# Coefficient of friction - varying normal force

I'm trying to get my head around the calculation for coefficient of friction: COF = Friction/Normal force. And what happens if you vary normal force.

Am I right in saying:
1. The COF is a constant - every pair of materials has a specific COF which is independent of how hard they are pressed together.
2. When normal force increases, friction also increases.
Any help in explaining this would be appreciated!

I realise I've been thinking of friction and COF as the same thing - the degree of grip or slipperiness between two surfaces. Does this layman's definition reflect more friction or COF?

What is a descriptive definition of COF?

I'm really not good at physics, sorry!

nasu
Gold Member
You just described it yourself. The coefficient of friction is a ratio of two forces: the friction force and the normal force.
It depends on the two materials in contact. It is also assumed that is independent of the normal force, as an approximation which is good in many cases.
So yes, if you increase the normal force, the friction force increases too.

Thanks nasu - a ratio of two forces!

So if the bottom surface is deformable (in both a perpendicular and horizontal direction) and it has an object on it, is it fair to say that the coefficient of friction describes the propensity for shear within that material?

nasu
Gold Member
It may be related to the shear properties but this is not what it "describes".
Two pair of surfaces of the same material may have different COF even though the shear modulus is the same.
If you pull a body along a surface, the shear stress induced by this will depend on the friction forces, so on COF. But I don't see something relevant in this connection.

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I'm thinking of skin. If you press your fingertip into the back of your hand and wobble it back and forth (but keep it stuck to the same bit of skin), the amount of shear in the skin on the back of your hand depends on how hard you press and the friction level (put Vaseline on the back of your hand and there's hardly any shear). So in that way, if by varying normal force and/or friction you get a different amount of shear, I was thinking the COF describes the propensity for shear.

nasu
Gold Member
Yes, the amount of shear you can apply this way depends on the coefficient of friction.
But this does not mean that the coefficient of friction describes the shear properties of the skin.

Chestermiller
Mentor
I'm thinking of skin. If you press your fingertip into the back of your hand and wobble it back and forth (but keep it stuck to the same bit of skin), the amount of shear in the skin on the back of your hand depends on how hard you press and the friction level (put Vaseline on the back of your hand and there's hardly any shear). So in that way, if by varying normal force and/or friction you get a different amount of shear, I was thinking the COF describes the propensity for shear.
If your finger doesn't slip relative to your skin, then this simply means that the static frictional force is less than the COF times the normal force. So, in this case, friction is not playing any role whatsoever in determining the stress/deformation behavior of your skin and flesh.

Please understand that, when static friction is involved, the frictional force is only equal to the normal force times the COF when the contact surfaces are just on the verge of slipping. Otherwise, the frictional force must be less than the normal force times the COF.

Chet

Thanks nasu. That's obvious to me now. The amount of shear that occurs within the skin will be related to both friction and normal force (therefore COF). But the shear modulus of the skin describes its ability to undergo shear. Thanks.

So getting back to COF again. Every pair of materials has a COF - it just is what it is. You can find lists of COFs for materials (glass on wood, rubber on glass, rubber on ice, cotton on plastic, skin on cotton etc). It's a constant number that is not altered by altering normal force or friction. But normal force and friction levels change. So am I right in saying:
• If you increase normal force, in the example of pressing on the back of your hand, you are automatically increasing the level of friction, in order to keep the COF a constant number.
• And by increasing friction, in order to maintain the COF as a constant number, which it always will be, you have to increase normal force. Does that sound right?
But what if you increase the friction level but normal force stays the same?

Chestermiller
Mentor
Thanks nasu. That's obvious to me now. The amount of shear that occurs within the skin will be related to both friction and normal force (therefore COF). But the shear modulus of the skin describes its ability to undergo shear. Thanks.

So getting back to COF again. Every pair of materials has a COF - it just is what it is. You can find lists of COFs for materials (glass on wood, rubber on glass, rubber on ice, cotton on plastic, skin on cotton etc). It's a constant number that is not altered by altering normal force or friction. But normal force and friction levels change. So am I right in saying:
• If you increase normal force, in the example of pressing on the back of your hand, you are automatically increasing the level of friction, in order to keep the COF a constant number.
• And by increasing friction, in order to maintain the COF as a constant number, which it always will be, you have to increase normal force. Does that sound right?
But what if you increase the friction level but normal force stays the same?
The answers to these questions are both covered in my post #8. I will reiterate: the friction force is less than the normal force times the coefficient of static friction unless than the surfaces are just on the verge of slipping relative to one another.

Chet

Thanks Chet. Wow, I'm going to have to think about this for a bit ... I'm pretty thick.

So would you mind indulging me for a moment Chet. The two points I make in post #9, are they correct or incorrect. Sorry!

I understand there is a difference between static and kinetic friction. And that the former is higher than the latter.

I don't understand Chet, because to my way of thinking, you can have a state of static friction between your finger tip and the back of your hand and still have different amounts of shear depending on how sticky or slippery it is between the two (variable friction level), even if you don't vary normal force.

So in that way, I'm having trouble with this equation: COF = Friction/Normal force
Because if COF is constant and you keep normal force constant, how can friction be variable?

Chestermiller
Mentor
I understand there is a difference between static and kinetic friction. And that the former is higher than the latter.

I don't understand Chet, because to my way of thinking, you can have a state of static friction between your finger tip and the back of your hand and still have different amounts of shear depending on how sticky or slippery it is between the two (variable friction level), even if you don't vary normal force.

So in that way, I'm having trouble with this equation: COF = Friction/Normal force
Because if COF is constant and you keep normal force constant, how can friction be variable?
You are having trouble understanding it because this equation is incorrect. It should be an inequality:
$$COF≥F/N$$
where COF is the coefficient of static friction.

The equality sign applies only if the frictional force is high enough for the two surfaces to be just on the verge of slipping. If it is less than that, then the > sign applies and the surfaces will not slip. The coefficient of friction only tells us how high the frictional force has to be in order for slippage to begin to occur.

Chet

Got it Chet. Thank you so much for your time. And thank you nasu. I really appreciate it!
What a great forum.

sophiecentaur
Gold Member
2020 Award
I remember having read a description of how / why the COF remains constant over a big range of loads. Firstly, you have to assume that the two surfaces are flat enough to have no 'teeth' which could mesh and ruin the simple relationship. But no two surfaces are truly flat. Contact will be over quite a small fraction of the 'contact' area in the form of islands of contact (I guess this would be down at the molecular level). As the normal force increases, the raised bits will deform and increase the contact area, proportionally with the force. The drag force between the two surfaces will also increase proportionally with the area of actual contact (number of molecules coming into contact). So the ration between the two forces will remain the same until the non linearity of the materials kicks in. This would be when the two surfaces merge completely.
Is that just whimsey or did I read it in a text book?

nasu
Gold Member
Well, I remember reading something similar and I think in more than one place.
So it may be a quite common whimsy. sophiecentaur