Static Friction

What static friction is

Static friction is the force that prevents two surfaces in contact from sliding relative to each other.

It is a self-adjusting force — it takes whatever value is needed to prevent sliding, up to a maximum limit.

$f_s \leq \mu_s N$

where $\mu_s$ is the coefficient of static friction and $N$ is the normal force between the surfaces.

The self-adjusting nature

This is what makes static friction different from kinetic friction.

Push a heavy box with a small force. The box does not move. Static friction exactly equals your push — it adjusts to match. Push harder. The box still does not move. Friction increases to match your push again.

Push hard enough, and the box finally moves. At that point, static friction has reached its maximum value $\mu_s N$ — called limiting friction — and can no longer increase to prevent sliding.

Where the friction force comes from

At the microscopic level, surfaces are not perfectly smooth. Even surfaces that appear smooth have microscopic asperities — tiny bumps and valleys. When two surfaces are in contact, these asperities interlock.

Static friction arises from:

• Mechanical interlocking of surface asperities
• Adhesive forces (molecular attraction) between surface atoms in contact

The normal force $N$ pushes the surfaces together harder, increasing the real area of contact and thus the total interlocking and adhesion — which is why friction is proportional to $N$.

What $\mu_s$ depends on

The coefficient of static friction $\mu_s$ depends on:

• The materials of the two surfaces in contact
• The surface condition (dry, wet, lubricated, rough, polished)

It does not depend on:

• The area of contact (a surprising result — a large block and a small block of the same material have the same $\mu_s$)
• The magnitude of the normal force

Direction of static friction

Static friction acts opposite to the direction of impending motion — the direction the body would move if friction were removed.

It is not always opposite to the applied force. If a force is applied at an angle, the impending motion might be in a different direction, and friction opposes that direction.

Static friction and equilibrium

For a body in static equilibrium on a rough surface:

$f_s = F_{applied} \quad \text{(if body does not move)}$

The static friction force equals whatever is needed for equilibrium — it is found from the equilibrium condition, not from $\mu_s N$.

$\mu_s N$ only gives the maximum value. The actual value of static friction is determined by the equilibrium equations.