# Coefficient of friction

I know that coefficient of friction=f/N , and I also know that it depends on that surface area of contact and the material.

But my doubt is ,from this formula if N is halved then coefficient of friction should increase but that does not happen, it remains unchanged, why?

If it's because f might adjust itself accordingly to keep it constant ,then what about in case of know kinetic friction?

Only static friction is self adjusting, right!

• The coefficient of friction $f$ is a constant and is defined by the ratio of the tangential and normal components of the reaction. – Dimitri Mar 25 '16 at 10:08
• Friction is a limit such as $$|f| \leq \mu |N|$$. Friction does not change when the forces change and is not defined by them. – ja72 Mar 25 '16 at 16:42

## 3 Answers

First of all,

friction is the force that arises between surfaces when there is relative motion between surfaces. And when the system is in equilibrium even after applying the force in some direction we say static friction is acting and this is the only adjusting friction

now as you have written coefficient of static friction =f/N (where f is the force and N is normal reaction). This equation is ONLY valid if the system is in equilibrium and force acts in the direction, in which there will be relative motion.

I also know that it depends on that surface area of contact and the material.

this is the biggest fallacy coefficient of friction never depends on the area of contact(think about this point and if confusion comment)

if N is halved then coefficient of friction should increase but that does not happen, it remains unchanged, why?

N can be halved only in one way in the picture i have shown and the way is by applying force in upward direction, so in this way N is reduced , but by doing this to keep system in equilibrium in horizontal direction force required will also be reduced (because in this $\mu N=friction$, N is reduced in)

Only static friction is self adjusting, right!

yup :-)

• Thanks, I understand it now. But, about coefficient of friction depending on surface area of contact - I think surface area of contact will be effecting f ,right ! And not this. But could you please tell me more about on what does it depend like it depends on the material used right! – shaistha Mar 25 '16 at 12:50
• @shaistha yup it depends on the type of material. But it does not depend on area of contact e.g when you keep a big block on the surface with huge contact are and you measure coefficient of friction this will be same as when you keep a small block of same material as big block. NOTE :-for two surfaces coefficient of friction is a constant whether it be big or small – user5954246 Mar 25 '16 at 14:24

Yes It is true that static friction is a self adjusting force. The maximun value of static friction is limiting friction. Here, f adjusts only if the friction is less than limiting friction. In case of kinetic friction, the coefficient of friction not only depends upon area and material, it also depends upon the speed with which the body is moving. If you go on increasing the value of f, at certain time it becomes maximum and kinetic friction becomes constant.

i want to answer the question you asked about the dependence of friction to the surface area of contact.......... first of all you have to know why does the friction occur... it is because of that each substance like its own molecules, actually friction is an interaction among two kind of molecules. i want to teach you something important about physical formulas so you can easily understand my explanations...... think of the OHMS law R=V/I as you all know resistance of something is influenced just by its internal construction like the length...etc since R is not influenced by I(current) and V(voltage) if you double current of the electric circuit , voltage will be doubled too. in another point if view I can say that since current and voltage are related to each other the result of their division which is resistance is neither related to current nor to voltage. lets go back to our friction stuff as you can easily feel friction means the pressure which two substance have with each other .as you know pressure formula in physics is P=FN/A (vertical force) so ...... friction ~ PA=FN A so as i explained in the OHMS law friction is not related to the surface area.

• sorry but your explaination is quite wrong , friction is not the pressure, it is a force, like when a block is on horizontal ground it has pressure but no friction is there between surfaces(no force except newtonian gravity is acting) .. i hope you got it :-) – user5954246 Mar 25 '16 at 16:26