Coefficient of friction

Consider a body lying on a horizontal surface. If \( R \) is the normal reaction and \( F \) is the limiting friction (the value of applied force when the body just begins to slide), then

\[
F \propto R
\]
\[
F = \mu R
\]

i.e. $ \displaystyle \mu =\dfrac{F}{R}$

$ \displaystyle \text{(limiting friction)}\div \text{(normal reaction)}$

The constant of proportionality \( \mu \) is known as the coefficient of limiting friction.

Therefore, coefficient of limiting friction is defined as the ratio of the limiting friction to the normal reaction.

4. The value of limiting friction for any two given surfaces is independent of the shape or area of the surfaces in contact so long as the normal reaction remains the same.The laws of limiting friction are also applicable to the kinetic friction. As the kinetic friction is quite smaller than limiting friction, the coefficient of kinetic friction given by

$ \displaystyle {{\mu }_{k}}=\frac{{{{F}_{k}}}}{R}\quad $

i.e. $ \displaystyle {{\mu }_{k}}=\frac{{\text{kinetic friction}}}{{\text{normal reaction}}}$

is also much smaller than the coefficient of limiting friction.

Example:

A horizontal force of 490 N is required to slide a sledge weighing 600 kgf over a flat surface. Calculate the coefficient of friction.

Solution:

$ \displaystyle \begin{array}{l}F=490\text{N},\\R=Mg=600\text{kgf}=600\times 9.8\text{N}\end{array}$

Now,
\[
\mu = \frac{F}{R} = \frac{490}{600 \times 9.8} = 0.083
\]