Cho hệ cơ học như hình vẽ: Thanh AB = 3cm, trọng lượng 100N. Vât m có trọng lượng P = 50N. Thanh AB được giữ cân bằng nhờ dây CD; góc α = 30 độ. Tính các lực tác dụng lên thanh AB, biết AC = 2cm

To solve the problem, we need to analyze the system of forces acting on the beam AB.

1. **Given Data**:
- Length of AB (L) = 3 cm
- Weight of the beam (W) = 100 N
- Weight of mass (P) = 50 N
- Distance AC = 2 cm
- Angle α = 30°

2. **Identify the Forces**:
- The weight of the beam acts at its center (1.5 cm from A).
- The weight of mass P acts downward at point C (2 cm from A).
- Tension in cable CD, which we'll denote as T.

3. **Set up the Equilibrium Conditions**:
Since the system is in equilibrium, we apply the following conditions:
- **Sum of vertical forces (Y-axis)**:
\[
T \, \text{(vertical component)} - W - P = 0
\]

- **Sum of moments about point A** (to eliminate the weight of the beam):
- Moment due to the weight of the beam = \(\frac{W \cdot L}{2} = \frac{100 \cdot 1.5}{100} = 150 \, \text{N.cm}\)
- Moment due to the weight of the mass P = \(P \cdot 2\)
- Moment due to tension (considering the vertical component): \(T \cdot 2 \cdot \sin(30^\circ)\)

\[
\sum M_A = 0 = T \cdot 2 \cdot \sin(30^\circ) - 150 - (50 \cdot 2)
\]

4. **Calculate Components**:
- \(\sin(30^\circ) = \frac{1}{2}\)
- The equation becomes:
\[
T - 150 - 100 = 0
\]
\[
T = 250 \, \text{N}
\]

5. **Calculate the Vertical Component**:
To find the vertical component of the tension:
\[
T_y = T \cdot \sin(30^\circ) = 250 \cdot 0.5 = 125 \, \text{N}
\]

6. **Final Summary**:
The forces acting on the beam are:
- Tension in cable CD = 250 N
- Vertical reaction at A = 125 N (from the tension).
- The weights (100 N downwards for beam and 50 N downwards for mass).

**Conclusion**: The tension in the cable is **250 N**, and the upward force at A is **125 N**.