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.
Answers
Answer:
F₁ = 160
F₂ = 80
θ = 90°
Explanation:
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
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