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Take two flat non-smooth ($\mu\neq 0$) surfaces and rub them against each other. You feel the friction as you are doing work to displace them relative to each other.

We usually think that friction originates due to relative motion of contacting surfaces. But I think we miss this important point that even before relative motion we must check for existence of some mutual normal reaction.(This however has nothing to do with the fact that$ f<=\mu N$ which is just an upper limit and so one might mistakenly take the appearance of N in the equation to mean some direct correlation).

So the question is can frictional force act in absence of normal reaction, given that relative motion is there(eg. sliding of surfaces against each other in gravity free space)?

Qmechanic
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  • $|\vec{F}| = \mu_k |\vec{N}|$, so isn't a normal force essential? Am I missing the point of your question? – garyp Jul 12 '16 at 14:18
  • What I am asking is, can friction come without any normal reaction. My idea seems to suggest no. I can provide an example if you like. –  Jul 12 '16 at 14:24
  • No normal force, no friction. If you have a special situation you'd like to discuss, edit your original post and add it. – garyp Jul 12 '16 at 14:29
  • Oh ... are you equating the normal force with the force that opposes gravity when, say, a book is laying on a table? "Normal" is a mathematical synonym for "perpendicular". It has to do with the geometry of the situation, not the source of the force. Any perpendicular force can produce a normal force. – garyp Jul 12 '16 at 14:35

3 Answers3

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Friction is an adhesive process. The friction isn't caused by the load, what the load does is flatten asperities on the surfaces and increase the area where adhesion can take place. For a discussion of this see How is frictional force dependent on normal reaction?.

So you can have friction without a normal load if the surfaces are already smooth enough for large areas of contact to exist. An example of this is cold welding.

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John Rennie
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Are you suggesting that friction could come about as a result of the Normal Force (Fn) between the two interacting objects?

If so, Normal Forces act only perpendicular to an object's surface (opposite to the force of Gravity. The Normal Force serves basically to prevent solid objects from moving thorough each other.

Friction implies some horizontal motion (parallel to the surface), thus if a force is applied between the two pieces of paper in your question, there would be a component perpendicular to the surface, Fn, and one parallel, Ff, which is friction.

Garrettfromhp
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  • Note that a normal force is not defined by being "opposite to the force of gravity". Normal force needs no gravity at all. – garyp Jul 12 '16 at 14:20
  • @garyp Of course, but as the question was set, supposedly, within Earth's gravitational field, I referred to Fn as such. :)

    You can most definitely have Fn without Fg. Anytime objects come in contact with each other there must be a Fn.

    I suppose I am used to doing physics problems where you have a box on the ground/a plane, etc.

     – Garrettfromhp Jul 12 '16 at 14:24
  • Sorry, if I couldn't communicate my question properly. I am totally aware of the things you mentioned. My singular point is that friction(a horizontal force relative to contact surfaces) depends on the normal reaction(perpendicular to surface) even when the static limit is not reached. –  Jul 12 '16 at 14:28
  • The OP put his experiment in "gravity free space", so I think mentioning gravity at all just confuses the issue. Aside from that small point, your answer is correct. – garyp Jul 12 '16 at 14:31
  • Ah, I had not seen the edit mentioning gravity free space until after my post.

    So if your questions is such, and NO normal force is present then the objects are not in contact with each other and cannot have any frictional forces.

     – Garrettfromhp Jul 12 '16 at 14:39
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Macroscopic friction forces depend on two types of microscopic physics.

  • Long range forces between interfaces. Two surfaces which are not in physical contact exert on each other long range forces. These forces are due to the interaction of the molecules in the last layers, close to the surface of the material. They can be hydrogen bonds, Van der Wall's forces or Pauli exclusion in nature. One can read in this paper that friction coefficient changes by two orders of magnitude depending on the absence or presence of hydrogen molecules on the surface. Vertical intermolecular forces sum up to macroscopic adhesion force, while lateral ones sum up to friction forces.

  • Coulomb's friction force is different in nature. The Coulomb's friction force is the force necessary to tear material away. It is proportional to $S_{contact}$, the physical area of contact between the two surfaces which is a lot smaller than the macroscopic surface. $$ F_{Coulomb} = \tau _{c}~S_{contact}$$

where $\tau _{c}$ is the yield stress during shear. One can prove that:

$$ S_{contact}= \frac{F_{N}}{ \sigma _{c}} $$

$ \sigma _{c}$ is the penetration hardness, i.e. the largest stress the material can bear before plastic yielding. Combining these two relations we get: $$F_{Coulomb} = \frac{ \tau _{c}}{ \sigma _{c}}~ F_{N}$$

In plain English:

The more you push down, the larger $F_{N} \nearrow$.

The larger $F_{N}$, the larger the surface of contact ($S_{contact} \nearrow $).

The larger $S_{contact}$ , the more material to tear off.

The more material to tear off, the larger the force $F_{Coulomb}$.

The Coulomb's friction force is the maximum force to apply before tearing appears. The model is very crude but catches most of the physics. Long range forces and Coulomb's force are always both present, the former dominate the static case, the latter the kinetic one. Their relative importance varies with the conditions, that is why it is not uncommon to have large departures from the Coulomb's force. Tribology is the branch of science dedicated to the study of friction force. You can get a good idea of the field with these two books:

Contact Mechanics and Friction Physical Principles and Applications -Valentin L. Popov.

Sliding Friction Physical Principles and Applications

Shaktyai
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