> [!summary] Static friction is the friction of objects that don't move > **Key Equations:** > Static friction inequality: $f_s \leq f_{max}$ >[!info]+ Read Time **⏱ 1 min** # Definition Static force is the friction created by an object to keep it in place. Friction is created by [[Newton Laws|Newton's second and third laws]]. For there to be static friction, the object must not move, and the forces must be balanced. The amount of friction present on a system is described as the coefficient of static friction. This describes the surface the object is on creating static friction. Mathematically, static friction is described as an inequality where it is less or equal to the coefficient of static friction times the magnitude of the normal force. $\begin{array}{c} f_s \leq f_{max} \\ f_s \leq \mu_s |\vec{N}| \end{array}$ ## Examples > [!example] Static friction of the box on the slope Determine the minimum coefficient of static friction for the box not to slide down the ramp. > ![[dy_4.png|300]] > > $ \begin{array}{c} x: \\ Nsin(\theta) - f_s cos(\theta) = 0 \\ \\ y: \\ f_s sin(\theta) + Ncos(\theta) -mg = 0 \\ \\ N = mgcos(\theta)\\ f_s = mgsin(\theta) \\ \text{So from the inequality} \\ f_s \leq f_{max} \\ f_s \leq \mu_s N \\ mgsin(\theta) \leq \mu_s mgcos(\theta) \\ tan(\theta) \leq \mu_s \end{array} > $ --- > 📂 Want to see more structured notes like these? > Help grow the project by [starring Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidian-MathMatter). ---