《 SECTION 5.2 defined static friction $\vec{f}{}_{\text{s}}$ as the force on an object that keeps it from slipping. FIGURE 6.11 shows a rope pulling on a box that, due to static friction, isn’t moving. The box is in equilibrium, so the static friction force must exactly balance the tension force:

To determine the direction of $\vec{f}{}_{\text{s}}$, decide which way the object would move if there were no friction. The static friction force $\vec{f}{}_{\text{s}}$ points in the opposite direction to prevent the motion.

FIGURE 6.11 Static friction keeps an object from slipping.

Unlike the gravitational force, which has the precise and unambiguous magnitude $F_{\text{G}}=mg$, the size of the static friction force depends on how hard you push or pull. The harder the rope in FIGURE 6.11 pulls, the harder the floor pulls back. Reduce the tension, and the static friction force will automatically be reduced to match. Static friction acts in response to an applied force. Figure 6.12 illustrates this idea.

FIGURE 6.12 Static friction acts in response to an applied force.

But there’s clearly a limit to how big $f_{\text{s}}$ can get. If you pull hard enough, the object slips and starts to move. In other words, the static friction force has a maximum possible size $f_{\text{s max}}$.

• An object remains at rest as long as $f_{\text{s}}{<}_{}{f}_{\text{s max}}$.

• The object slips when $f_{\text{s}}=f_{\text{s max}}$.

• A static friction force $f_{\text{s}}>f_{\text{s max}}$ is not physically possible.

Experiments with friction show that $f_{\text{s max}}$ is proportional to the magnitude of the normal force. That is,

where the proportionality constant ${\mu }_{\text{s}}$ is called the coefficient of static friction. The coefficient is a dimensionless number that depends on the materials of which the object and the surface are made. TABLE 6.1 shows some typical coefficients of friction. These are only approximate; the exact value of the coefficient depends on the roughness, cleanliness, and dryness of the surfaces.