1. **Problem Statement:** We need to solve a problem involving jointed wedges, which typically involves forces and equilibrium conditions. 2. **Key Concept:** For wedges in equilibrium, the sum of forces in both horizontal and vertical directions must be zero. The friction and normal forces at the contact surfaces are important. 3. **Formula:** The equilibrium conditions are: $$\sum F_x = 0$$ $$\sum F_y = 0$$ 4. **Step-by-step solution:** - Identify all forces acting on each wedge. - Resolve forces into components. - Write equilibrium equations for each wedge. - Use the friction condition: $$f = \mu N$$ where $f$ is friction force, $\mu$ is coefficient of friction, and $N$ is normal force. - Solve the system of equations simultaneously. 5. **Example:** Suppose two wedges with angles $\theta_1$ and $\theta_2$ are jointed and a force $F$ is applied. - Write horizontal equilibrium: $$F - N_1 \cos \theta_1 - N_2 \cos \theta_2 = 0$$ - Write vertical equilibrium: $$N_1 \sin \theta_1 - N_2 \sin \theta_2 = 0$$ 6. **Intermediate step:** Simplify and solve for $N_1$ and $N_2$: $$N_1 = \frac{N_2 \sin \theta_2}{\sin \theta_1}$$ Substitute into horizontal equation: $$F - \frac{N_2 \sin \theta_2}{\sin \theta_1} \cos \theta_1 - N_2 \cos \theta_2 = 0$$ 7. **Final step:** Solve for $N_2$: $$N_2 = \frac{F}{\frac{\sin \theta_2}{\sin \theta_1} \cos \theta_1 + \cos \theta_2}$$ Then find $N_1$ using the relation above. This approach allows solving jointed wedge problems by applying equilibrium and friction conditions.