Answer to Question #259872 in Analytic Geometry for Hamad

Question

Two forces act a point The magnitude of the Two forces are F, 2 newton and the measure of the angle between them is 60, if their resultant equal 2√3 newton,then F =newton

Answer 1

Given: Two forces as 2 N and F N, angle between them is $60\degree$and their resultant is $2\sqrt{3}$ N.

We know that,

$R=\sqrt{R_1^2+R_2^2+2R_1R_2\cos\theta}$

$\Rightarrow 2\sqrt{3}=\sqrt{2^2+F^2+2\times2\times F\cos 60\degree} \\\Rightarrow 2\sqrt{3}=\sqrt{4+F^2+2F} \ [\because \cos 60\degree=\frac 1 2] \\\Rightarrow 12=4+F^2+2F \\\Rightarrow F^2+2F-8=0 \\\Rightarrow (F-2)(F+4)=0 \\\Rightarrow F=2,-4 \\\text{As the magnitude of force can't be negative } \\So, F=2N$