1. **Stating the problem:** You need to understand how to use different formulas for mechanical actions, especially for calculating the reaction force of a plane and determining the correct formula to apply in various exercises. 2. **Understanding the context:** In mechanics, the reaction force of a plane or surface is often determined by considering equilibrium of forces and moments. The key is identifying what forces act on the body and how they interact. 3. **General approach:** When you want to find the reaction force $\mathbf{R}$ or its components, you often use the principle of equilibrium: $$\sum \mathbf{F} = 0 \quad\text{and}\quad \sum \mathbf{M} = 0$$ which mean the sum of forces and the sum of moments must be zero for a system at rest or in uniform motion. 4. **Formulas and usage:** - To find the normal reaction force $N$, use the balance of vertical forces: $$N = mg - F_{applied extunderscore vertical}$$ - To find frictional force $f$, use: $$f = \mu N$$ where $\mu$ is the coefficient of friction. - For moments, calculate using: $$\sum M = 0$$ to find unknown forces via torque equilibrium. 5. **Choosing the right formula:** - If the problem asks for force components or reaction on a surface, use force equilibrium equations. - If the problem involves rotation or lever arms, use moment equilibrium. - If friction is involved, ensure to include frictional force $f=\mu N$. 6. **Tips:** - Draw a detailed free-body diagram labeling all known and unknown forces. - Write equations for each direction (usually horizontal and vertical). - Use moments if forces create rotation or to eliminate unknowns. - Check units and signs carefully. 7. **Example:** If a block rests on a plane inclined at angle $\theta$ with mass $m$, the normal force is: $$N = mg\cos\theta$$ and the friction force to prevent slipping is: $$f \leq \mu N$$ **Summary:** Different formulas apply depending on whether you are dealing with normal force, friction force, or moments. Start with drawing forces, then apply equilibrium principles accordingly. Final answer: Use forces equilibrium ($\sum F=0$) for reaction forces and moments equilibrium ($\sum M=0$) for torque-related problems, including friction where needed.