Static Friction

When two surfaces are in contact but not sliding, static friction prevents relative motion. This force adjusts its magnitude and direction to oppose whatever would cause slipping.

The magnitude of static friction $f_s$ ranges from zero up to a maximum:

Here $\mu_s$ is the coefficient of static friction (a dimensionless constant for the two materials) and $N$ is the normal force magnitude. Static friction takes on whatever value is needed to prevent slipping, up to $f_{s,\text{max}} = \mu_s N$. When the applied force reaches this maximum, the object is on the verge of slipping—called impending motion.

The direction of static friction is always opposite to the direction the object would slip if there were no friction. For example, if you push gently on a book resting on a table, static friction pushes back on the book opposite to your applied force, keeping it stationary.

In this diagram, an applied force $\vec{F}_{\text{app}}$ pushes right on a stationary box.

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