Question

Find the resultant /net/total force under the following conditions.

1) equal force acting on an object in different directions.

2) unequal forces acting on an object in a same direction and opposite direction.

Answer 1

$$\begin{gathered} Ifthe\mathrm{equal}\mathrm{force}\mathrm{acting}\mathrm{on}\mathrm{an}\mathrm{object}\mathrm{in}\mathrm{different}\mathrm{directions}then \\ Netforceis=\sqrt{F^2+F^2+2F^2\cos \theta }=2F\cos \theta /2 \\ whereFistheindividualforceand\theta theanglebetweenthem. \\ Ifthe\mathrm{unequal}\mathrm{forces}\mathrm{acting}\mathrm{on}\mathrm{an}\mathrm{object}\mathrm{in}\mathrm{same}/opposite\mathrm{direction} \\ Thenwecanwrite=\sqrt{{F_1}^2+{F_2}^2+2F_1{F}_2\cos \theta } \\ atanangle\left(\alpha \right)of \\ Tan\alpha =F_2\sin \theta /F_1+F_2\cos \theta \end{gathered}$$
$$\begin{gathered} insamedirection\theta =0^0 \\ F=F_1+F_2 \\ indifferentdirection\theta =180{}^o \\ F=F_1-F_2 \end{gathered}$$