Question

Find shown in the figure P and Q are two unknown forces. There resultant is 18 N along x-axis. ​

Answer 1

Answer:

Explanation:

F₁ = 160

F₂ = 80

θ = 90°

In the figure , F1 and F2, the two unknown forces give a resultant of 80√3 along the y-axis. It is required that F2 must have minimum magnitude. Find the magnitudes of F1 and F2

F₁Cos30° + F₂Cosθ = 80√3

F₁Sin30° = F₂Sinθ

=>F₁/2 = F₂Sinθ

=> F₂ = F₁/2Sinθ

=> F₂ = F₁Cosecθ/2

Differentiating

=> d F₂/dθ = (F₁/2)(- Cosecθ * Cotθ)

- Cosecθ * Cotθ = 0

=> Cosθ/Sin²θ = 0

=> Cosθ = 0

=> θ = 90°

F₂ = F₁/2Sinθ

=>F₂ = F₁/2

=> F₁ = 2F₂

F₁Cos30° + F₂Cosθ = 80√3

=> F₁√3/2 + 0 = 80√3

=> F₁ = 160

=> F₂ = 80