Friction Forces and Traction Made Simple

Friction, or the force of friction, is used to analyze and determine potential movement between the surfaces of two contacting bodies. More specifically, it is the force that resists movement, and consists of several different types. The kind that people are probably most familiar with is called dry friction – as opposed to fluid friction, skin friction, and internal friction. Dry friction is divided into static friction and kinetic friction.

Man making fire using friction

Static Friction and Kinetic Friction

The name pretty much says it all, but here’s a basic rundown for good measure. Static friction is the frictional force that resists movement between stationary bodies, or bodies that are not moving relative to each other. The force of friction between a rubber tire and pavement that enables a vehicle to accelerate is a good example of static friction.

This can be mistaken for kinetic friction due to the fact that both the tire and vehicle are moving. However, because the given section of rubber that is in contact with the pavement is stationary relative to the pavement, it is static friction. If it wasn’t for the force of static friction, the vehicle would not be able to accelerate – or at least not very fast.

A good example of kinetic friction is when you slam on the brakes while traveling at a high speed, locking the wheels so as to skid on the pavement. From the point the rubber tire begins skidding to the point you either release the brakes or come to a complete stop, it will experience kinetic friction.

The Coefficient of Friction COF (μ) and Traction

Traction is another way of describing the maximum value of static friction prior to movement or slippage. But in order to determine the value of traction, the coefficient of static friction (COF) between the two bodies in question becomes needed. The COF is a value that cannot be derived by calculations but must be found empirically through experimentation.

But thanks to smart people with the time and know-how needed, these values can for the most part be found in various publications, handbooks, and resources, available even for free on the internet (Table of Approximate COF). The reason it can’t really be calculated via specific formulas is because every substance is slightly different, and various factors such as temperature and atmosphere often affect accuracy.

The coefficient of friction is the ratio of the force of friction between two bodies and the normal force, or the force that is pressing them together – equal to the weight-force of the upper of the two bodies. There are two types of coefficients of friction: the coefficient of static friction (μs) and the coefficient of kinetic friction(μk). The μs is usually greater than μk.

To put it simply, the force of traction is equal to the force of static friction – meaning the two are synonymous. Likewise, the coefficient of traction is also equal to the coefficient of static friction. Traction and friction are not only very similar but are actually synonymous when it comes to static friction. Kinetic friction takes over once traction is overcome.

The COF of two solid bodies can also vary significantly depending on whether it is dry friction or what is called lubricated friction – a form of fluid friction. This may seem obvious, but there are also certain materials whose COF remains the same regardless of the presence or absence of lubricant such as steel on teflon and steel on polythene.

The Three Laws of Dry Friction and Amontons’ First and Second Laws of Friction

Amontons’ First Law: “The force of friction is directly proportional to the applied load.” For example, if you double the applied load the force of friction will also double – increases or decreases as a ratio.

Amontons’ Second Law: “The force of friction is independent of the apparent area of contact.” This is the more tricky of the two. The key in understanding this principle is to visualize a microscopic view between the two surfaces in question. “Flat” surfaces such as the face of a smooth brick or steel plate are only flat insofar as the nerve endings in your finger tips can detect.

Illustration of friction and components

Break this down to the molecular level and you’ll discover something completely different. All surfaces form a range of peaks and valleys when viewed microscopically, the peak-heights of which are determined by material type. Now place two of these “mountainous” surfaces together and it’s easy to see that it is only the peaks that will actually be making contact with each other.

As per Amontons’ first law, these peaks will be crushed or bent down in proportion to the normal force, causing either more or less of the peaks to be making frictional contact. But if you spread a given weight across a larger area, all you’re doing is decreasing the weight at any one point as per the equation for pressure, P=F/A, with P for pressure, F for force, and A for area.

The force is constant as the weight of the object in question doesn’t change, which means that as the area changes, the pressure must also change with inverse proportion. This means that less material will actually be in contact per unit area. This then translates into an overall equal amount of frictional force given the same weight-force, proving Amontons’ second law.

Rubber Tires and Amontons’ Second Law

Well, what about rubber tires? Good question. Amontons’ second law is an idealization which assumes more or less rigid and inelastic materials. Apparent superior traction on wider tires can then be attributed to the fact that the comparatively softer rubber is actually deforming elastically to fit the geometry of various ground conditions and therefore be seen as an exception to this law.

However, according to various experts, this apparent exception to Amontons’ second law is often misconstrued to mean that the traction of a rubber or otherwise elastic body will always increase in proportion to the surface area of contact. This is not the case. Whatever additional frictional forces elastic materials offer is often negligible when compared to the amount of adhesive friction defined by the material’s μ.

To explain further, I’ll need to answer the question of why high-performance tires or those used for off-road purposes are often made wider. – Because wider tires compensate for the faster wear rates of rubber with higher μ by spreading the weight across more area! Contrary to popular belief, this is the primary reason for wider tires, not because the width in itself provides more traction. For most intents and purposes, Amontons’ second law still holds.

(Here’s a webpage I found helpful along these lines – Steve Munden.)

Coulomb’s Law of Friction: “Kinetic friction is independent of the sliding velocity.” This is pretty straight forward and simply says that the speed at which two bodies are moving relative to each other is irrelevant when trying to determine the force of kinetic friction. This does not however, negate the fact that the coefficient of static friction for most materials is higher than that of kinetic friction.

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