Question

Two forces whose magnitudes are in the ratio 3 : 5 give a resultant of 28 N. If the angle between them is ${60}^{\circ }$, find the magnitude of each force and report $n$, where $n$ is the sum of the two forces in newtons.

Answer 1

Let $A$ and $B$ be the two forces.
Then $A=3x;B=5x;R=28N$ and $\theta ={60}^{\circ }$
Diving $A$ by $B$, $\frac{A}{B}=\frac{3}{5}$
We know that $R=\sqrt{A^2+B^2+2ABcos\theta }$
$\Rightarrow 28=\sqrt{(3x{)}^2+(5x{)}^2+2\left(3x\right)\left(5x\right)cos{60}^{\circ }}$
$\Rightarrow 28=\sqrt{9x^2+25x^2+15x^2}=7x\Rightarrow x=\frac{28}{7}=4$
Hence, the forces are: $A=3\times 4=12N,B=5\times 4=20N.$