If F1 = F2 = 30lb, determine the angles and so that the resultant force is directed along the positive x axis and has a magnitude of FR = 20 lb.

If F₁ = F₂ = 30lb, determine the angles  and  so that the resultant force is directed along the positive x axis and has a magnitude of F_R = 20 lb.

 

Solution

It may be possible to solve this problem using Parallelogram Method cause in answer both θ and πare same,

R= √(P^2 + Q^2 +2P*Q*Cos(α))
and
Cos(α) = (R^2 - P^2 - Q^2)/(2*P*Q)
= (20^2 - 30^2 - 30^2)/(2*30*30)
= -0.778.

α = Cos ^-1(-0.778).
α = 141.06 °
As α =π+ θ = 2θ or 2π
Since in answer it is mention that both are equal.
θ = α/ 2,
= 141.06 / 2,
= 70.52°