Why doesn't friction depend upon area of contact?

Question

Even though the pressure increases when the area of contact decreases why doesn't friction increase with decrease in area?

Answer 1

Friction is directly proportional to the normal force acting on the body, i.e.;

$$f \propto N$$ where $f =$ friction force and $N =$ Normal force

$$\boxed {f = \mu N}$$

where $\mu$ is the coefficient of friction and depends upon the surface.

We can also say that the normal force does not depend upon the area of contact and hence the friction.

Pressure, on the other hand is:

$$\boxed{P = \frac{F}{A}}$$

where $F$ is the force acting and $A$ is the Area of contact. Thus pressure depends upon the area of contact.