Equilibre D 39un Solide Soumis A 3 Forces Exercice Corrige Pdf Exclusive Fix May 2026

TITLE: EQUILIBRIUM OF A SOLID SUBJECTED TO THREE FORCES

Méthode B : Résolution analytique (Par projection)

On projette la relation vectorielle $\vecP + \vecT_1 + \vecT_2 = \vec0$ sur un repère orthonormé $(O, \veci, \vecj)$, avec l'axe $(Ox)$ horizontal et $(Oy)$ vertical.

Sur l'axe vertical (Oy) : $-P + T_2 \sin(30^\circ) = 0$ $T_2 \sin(30^\circ) = P$ $T_2 \times 0,5 = 100$ $T_2 = \frac1000,5 = \mathbf200\text N$.
Sur l'axe horizontal (Ox) : $-T_1 + T_2 \cos(30^\circ) = 0$ $T_1 = T_2 \cos(30^\circ)$ $T_1 = 200 \times \frac\sqrt32$ $T_1 = 100\sqrt3 \approx \mathbf173\text N$. TITLE: EQUILIBRIUM OF A SOLID SUBJECTED TO THREE

Conclusion : Le câble oblique supporte tout le poids ($200\text N$), tandis que le câble horizontal équilibre la composante horizontale de la tension oblique ($173\text N$).

✅ Strengths (What to expect from a good resource)

Clear theoretical recap – Usually includes the three conditions for equilibrium of a solid under 3 non-parallel forces: Sur l'axe vertical (Oy) : $-P + T_2
- The three forces must be coplanar.
- Their lines of action are concurrent (meet at one point).
- The vector sum is zero → closed force triangle (dynamic method) or polygon.
Step-by-step corrections – Good PDFs show:
- Isolating the solid.
- Identifying forces (weight, tension, reaction, etc.).
- Using graphical method (force triangle) or analytical method (projection on axes).
Variety of typical problems:
- Rod leaning against a wall and floor.
- Object suspended by two cables.
- Beam on two supports with an additional force.
- Sphere in a V-shaped groove.
Diagrams – Essential for understanding concurrence and force directions.
Exclusive claim – Might include original problems, detailed teacher commentary, or exam-style questions with marking schemes. Sur l'axe horizontal (Ox) : $-T_1 + T_2

C. Le Cas Particulier : Les Forces Parallèles

Si les trois forces sont parallèles entre elles, la condition de concourance ne s'applique pas. Dans ce cas, l'équilibre est régi par la loi des leviers (somme des moments nulle). Cependant, dans la grande majorité des exercices scolaires classiques, on se retrouve avec trois forces concourantes.