Exercice Corrige Pdf - Equilibre D 39-un Solide Soumis A 3 Forces

Ignore friction at the hinge.

Numerically: (\tan50° \approx 1.1918) → ( \tan\alpha \approx 2.3836) → ( \alpha \approx 67.2°) above horizontal? That seems too steep. Let's check: I is above and left of A? No, A is at origin, I has x positive (2.5cos50°=1.607), y positive (5sin50°=3.83). So R points up-right? But rope pulls left, so hinge must pull right-up to balance. Yes, so R angle ≈ 67° from horizontal upward right. Ignore friction at the hinge

Forces in y-direction: [ R_y = W = 200 , N ] Let's check: I is above and left of A

Given the intersection I, distances: Let’s put coordinates: A = (0,0), B = (5 cos50°, 5 sin50°). Weight at midpoint M = (2.5 cos50°, 2.5 sin50°). Rope at B, horizontal left. Intersection I: Horizontal line through B: y_B = 5 sin50°. Vertical through M: x_M = 2.5 cos50°. But rope pulls left, so hinge must pull right-up to balance

Forces in x-direction: [ R_x = T \quad (\textsince R \text has a horizontal component toward the right) ]

Then equilibrium: Horizontal: ( R\cos\alpha = T ), Vertical: ( R\sin\alpha = W = 200 ) N.

So ( R = \frac200\sin\alpha = \frac200\sin 67.2° \approx \frac2000.922 \approx 216.9 , N).