\(
\mu
\)Friction
Types& Characteristics of static friction
a)When there is no component of external force parallel to the two surfaces in contact with each other, the force of static friction is zero.
b) When an external force is applied parallel to one of the surfaces in contact with each other, and the two surfaces are at rest relative to one another, the force of static friction between the two surfaces is equal to the applied force.
c) In the above case, if the surfaces continue to remain at rest relative to one another, the force of static friction always equals to the external force and increases as the external force increases.
d) The force of static friction between two surface attains a maximum value when, the two surfaces just begin to slide or slip relative to each another.
e) The maximum force of static friction (fs) equals the external force applied parallel to one of the two surfaces, required to just cause sliding or slipping between the two surfaces.
f) The maximum force of static friction between two surface is also called limiting frictional force.
g) The limiting frictional force between two surfaces is given by \(
\boxed{f_s = \mu _s N}
\)
\(
\mu
\)s is called the coefficient of static friction between the two surfaces and N is the normal force between the two surfaces.
h) The static frictional force between two surfaces is \(
\boxed{f \leqslant \mu _s N}
\)
i) \(
\mu
\)s is a dimensionless, unitless physical quantity which depends upon the nature of the surfaces in contact with each other, condition of the surfaces (presence of impurities, extent of roughness, presence of lubricant, temperature etc).
j) \(\mu\)s between two given surfaces is independent of the normal force between the two surfaces.
k) \(\mu\)s > 0, it can also be greater than one, but in most of the cases it is less than one.
Kinetic friction:Kinetic friction is independent of area of contact.
b)Kinetic friction is independent of relatice speed between the two contact surfaces.
c)Kinetic friction is directly proportional to the normal force.
\(
\begin{gathered}
f_K \alpha N(or) \hfill \\
f_K = \mu _K N \Rightarrow \mu _K = \frac{{f_K }}
{N} \hfill \\
\end{gathered}
\)
Where is called coefficient of kinetic friction.
Rolling firction:Rolling firction is due to the deformation of the surface on which the body rolls and due to the deformation of the rolling body at the point of contact with the surface.
Greater the deformation greater is the rolling frictional force.
Rolling friction is inversely proportional to the radius of the rolling body.
Rolling friction is directly proportional to the normal force
\(
\begin{gathered}
f_r \alpha N(or) \hfill \\
f_r = \mu _r N \Rightarrow \mu _r = \frac{{f_r }}
{N} \hfill \\
\end{gathered}
\)
Where \(
\mu _r
\) is called coefficient of rolling friction.
Coefficient of rolling friction(\(
\mu _r
\))\(
= \frac{{Rollingfriction(f_r )}}
{{Normalforce(N)}}
\)
Rolling friction between two surfaces is lesser than the Kinetic friction.
For a given pair of surfaces \(
\mu _s > \mu _K > \mu _r
\)