# Does static friction apply when an object stops for a very small amount of time?

It is my understanding that static friction between two surfaces arises at least partly due to inter-molecular forces, e.g. Van der Vaals forces.

The question: Consider this scenario: If I push a box, let it go, and the box slides up a ramp, its velocity will become zero at some point, due to gravity, and then the box will slide down. At that point, when velocity became zero, will static friction have come into play? (E.g. will the gravitational force in the direction down the ramp have to exceed the static friction force?)

My thoughts: Intuitively I would argue yes, but my philosophical problem with it is that, at least mathematically speaking, the box was at that point only an infinitesimal amount of time; how could bonds be formed in that amount of time?

As an extension to the question, whose answer I'm guessing is that there's indeed enough time for bonds to form; is there ever any situation where there is not enough time for such bonds to form, despite having zero velocity at some point? (E.g. a box pushed up with a very strong force on a planet with a very strong gravitational force, so that the change of velocity occurs more quickly.)

• As an aside, I was told by the director of undergraduate labs at my university that the strength of static friction does have a dependency on how long the object is at rest on the surface. However, for such a simple model of friction, I don't know if you even need to consider this for most problems. Nov 8, 2018 at 0:50

I think the biggest issue with your understanding was in the first sentence:

It is my understanding that static friction between two surfaces arises at least partly due to inter-molecular forces, e.g. Van der Vaals forces.

This is true that friction would involve the formation of bonds; but it's not the only factor, and it varies with the different types of friction.

For static friction; the inter-molecular forces are actually less important than the surface characteristics. From Wikipedia:

Static friction is considered to arise as the result of surface roughness features across multiple length-scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area.

The static friction is mostly dictated by the actual shape of the interfacing materials (essentially the surface roughness).

It's the kinetic friction which is mostly affected by the inter-molecular forces. To again quote Wikipedia:

Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities

So to summarize, I believe the box at the apex of it's travel up the ramp will experience static friction. The amount of force shouldn't be overly relevant. That said, because the static friction force is only approximated by the usual friction formulae; you're approximations might break down if higher-order effects become relevant when there are extreme forces involved.