Question

Two forces with equal magnitude f act on a body and the magnitude of the resultant force is f/3.theanglebetweenthetwoforces

Answer 1

The angle between the two forces is given by $cos^{-1}(\frac{-17}{18})$

• Force is a vector quantity.
• Magnitude of the resultant of two vectors acting at a point is calculated using parallelogram law of vectors.

                         $R = \sqrt{F_{1} ^{2}+F_{2} ^{2}+2F_{1}F_{2} cos\alpha }$

• Given,

                        R = F/3

                        $F_{1} = F_{2} = F$

                       $(\frac{F}{3}) ^{2} = {F ^{2}+ F^{2}+2FF cos\alpha }$

                         1/9 = 2 + 2cos$\alpha$

                         1/9 = 2(1 + cos$\alpha$)

                         1/18 = 1 + cos$\alpha$

                         1/18 -  1 = cos$\alpha$

                          cos$\alpha$ = -17/18

                          $\alpha$ = $cos^{-1}(\frac{-17}{18})$