i + j) and (i + j) respectively. Calculate, correct to one decimal place, the magnitude of the resultant of the forces.
Explanation
Resultant :
(R = R_{1} + R_{2} + R_{3})
= (begin{pmatrix} -4 cos 45 \ -4 sin 45 end{pmatrix} + begin{pmatrix} 0 \ 3 sin 90 end{pmatrix} + begin{pmatrix} 2 cos 45 \ 2 sin 45 end{pmatrix})
= (begin{pmatrix} -2sqrt{2} \ -2sqrt{2} end{pmatrix} + begin{pmatrix} 0 \ 3 end{pmatrix} + begin{pmatrix} sqrt{2} \ sqrt{2} end{pmatrix})
= (begin{pmatrix} – sqrt{2} \ 3 – sqrt{2} end{pmatrix})
(|R| = sqrt{(-sqrt{2})^{2} + (3 – sqrt{2})^{2}})
= (sqrt{2 + 11 – 2sqrt{2}})
= (sqrt{13 – 2sqrt{2}})
= (10.1718)
(|R| = 3.1893 approxeq 3.2N)