Question

If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is
A.30°
B.60°
C. 90°
D.120°

Answer 1

The angle between the two forces is θ = 120°

Explanation:

Let the two forces be P and Q

|P| = |Q|

Given

Also R = P

R = √ P^2 + Q^2 + 2PQcos θ

P =  √ P^2 + P^2 + 2P^2 cosθ

P = √2P^2 ( 1 + cosθ)

P = P √ 2 x 2 cos^θ/2

1 = √ 4 cos^2θ/2

1 = 2 cosθ/2

cosθ/2 = 1/2

cosθ/2 = cos(60)

θ/2 = 60

θ = 120°

Hence the angle between the two forces is θ = 120°