# What the IB thinks of friction

#### Chi Meson

Homework Helper
I teach an AP/IB physics class in a high school. On the last IB ("International Baccalaureate") examination, there was a question about friction that went like this:

[an object was described to be at rest on an incline] "Show that the object must start to slip when the angle of incline is 45 degrees or less."

The IB is convinced that a coefficient of friction cannot be greater than 1.0 . I and many other physics teachers across the globe scratched our collective heads at this. What are we supposed to do with all the tables and textbooks that describe coefficients of static friction which are greater than 1.0? Rubber on pavement, for example (1.2--1.4) .

The report issued by the IB organization says "teachers are advised to tell students that when the coefficient of friction appears to be greater that 1.0, factors other than friction must be considered."

I am at this moment looking at a rubber stopper at rest on a sheet of 150 grit sandpaper (stapled to a board) at an angle of nearly 50 degrees. I need to know, what is not "friction" about that?

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#### ZapperZ

Staff Emeritus
2018 Award
I'd say show your example to that organization, and ask them to tell you what ARE the "other factors" that they had in mind.

That is utterly ridiculous. Who are the clowns who make up that organization anyway?

Zz.

#### Chi Meson

Homework Helper
Interstingly, the rubber stopper sticks better to 180 grit sandpaper, to which it holds up to 60 degrees, indicating a coefficient of 1.7. Furthermore, the stopper slides with constant speed down a smooth piece of masonite while at 52 degrees, indicating a coefficient of KINETIC friction of 1.3.

COrrect me if I am wrong, but I have been teaching that friction is the name given to the cumulative effect of all dissipative forces that arise from two surfacesin contact. The forces can include: normal forces of micro size bumps among the surface, cohesiona dnadhesion effects, electrostatic attraction, and vacuum/atmospheric pressure effects, surface tension, and heck even Van der Waals if the surfaces are smooth enough.

There is no "law of friction." Any of the general rules of friction (does not depend on surface area or speed of motion) have exceptions.

In answer to Zz's query, I don't know who or what is the IB authority on Physics.

#### ZapperZ

Staff Emeritus
2018 Award
I can try looking up some references on the origin/mechanism that creates friction between surfaces when I get back to the office, but I highly doubt that there's any First Principle derivation for it. So if this is true, then friction is purely a phenomenological effect, and you simply measure it to get its value. Thus, there is no a priori physical limit to the value of its coefficient - at least, within reason.

Zz.

#### Gokul43201

Staff Emeritus
Gold Member
1. Although I "feel" I too was somehow given the impression that the coefficient can never exceed 1 (sometime during my highschool education, I imagine), I've never subsequently seen an explanation for this. If you do find any attempts, please link them in this thread.

2. I think it's okay to talk of other forces than friction that prevent slipping between a pair of surfaces. The way I like to distinguish between what I'd call friction and what I wouldn't is using the relationship between the force and the normal reaction. If the force scales roughly like the normal reaction (ie: the coeff. is independent of mass), I call it friction. When it doesn't (eg: a block with sticky tape on the bottom), I say there's other forces involved, and I label them "adhesion".

That's just the nomenclature I like to follow. While it provides for a consistent meaning for the coefficient, it doesn't impose an upper limit on its value.

3. Have you tried the rubber stopper on sandpaper experiment with different masses of rubber?

#### berkeman

Mentor
Chi Meson said:
I am at this moment looking at a rubber stopper at rest on a sheet of 150 grit sandpaper (stapled to a board) at an angle of nearly 50 degrees. I need to know, what is not "friction" about that?
You can also use race car cornering as an example. To get the > 1g lateral accelerations that are common with good tires, the mu has to be >1, right?

#### Cyrus

Chi Meson said:
I teach an AP/IB physics class in a high school. On the last IB ("International Baccalaureate") examination, there was a question about friction that went like this:

[an object was described to be at rest on an incline] "Show that the object must start to slip when the angle of incline is 45 degrees or less."

The IB is convinced that a coefficient of friction cannot be greater than 1.0 . I and many other physics teachers across the globe scratched our collective heads at this. What are we supposed to do with all the tables and textbooks that describe coefficients of static friction which are greater than 1.0? Rubber on pavement, for example (1.2--1.4) .

The report issued by the IB organization says "teachers are advised to tell students that when the coefficient of friction appears to be greater that 1.0, factors other than friction must be considered."

I am at this moment looking at a rubber stopper at rest on a sheet of 150 grit sandpaper (stapled to a board) at an angle of nearly 50 degrees. I need to know, what is not "friction" about that?
This is wrong, end of discussion. The angle of static friction, or angle of repose is simply the phi=arctan(mu-static).

What is true is that the angle is 45 degrees for the variation of friction force vs applied load. This is obvious, becuase there is no motion and the friction force = applied load up until kinetic motion occurs.

#### Gokul43201

Staff Emeritus
Gold Member
cyrusabdollahi said:
What is true is that the angle is 45 degrees for the variation of friction force vs applied load. This is obvious, becuase there is no motion and the friction force = applied load up until kinetic motion occurs.
It's not at all obvious to me what you are saying here.

#### Cyrus

Draw a graph. Label the x axis the applied load P. Label the Y axis the friction force F.

Because it is static, F=P for all values of P until kinetic friction.

Therefore, the slope is 45%. But that is the slope of the friction force vs applied load.

That slope is NOT the slope of the physical system.

#### Chi Meson

Homework Helper
cyrusabdollahi said:
What is true is that the angle is 45 degrees for the variation of friction force vs applied load. This is obvious, becuase there is no motion and the friction force = applied load up until kinetic motion occurs.
You're just saying that this slope is 1.0, right?

Edit:

right

#### Chi Meson

Homework Helper
ZapperZ said:
I can try looking up some references on the origin/mechanism that creates friction between surfaces when I get back to the office, but I highly doubt that there's any First Principle derivation for it. So if this is true, then friction is purely a phenomenological effect, and you simply measure it to get its value. Thus, there is no a priori physical limit to the value of its coefficient - at least, within reason.

Zz.
I like the way you said that.

#### Gokul43201

Staff Emeritus
Gold Member
cyrusabdollahi said:
That slope is NOT the slope of the physical system.
Okay. That's clearer.

#### tehno

Chi Meson said:
"Show that the object must start to slip when the angle of incline is 45 degrees or less."
Hmm."Must" is a heavy term.Good glue make miracles.

#### student85

I think it is illogical for a friction coefficient to exceed 1 because that would mean the friction would be equal or greater than the normal force. (friction= (coef.)(Normal)) So imagine the microscopic look at the edge of the object and the slope... how could all the normal force be destined to friction, that is, with what shape would the microscopic peeks cause this? I don't know if I'm explaining myself, let me now. Those are just my thoughts.
I'm just 19 but I too have wondered that ever since I was at highschool and just saw coef. that were smaller than 1 .
I was an IB student btw.

#### Chi Meson

Homework Helper
student85 said:
I think it is illogical for a friction coefficient to exceed 1 because that would mean the friction would be equal or greater than the normal force. (friction= (coef.)(Normal)) So imagine the microscopic look at the edge of the object and the slope... how could all the normal force be destined to friction, that is, with what shape would the microscopic peeks cause this? I don't know if I'm explaining myself, let me now. Those are just my thoughts.
I'm just 19 but I too have wondered that ever since I was at highschool and just saw coef. that were smaller than 1 .
I was an IB student btw.
The normal force does not "become" the frictinal force. The coefficient is merely defined as the ratio of these two dinstinct forces. Normal forces are by definition the force from the surface that points in a direction perpendicular to the surface. It arises entirely due to the electrostatic repulsion of the electrons that surround the exterior of all objects.

The frictional force(s) are those surface forces that act parallel to the surface at the point of contact. As I mentioned, there is not a single cause of this "parallel componant of surface forces." The bumpiness of the surfaces is one aspect, forces of electrostatic attraction (adhesion and cohesion, hydrogen bonding, Van der Waals, all names for the same underlying phenomenon) account for most of the other sources of the frictional force. Here is an engineers table decribing some standard coefficients.
http://www.engineershandbook.com/Tables/frictioncoefficients.htm

Note that rubber against some "solids" can have a coefficient as high as 4.0 . ZapperZ described it as "phenomenological effect," which means we describe friction in terms of "what it does" rather that "what it is."

And we describe the coefficient as the ratio of the frictional force over the normal force. There is no "Law" to friction. If we define the coefficient in such a way, and if I observe rubber stopper at rest on a piece of masonite at an angle of 60 degrees, the coefficient of static friction is 1.7 for this arrangement.

#### Gokul43201

Staff Emeritus
Gold Member
Chi Meson said:
If we define the coefficient in such a way, and if I observe rubber stopper at rest on a piece of masonite at an angle of 60 degrees, the coefficient of static friction is 1.7 for this arrangement.
I don't see how you can know this, unless you assume that this "static frictional force" is proportional to the normal reaction or you want to define the coefficient as a function of the weight of the stopper. With many soft, polymeric materials (like rubber), there's either a non-zero value of friction in the limit of zero normal force and/or a non-linearity in the friction vs. normal force that becomes pronounced above certain values.

For related discussion:
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JCPSA6000113000024011293000001&idtype=cvips&prog=normal [Broken]

Also see: Physics of Sliding Surfaces, edited by B. N. J. Persson and E. Tossati ~Kluwer, Dordrecht, 1996

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#### Chi Meson

Homework Helper
Gokul43201 said:
I don't see how you can know this, unless you assume that this "static frictional force" is proportional to the normal reaction
This is exactly the assumption made by elementary analysis of friction.
With many soft, polymeric materials (like rubber), there's either a non-zero value of friction in the limit of zero normal force and/or a non-linearity in the friction vs. normal force that becomes pronounced above certain values.
That's interesting news. It again shows that friction is a very sticky subject (heh heh) when going into deeper analysis.

Thanks for the link. More ammo for my letter to the IBO.
Edit: Hey, they want $23 for that article! Any other links to similar data? Last edited: #### student85 Chi Meson, where are you from? (just wondering cause I was an IB student...) #### vanesch Staff Emeritus Science Advisor Gold Member tehno said: Hmm."Must" is a heavy term.Good glue make miracles. Yes, that's also what came immediately to mind: what about glue ? I'm totally with Zapper here, there's no reason to have the STATIC friction coefficient limited to 1. The only requirement you have on friction, is that, overall, it can not *produce* work but can only at most "consume" it (that is, there has to be entropy production, and not an entropy sink), but that applies only to the dynamical case, because the static friction force doesn't do any work, and even then, one has to be careful of how the reference frames are set up. This essentially comes down to stating that a friction force must have a negative projection onto the relative velocity of the two objects. #### Gokul43201 Staff Emeritus Science Advisor Gold Member vanesch said: The only requirement you have on friction, is that, overall, it can not *produce* work but can only at most "consume" it (that is, there has to be entropy production, and not an entropy sink), but that applies only to the dynamical case, because the static friction force doesn't do any work, and even then, one has to be careful of how the reference frames are set up. This essentially comes down to stating that a friction force must have a negative projection onto the relative velocity of the two objects. So you do not require that the frictional force be proportional to the normal reaction between the surfaces? How then, do you define the coefficient? #### Gokul43201 Staff Emeritus Science Advisor Gold Member Chi Meson said: Edit: Hey, they want$23 for that article! Any other links to similar data?
I was able to access it for free. I'll take another look.

This is exactly the assumption made by elementary analysis of friction.
And are you sure this elementary analysis applies to your rubber stopper on masonite?

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#### PerennialII

Gold Member
Gokul43201 said:
So you do not require that the frictional force be proportional to the normal reaction between the surfaces? How then, do you define the coefficient?
Resonates pretty well with my experiences, every 'more detailed' investigation of surface phenomena studying & involving friction eventually "diverges" when friction couples with a number of phenomena and can't find a definition which would stand (or well, it becomes a complex model itself).

#### Chi Meson

Homework Helper
Gokul43201 said:
And are you sure this elementary analysis applies to your rubber stopper on masonite?
My rubber stopper adheres (ha ha) exactly to this elementary definition. There is no glue nor any form of "stickiness" on either of the surfaces (so adhesion cannot be blamed). Both surfaces are very, very smooth, so the effect can not be blamed on the soft rubber hanging onto a ledge of sorts or "grabbing on to pointy bits" (Can't come up with a better line for that). It is a straight forward case of micro-sized bumps and the "nature" of the two surfaces in contact. When on an incline the ratio of parallel frictional force to perpendicular normal force equals the tangent of the angle of incline. This again is exactly the basic, elementary analysis of the frictional force.

THe IBO "authorities" explicitly said that "all objects will slide when the angle of incline is 45 degree or less," and came back with the further statment that coefficients of friction are never greater than one.

Both of these statements are not true. If they define "friction" such that only certain contributors to the overal frictional effect are considered, then they are all alone.

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#### vanesch

Staff Emeritus
Gold Member
Gokul43201 said:
So you do not require that the frictional force be proportional to the normal reaction between the surfaces? How then, do you define the coefficient?
Well, first of all, a static frictional force is a binding force which links 2 potentially free parameters. It can be replaced by a holonomic binding as long as the "friction force" which is the replacement of this holonomic binding by a force remains within certain boundaries. So a static friction force is a holonomic binding with a limit on its validity ; this limit makes it actually a non-holonomic binding (a binding which cannot be expressed by a relationship between the generalized coordinates and time alone but involves also the generalized velocities).

So in a way, you can replace, in a Lagrangian formulation, the static "friction" aspect by a holonomic binding (using a lagrange parameter), from the lagrange parameter, you can calculate the equivalent binding "force" F_B and then you can find out whether this binding force F_B is within its allowed limits (for instance as a function of the normal force F_N). If this is so, then the problem has been correctly solved involving the binding. If not, then the static force f_B has been overcome and must be replaced by another binding (a kinematic friction force, for instance, or nothing), in other words, the binding itself has been released.
Nothing stops you, for a given configuration, to calculate the ratio of F_B_max over F_N, and call that the static friction coefficient, but there's no reason that this should be a constant, for several situations. In some dry friction situations, this is applicable, but not always.
Glue is such an example: F_B_max = f(F_N), but it has a non-zero offset (even without F_N, or worse, with negative F_N, there is a non-zero F_B_max as long as the glue doesn't break). A big F_N on a glued surface will however increase the F_B_max.
So a glued surface does everything a static friction force should do: introduce a potential holonomic binding between generalized coordinates, as long as the binding force is within certain limits, as a function of the normal force. Given the non-zero offset, for zero F_N, we have an infinite ratio of F_B_max and F_N, and hence an infinite coefficient of friction.

#### arildno

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Gold Member
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First of all, whether the friction force is strictly proportional to the magnitude of the normal force,
i.e, $$\frac{\partial\frac{F}{N}}{\partial{N}}=0$$)
, should be resolvable by experiment, for example by measuring the frictional force for different loads.
And from what I know, the N-independence of $\mu$ is at least as strongly verified as the area-independence of $\mu$

I don't see why one should bother to try to make a quasi-theoretical formulation out of an evidently macroscopic phenomenon like static/kinetic friction. A waste of time, if you ask me..