4.9: Solving Problems Using Newton's Second Law: Friction

Friction is the force between two surfaces in contact that opposes parallel motion between them. Kinetic friction is the friction between surfaces that are moving or sliding relative to each other. Static friction is the friction that occurs that prevents two surfaces from moving or sliding with respect to each other.

Static friction varies based on how much counter force is needed to prevent two objects from sliding. When a certain amount of force is applied to a stationary object in contact with a surface, static friction serves to counter that applied force in order to keep the object and surface in contact from sliding. The more force that is applied, the more static friction is summoned to counter it.

However, static friction is only so strong. So once the maximum static frictional force is summoned, the object will start to slide and the static friction force will give way to kinetic friction force. Generally, the maximum ability of static friction is higher than the maximum ability of kinetic friction. That is, once the maximum static friction force is met, the object undergoing applied force will jolt forward because the kinetic friction that took over is weaker than the maximum static friction force that held it previously.

Kinetic and static frictional forces are given by the equations:

$F_{fr,k}=\mu _{k}F_{N}$
$F_{fr,s}\leq \mu _{s}F_{N}$

Note that the static friction force equation is an inequality. That is because static friction only aims to counter potential movement or sliding between two surfaces, which vary based on the magnitude of the applied force. Both equations have a $\mu$ symbol which is called the coefficient of friction and depends solely on the types of materials that make up the two surfaces. For example, between steel and ice, the coefficient of friction would be very small (perhaps 0.1). However, between rubber and concrete, the coefficient of friction would be rather large (perhaps 0.8). The coefficient of friction is rarely larger than one.

We experience friction often in our everyday lives. For example, if you slide a box across a room, the box's motion will eventually stop due to the friction that occurs between the surface of the box and the surface of the floor. A box will slide relatively well across a smooth tile floor because the smooth tile floor provides a lower frictional force. It will slide less well across a floor with a rough carpet because the carpet provides a higher frictional force.

When we walk on a sidewalk our shoes do not generally slip because the static friction between our shoes and the sidewalk opposes the forward force of our shoes. However, we know that icy surfaces are "slippery" when the ice exerts less friction on our shoes than concrete.