three forces act on the bracket. determine the magnitude and direction θ of f₁ so that the resultant force…

three forces act on the bracket. determine the magnitude and direction θ of f₁ so that the resultant force is directed along the positive x - axis and has a magnitude of 800 n.\n\nsolution\n→f_{rx}=σf_x: 800 sin 60° = f₁ sin(60°+θ) + \\frac{12}{13}(180)\n↑f_{ry}=σf_y: 800 cos 60° = f₁ cos(60°+θ) + 200+\\frac{5}{13}(180)\n60° + θ = 81.34°\nθ = 21.3°\nf₁ = 869 n

three forces act on the bracket. determine the magnitude and direction θ of f₁ so that the resultant force is directed along the positive x - axis and has a magnitude of 800 n.\n\nsolution\n→f_{rx}=σf_x: 800 sin 60° = f₁ sin(60°+θ) + \\frac{12}{13}(180)\n↑f_{ry}=σf_y: 800 cos 60° = f₁ cos(60°+θ) + 200+\\frac{5}{13}(180)\n60° + θ = 81.34°\nθ = 21.3°\nf₁ = 869 n

Answer

Explanation:

Step1: Resolve forces in x - direction

$800\sin60^{\circ}=F_1\sin(60^{\circ}+\theta)+\frac{12}{13}(180)$

Step2: Resolve forces in y - direction

$800\cos60^{\circ}=F_1\cos(60^{\circ}+\theta)+200 + \frac{5}{13}(180)$

Step3: Solve for $\theta$

Given $60^{\circ}+\theta = 81.34^{\circ}$, so $\theta=21.3^{\circ}$

Step4: Solve for $F_1$

Substitute $\theta$ into equations to get $F_1 = 869\ N$

Answer:

$\theta = 21.3^{\circ},F_1 = 869\ N$