Origins of Coefficient of Friction and Normal Force

[jamesnb]

This is my first year teaching High School Physics and I'm finding there are a lot of questions I should have asked 25 years ago when I was in college.
1. Does anybody know what the coefficient of friction is based on? Usually these things are based on something like getting units to cancel or amount of something to do something or an absolute. The only thing I've been able to find is mu of rubber on concrete = 1.0
2. Why is it called "normal" Force. Of course I understand what it is and how to calculate it but I'm at a lose to explain how they came up with "normal" as opposed to something more reasonable like perpendicular, complimentary or even opposite.
Any ideas?

 

[tiny-tim]

welcome to pf!

hi jamesnb! welcome to pf!

1. From the PF Library on friction …

Tables of coefficients of friction:

Many tables can be found on a http://www.google.com/search?client...ficients+of+friction+table&ie=UTF-8&oe=UTF-8", which begins

"Extreme care is needed in using friction coefficients, and additional independent references should be used. For any specific application the ideal method of determining the coefficient of friction is by trials. A short table is included above the main table to illustrate how the coefficient of friction is affected by surface films. When a metal surface is perfectly clean in a vacuum, the friction is much higher than the normal accepted value and seizure can easily occur."
​

For some materials, the coefficient can be greater than one, and for solids on rubber it can be as high as four.​

2. From my copy of Smith's Latin-English Dictionary …

norma a square, employed by carpenters and masons for making right angles​

… so the original meaning of a normal line was the line made by a square (a set-square), ie the perpendicular!

 

[tiny-tim]

2A. Again from Smith's Latin-English Dictionary …

perpendiculum a plummet, plumb-line​

from

perpendo, perpendere to weigh carefully or exactly​

from

pendo, pendere to make or cause to hang down, especially of scales; hence to weigh, weigh out​

from

pendeo, pendere to hang from on or by something to be hung, suspended​

(pendo from pendeo is a causative construction, fairly rare in English … examples are rise and raise, fall and fell … but fairly common in Hebrew and Arabic)

So, etymologically, "perpendicular" should only be used to describe a vertical line in a gravitational field, the line that a plumb-line follows!

 

[AlephZero]

It is the same use of "normal" as in the expression "the normal and tangent to a curve" in geometry and calculus. (OK, that doesn't explain WHY it is called "normal", but at least the usage in mechanics is consistent with something else).

Re friction coefficients, you need to understand that Coulomb's "law" of friction is not really a universal law at all (compared with other laws in classical physics like universal gravitaition of the gas laws). It is just a simple MODEL that describes how to calculate friction forces. It works pretty well for hard, fairly smooth surfaces, large displacements, and fairly slow velocities - in other words the sort of thngs that occur in school physics situations, like blocks sliding down inclined planes.

There are plenty of real life engineering situations where the Coulomb friction model based on constant static and dynamic friction coefficients works very badly. However the alternatives models that work better are too complicated to use in hand calculations, and often they need quite sophisticated experiments to measure the model parameters (i.e. the equivalent of "the friction coefficient").

One downside of this is that many people seem to take away from school-level physics the over-simplified idea that Coulombs "law" tells you everyting there is to know about friction. It doesn't!

 

[PJC01]

The coefficient of friction and normal force are both important concepts in understanding the behavior of objects in contact with each other. The coefficient of friction, represented by the symbol μ, is a dimensionless quantity that describes the amount of friction between two surfaces in contact. It is based on the ratio of the force required to overcome the friction between two surfaces to the force pressing the surfaces together.

The origins of the coefficient of friction can be traced back to the work of Leonardo da Vinci, who observed that the force required to slide an object over a surface is proportional to the weight of the object. This relationship was further explored by scientists such as Amontons and Coulomb, who developed the concept of static and kinetic friction. The coefficient of friction is based on this relationship and is used to quantify the amount of friction between two surfaces.

As for the term "normal" force, it is derived from the Latin word "normalis" which means perpendicular. This force is called normal because it is perpendicular to the surface of contact between two objects. In other words, it is the force that is exerted by one object on another in a direction perpendicular to the surface of contact.

I can understand your confusion about the term "normal" as it may seem arbitrary. However, it is a commonly used term in physics and engineering to describe this particular type of force. It is also important to note that the normal force is not always equal to the weight of an object, as it depends on the angle of the surface and the forces acting on the object.

In conclusion, the coefficient of friction and normal force are both important concepts that have been studied and refined over many years. They are based on empirical observations and have been used to successfully predict and explain the behavior of objects in contact with each other. I hope this explanation helps clarify any questions you may have about these concepts.