Question

Hamida is pushing a table in a certain direction with a force of magnitude 10 N. At the same time her, classmate Lila is pushing the same table with a force of magnitude 8 N in a direction making an angle of 60o to the direction in which Hamida is pushing.

Calculate the magnitude of the resultant force on the table and its direction.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{magnitude}\mathrm{of}\mathrm{the}\mathrm{resultant}\mathrm{of}\mathrm{two}\mathrm{forces}\mathrm{of}10\mathrm{N}\mathrm{and}8\mathrm{N}\mathrm{making}\mathrm{an}\mathrm{angle}{60}^0\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{R}=\sqrt{{10}^2+8^2+2\times 10\times 8\times \cos 60} \\ =\sqrt{244} \\ =15.6\mathrm{N} \\ \mathrm{The}\mathrm{direction}\mathrm{of}\mathrm{the}\mathrm{resultant}\mathrm{force}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{the}\mathrm{force}10\mathrm{N}\mathrm{is}\mathrm{given}\mathrm{as}, \\ \tan \mathrm{\theta }=\frac{8\sin 60}{10+8\cos 60} \\ =0.49 \\ \mathrm{or}\mathrm{\theta }={\tan }^{-1}(0.49) \\ ={26}^{0}6\text{'} \end{gathered}$$