Frictional force nonrelated to N

[Breston]

The classical approximated formula describing frictional force is $f = N\mu$, directed oppositely to the motion direction.
What about that kind of friction that arises when N is 0? How can I account of that?
For example, suppose I let a cylinder fall inside a pipe nearly the same size, so that air cannot slip through the cylinder and the pipe. The motion is perfectly vertical (parallel to gravitational force). The cylinder falls slowly than it would otherwise, and produces heat on the surface of the pipe, displaying evident friction. Still, no vector N exists since the cylinder is falling and does not stand on a surface.

 

[PaulDirac]

The cylinder falls slowly than it would otherwise, and produces heat on the surface of the pipe, displaying evident friction. Still, no vector N exists since the cylinder is falling and does not stand on a surface.

You are saying that it would produce heat so how it would have produced heat if it had not contacted to the pipe? You can imagine this motion such as an object being pushed on a frictional surface.

 

[A.T.]

For example, suppose I let a cylinder fall inside a pipe nearly the same size, so that air cannot slip through the cylinder and the pipe. The motion is perfectly vertical (parallel to gravitational force). The cylinder falls slowly than it would otherwise, and produces heat on the surface of the pipe, displaying evident friction. Still, no vector N exists since the cylinder is falling and does not stand on a surface.

If you have air being compressed by the cylinder, the air heats up. As for the wall, even with zero normal force, and ideally smooth surfaces you can have adhesive forces between wall and cylinder:
http://en.wikipedia.org/wiki/Adhesion

 

[PaulDirac]

If you have air being compressed by the cylinder, the air heats up. As for the wall, even with zero normal force, and ideally smooth surfaces you can have adhesive forces between wall and cylinder:
http://en.wikipedia.org/wiki/Adhesion

It is supposed that we do not let air get into the pipe so there could be found nothing in between to have made it heated.

 

[A.T.]

It is supposed that we do not let air get into the pipe

As I understand it, the air cannot pass between cylinder and pipe. But the air under the cylinder is still being compressed, and exerts pressure on the cylinder bottom.

If the OP is mainly interested in the interaction with the wall, then let's assume it's all in vacuum.