Friction is a resistive force. It opposes the motion of objects. There are two kinds of friction:
- Static friction - the friction that resists any force serving to move any object from rest
- Kinetic friction - the friction that causes any object already in motion to slow down
The maximum force of friction is dependent on the force pressing the two surfaces together and a coefficient of friction, unique to the pair of surfaces:
$$ \begin{equation}\begin{aligned} F_{max}=\mu R\\ \end{aligned}\end{equation} $$where $\mu$ is the coefficient and $R$ is the force pressing the two surfaces together.
Example
Find the acceleration of an object of mass $3kg$ if we apply a force of $7N$ given that the coefficient of static friction is $0.7$.
The weight of the object is the force pressing the two surfaces together: $$ \begin{equation}\begin{aligned} W&=mg\\ &=3kg \times 9.81ms^{-2}\\ &=29.43N\\ &=R\\ \end{aligned}\end{equation} $$
The maximum possible friction that can be produced is: $$ \begin{equation}\begin{aligned} F_{max}&=\mu_s R\\ &=0.7\times 29.43N\\ &=20.60N\\ \end{aligned}\end{equation} $$
Because the force being applied to slide the surfaces alongside each other is only $7N$, the friction will match this in the opposite direction: $$ \begin{equation}\begin{aligned} F_{net}&=7N-7N\\ &=0N\\ \end{aligned}\end{equation} $$
Hence the acceleration of the object is: $$ \begin{equation}\begin{aligned} a&=\frac{F_{net}}{m}\\ &=\frac{0N}{3kg}\\ &=0ms^{-2}\\ \end{aligned}\end{equation} $$
- Find the acceleration if we apply a force of $50N$ to the object in the same scenario.
The units for coefficient of friction
The coefficient of friction is the ratio of the maximum friction to the force pressing the two surfaces together: $$ \begin{equation}\begin{aligned} \mu&=\frac{F_{max}}{R}\\ \end{aligned}\end{equation} $$
Both the force of friction and the force pressing the two surfaces together are measured in Newtons: $$ \begin{equation}\begin{aligned} \mu&=\frac{F_{max}}{R}\\ &\rightarrow \frac{N}{N}\\ &=\text{no units}\\ \end{aligned}\end{equation} $$
Friction on a slope
Given that the angle of inclination is $\theta$, the reaction force (the force pressing the two surfaces together) is: $$ \begin{equation}\begin{aligned} R&=mg\cos{\theta}\\ \end{aligned}\end{equation} $$
The maximum friction will thus be given as: $$ \begin{equation}\begin{aligned} F_{max}&=\mu R\\ &=\mu mg\cos{\theta}\\ \end{aligned}\end{equation} $$
The coefficient of friction is the ratio of the force sliding the two surfaces alongside each other to the force pressing the two surfaces together: $$ \begin{equation}\begin{aligned} \mu&=\frac{F_{along}}{F_{together}}\\ &=\frac{mg\sin{\theta}}{mg\cos{\theta}}\\ &=\tan{\theta}\\ \end{aligned}\end{equation} $$