Question

Magnitude of resultant of two forces is equal to the magnitude of their difference. What is the angle between the two?

Answer 1

Answer:

Assuming the forces have a magnitude of 1 unit:

Rotate the plane such that Force 1 is pointing towards the positive x axis and the plane two forces lie on is the x-y plane.

Now let θ be the angle between Force 1 and Force 2.

Then, we can resolve these to 3 forces:

Fx1=1

Fx2=1×cosθ=cosθ

Fy2=1×sinθ=sinθ

Therefore, the magnitude of the resultant force will be

(Fx1+Fx2)2+F2y2−−−−−−−−−−−−−−−√

=(1+cosθ)2+sin2θ−−−−−−−−−−−−−−−√

=1

(1+cosθ)2+sin2θ=1=sin2θ+cos2θ

(1+cosθ)2=cos2θ

1+2cosθ+cos2θ=cos2θ

cosθ=−12

∴θ=120°=2π3rad

Answer 2

Hope this help...........