The Friction Coefficient | Coefficient of Friction – questions, answers for class 11

Last updated on December 9th, 2022 at 09:14 am

This post is entirely focused on the Friction coefficient (also known as the coefficient of friction). We will define it and find out its types. Also, we will derive equations and get a list of values. Please note the symbol μ(mu) which denotes this coefficient.

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What is the friction coefficient?

The Friction coefficient is a constant for a pair of surfaces (made of the same or different materials) in contact which decides the amount of frictional force generated at the common layer when one surface moves or tends to move with respect to the other surface.
This coefficient μ is presented generally in this way: μ = F /N = ratio of frictional force and Normal reaction force.

It has 2 different sets of values for a pair of surfaces and these are known as
1] the Coefficient of static friction μ_s and
2] the Coefficient of Kinetic friction μ_k

What is the equation or formula of the Friction coefficient?

The equation is like this: μ = F /N = ratio of frictional force and Normal reaction force.

What is the Coefficient of static friction?

The coefficient of static friction is the ratio of the Limiting friction (maximum possible static friction) and the Normal reaction force.

What is Limiting Friction?

For static friction (when there is a tendency of movement of a layer with respect to another surface layer but there is no actual movement yet), the maximum possible frictional force before the object starts moving is called Limiting Friction.

Derive the equation of the Coefficient of static friction

The maximum static friction force or the Limiting friction F_smax is directly proportional to the normal force or normal reaction force N.
F_smax ∝ N  or F_smax = μ_s N.
Hence, μ_s = F_smax / N
This μ_s is a constant for 2 surfaces in contact and for static friction. This is called the coefficient of static friction between the 2 surfaces involved.

What is the formula for static friction?

As the limiting friction is the max possible static friction, so we can write the expression of static friction as
F_s <= F_smax
or, F_s <= μ_s N

What is the Coefficient of kinetic friction?

The coefficient of kinetic friction is the ratio of the kinetic frictional force and the Normal reaction force.

Derive the equation for the Coefficient of kinetic friction

For Kinetic friction F_k (when there is actual relative motion between 2 surfaces in contact), the frictional force is again directly proportional to the Normal reaction force N.
F_k ∝ N  or F_k = μ_k N
Hence, μ_k = F_k / N
This μk is a constant for 2 surfaces in contact and for kinetic friction. This is called the coefficient of kinetic friction between the 2 surfaces involved.

What is the Friction Coefficient table?

This table consists of the μ_s and the μ_k for different material pairs.

The values of these coefficients totally depend on what surfaces (material-wise) are in contact with where relative motion is happening or tending to happen.

We provide a set of such constants for different material pairs in a friction coefficient table. This table is also known as the Coefficient of Friction chart.

System	Static friction μs	Kinetic Friction μk
Rubber on dry concrete	1.0	0.7
Rubber on wet concrete	0.7	0.5
Wood on wood	0.5	0.3
Waxed wood on wet snow	0.14	0.1
Metal on wood	0.5	0.3
Steel on steel (dry)	0.6	0.3
Steel on steel (oiled)	0.05	0.03
Teflon on steel	0.04	0.04
Bone lubricated by synovial fluid	0.016	0.015
Shoes on wood	0.9	0.7
Shoes on ice	0.1	0.05
Ice on ice	0.1	0.03
Steel on ice	0.4	0.02

As an example, if we take the value of μs and μk for 2 wood surfaces in contact, we can easily observe that μk is less than μs.

This is true for all other material pairs in the above list. This clearly explains why the kinetic friction magnitude is less than static friction(generally).

Also find 2 interesting readings above: (1)Steel on dry steel and (2)Steel on oiled steel. It shows how lubrication reduces the value of friction.

What is the unit of μ?

Being a ratio of 2 forces, it has no unit. It is just a number.

What is the frictional coefficient of steel on steel?

For steel on steel, dry the values of μs and μk are respectively 0.6 and 0.3.
For steel on steel oiled the values of μs and μk are respectively 0.05 and 0.03

What is the μ of Teflon on steel?

It is 0.04 (both μ_s and μ_k )

Static friction and Kinetic friction – explanation with the molecular cohesion theory

When an object is static then due to molecular-level cohesion between its surface and the other surface on which it is resting, we need to apply a force to move it.

As we increase the magnitude of the force the opposing force (friction) also increases linearly up to a maximum value called limiting friction. Now if apply our force beyond that Limiting friction, the intra-layer cohesion is won over and the two surfaces now start experiencing relative motion.

At that point, the friction drops quickly from the maximum level of static friction(as mentioned earlier as limiting friction) to a little lower level and remains constant (kinetic friction) till the object is pushed to move and other criteria like normal reaction force and the sliding material remain unchanged.

Coming back to molecular cohesion theory, as you are pushing and it’s moving or sliding (facing the kinetic friction) the object’s surface is not getting enough time to get its cohesion with the sliding layer back. So during this sliding time, you are pushing with less amount of force just to maintain the speed winning over the kinetic friction.

Friction: Harmful and Helpful

Friction is both harmful and helpful to you and to the world around you. Friction can cause holes in your socks.
Friction by wind and water can cause erosion. On the other hand, friction between your pencil and your paper is needed for the pencil to leave a mark.

Without friction, you would slip and fall when you tried to walk. Because friction can be both harmful and helpful, sometimes it should be decreased and sometimes it should be increased.

Ways to Reduce Friction

Using lubricants is one way to reduce friction. Lubricants are substances that are put on surfaces to reduce the friction between the surfaces. Some examples of lubricants are motor oil, wax, and grease. Lubricants are usually liquids, but they can be solids or gases. An example of a gas lubricant is the air that comes out of the tiny holes on an air hockey table.

When you work on a bicycle, watch out for the chain! You may get dirty from the grease or oil that keeps the chain moving freely.
Without this lubricant, friction between the sections of the chain makes riding difficult.

Friction can also be reduced by switching from sliding kinetic friction to rolling kinetic friction. Ball bearings placed between the wheels and axles of in-line skates and bicycles make the wheels turn more easily by reducing friction. Read more about bearings and how it helps to reduce friction.

Another way to reduce the magnitude of friction is to smooth surfaces that rub against each other. For example, rough wood on a park bench can snag your clothes or scratch your skin because there is a large amount of friction between you and the bench. Rubbing the bench with sandpaper makes the bench smoother. As a result, the friction between you and the bench is less. So, the bench will no longer snag your clothes or scratch you. Read about the friction coefficient.

Suggested study: Definition & detailed explanation of Friction