How close do two objects have to be to considered 'in contact'?

Question

On a large scale, normal reaction force is supposed to occur when two objects come into contact. But how is contact defined here? If you have a book sitting on a table, how close do the particles that make up the book have to be to the table's particle in order to be considered 'in contact'?

Answer 1

The normal force comes into play on any scale where you are not directly considering the forces which make up the normal force.

In general, what we call "normal forces" is an aggregation of electrostatic repulsions from many many many atoms. On a large scale, we can use statistical tools like the central limit theorem to create a very good approximation of these electrostatic forces which acts macroscopically.

In situations where we use "normal forces," there is a clear macroscopic force which is driving the two objects together. Often this is the force of gravity acting on one object, but it can be any macroscopic force. This force will drive the objects together until some other force (the electrostatic force) repels them with an equal force. This distance is clearly quite small, it's on the atomic scale. However, compared to these distances, the book's surface is quite rough, so while some atoms will be very close to eachother, other parts of the surface might be a millimeter apart! What matters is that the distance is small enough for the electrostatic potentials between the electrons to generate enough force to combat gravity.

If you are in a situation where it is not clear if there is 'contact,' and thus it is not clear if the normal forces exist, you can always model the forces which make up the normal force, such as electrostatics.