Question

If contact forces (repulsion between atoms) does not exist then how friction is possible ?

Answer 1

Even though no two objects touch each other at atomic level because of weak repulsion between nucleus - nucleus and electron electron repulsion; those two objects also attract each other due to nucleus - electron attraction.

The repulsion only come into picture when the object surfaces come too close to each other. However, the attraction is stronger force and starts acting even before the two surfaces come close enough for repulsion to come into play.

Such attraction is one of the causes of friction.

Irregularities at molecular level in the surfaces in contact also causes interlocking, which is a major cause of friction.

Derivation -

1. When two surfaces are in contact their irregularities at molecular level causes them to interlock with each other, giving rise to friction. But then, to cause motion, you apply external forces to overcome those interlocking. This external force cause the interlockings to break. Resulting in smoother surfaces. That is why when you rub two surfaces on top of each other, they become smoother.
2. When two ultra smooth surfaces come in contact with each other, there are very little interlocking. But then the smooth, nicely arranged molecules on that smooth surfaces come in contact with each other very nicely, and causes a huge nucleus-electron attraction, giving rise to ultra-high friction, very difficult to overcome. Theoretically it is possible to not be able to start a motion (start a ball rolling) on a perfect frictionless surface.