Friction  (Page 4/5)

Here, we distinguish maximum static friction force by denoting it with the symbol “ $F_s$ ”, whereas static friction before motion is denoted by “ $f_s$ ”.

We summarize following characterizing aspects of static ( $f_s$ ) and maximum static friction ( $F_s$ ) :

• Static friction applies in the direction opposite to the component of net external force parallel to contact surface. This, as a matter of fact, is the criteria of deciding direction of friction.
• Self adjusting static friction ( $f_s$ ) is equal to the component of net external force parallel to contact surface. It ranges from 0 to a maximum value $F_s$ . Static friction is a self adjusting friction force. It is important to emphasize that static friction, unlike maximum (limiting) static friction, is not given by the expression of coefficient of friction. Note the relation for static friction : $f_s=F_{||}$ (and $f_s\ne {\mu }_{s}N$ )
• Maximum static friction is proportional to normal force applied on the body and is a single value (unlike static friction) quantity.
• The relation between maximum (limiting) static friction and normal force is a scalar relation. This relation connects forces, which are mutually perpendicular to each other.

Kinetic friction

If the external force parallel to contact surface exceeds maximum static friction, then the body starts moving over underlying surface. It does not mean, however, that friction between surfaces disappears. New contact points between surfaces come in contact, some of which are momentarily joined and then broken on continuous basis. The friction force is dropped slightly (almost instantly); but remains constant - independent of the velocity of the body.

We denote kinetic friction force as $F_k$ and corresponding friction coefficient as ${\mu }_k$ . The kinetic friction is related to normal force as :

$$\begin{array}{l}{F}_k\propto N\\ \Rightarrow F_k={\mu }_{k}N\end{array}$$

The coefficient of kinetic friction is generally independent of the velocity of the body and is practically considered constant.

Motion over a rough surface

Once the external force along the contact surface exceeds limiting or maximum static friction, the body starts moving on the surface. The nature of motion, subsequent to initiation, depends on the external force. There are two possibilities :

1: Uniform motion :