Question

What is the angle between two forces of equal magnitude, `F_a` and `F_b`, when the magnitude of their resultant is also equal to the magnitude of either of these forces?

Answer 1

`theta=(2pi)/3`

Explanation:

Let the angle between `F_a and F_b` be `theta` and their resultant is `F_r` So

`F_r^2=F_a^2+F_b^2+2F_aF_bcostheta`
Now by the given condition
let `F_a=F_b=F_r=F`

So

`F^2=F^2+F^2+2F^2costheta`

`=>costheta=-1/2=cos(2pi/3)`

`:.theta=(2pi)/3`