question_answer 80)

                  There are four forces acting at a point P produced by strings as shown in Fig. which is at rest. Find the forces \[{{F}_{1}}\] and \[{{F}_{2}}\].

Answer:

                                    Since point P is at rest, so net force acting along x-axing is zero, that is,                                   \[{{F}_{1}}+\,(1N)\,\cos \,{{45}^{o}}\,-(2N)\,\sin \,{{45}^{o}}=0\]                 or \[{{F}_{1}}=\,(2N)\,\sin \,{{45}^{o}}-\,(1N)\,\cos \,{{45}^{o}}\]                 \[=\frac{2}{\sqrt{2}}\,N\,-\frac{1N}{\sqrt{2}}\,=\frac{1}{\sqrt{2}}\,N\]                 Net force acting along y-axis is also zero i.e. \[(1\,N)\sin 45{}^\circ +\,(2\,N)\cos 45{}^\circ {{F}_{2}}=0\]                 or \[{{F}_{2}}\,=\,\frac{1}{\sqrt{2}}+\,\frac{2}{\sqrt{2}}=\frac{3}{2}N.\]