Question

find the angle between two forces of magnitude 27N and 30N if the magnitude of the resultant of the two force is 8N​

Answer 1

Answer:

$\theta=165^{\circ}$

Explanation:

$F_1=27\ N$

$F_2=30\ N$

Resultant of two forces, F = 8 N

It is required to find the angle between two forces. The resultant of two force is given by the :

$F=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta}$

$\theta$ is the angle between F₁ and F₂

So,

$F^2=F_1^2+F_2^2+2F_1F_2\cos\theta\\\\\cos\theta=\dfrac{F^2-F_1^2-F_2^2}{2F_1F_2}\\\\\cos\theta=\dfrac{(8)^2-(27)^2-(30)^2}{2\times 27\times 30}\\\\\cos\theta=-0.966\\\\\theta=\cos^{-1}\left(-0.966\right)=165^{\circ}$

So, the angle between two forces is 165 degrees.