Question

the resultant of two forces one double the other in magnitude is perpendicular to the smaller one of the two forces. the angle between the two forces is?

Answer 1

Let the forces be F1 and F2 respectively.

Also,

Let, F1 = x and F2 = 2x

Clearly, force F1 is smaller.

So,

We know,

tan ɑ = F2sinθ / F1 + F2cosθ

tan 90° = F2sinθ / F1 + F2cosθ

Here,

tan 90° = undefined

We get undefined because the numerator on the right hand side is divided by 0,

Therefore,

F1 + F2cosθ = 0

F2cosθ = -F1

Substituting values of F1 and F2 respectively,

=> 2x(cosθ) = -x

=> cosθ = -x/2x

=> cos θ = -1/2

We know,

cos 120° = -1/2 So,

θ = 120°

Hence, angle between the two forces is 120°

Answer 2

Answer:

120°

Explanation:

From the attached figure :

  cosA = base / hypotenuse

⇒ cosA = C / 2C

⇒ cosA = 1 / 2

⇒ cosA = cos60°

⇒ A = 60°

 

Angle between two vectors is taken from anticlockwise direction :

⇒ Angle between them = 180° - 60°

                          = 120°