Answer to Question #248472 in Mechanics | Relativity for Arees

Question

Two forces of magnitude 6N and 10N are inclined at an angle of 60 degree with each other calculate the magnitude of the resultant and the angle made by the resultant with 6N force (R=14N, alpha =38.21

Answer 1

$a=6$ and $b=10$ , $\alpha =120^\circ$ and $\beta =60^\circ$ , $\vec{R}=\vec{a}+\vec{b}$

Cosine Rule: $R^2=a^2+b^2-2ab\cos \alpha =6^2+10^2-2\cdot 6\cdot 10\cdot \cos 120^\circ=136-120\cdot (-\tfrac{1}2{})=196=14^2$

$R=14$

Sine Rule: $\frac{14}{\sin 120^\circ}=\frac{10}{\sin \gamma}$ , $\sin \gamma =\frac{10\sin 120^\circ}{14}$ , $\gamma =\arcsin \frac{10\sin 120^\circ}{14}\approx 38.21^\circ$

Answer: $R=14$ and $\gamma=38.21^\circ$