Laws of Friction

1. Introduction:

Friction is the force that prevents layers of fluid, surfaces of solids and material components sliding against one another. The force which resists the relative lateral movement between two solid contacting surfaces is known as dry friction. The two types of dry friction are static friction (“stiction”) on stationary surfaces and kinetic friction (“friction”) on moving surfaces. In general, the presence of asperities on the surface and the interaction between the surfaces causes dry friction.

Based on the application we have several types of friction such as fluid friction, lubricated friction, skin friction. In a viscous fluid the relative motion between the layers of a fluid causes fluid friction. If there is presence of lubricant between two bodies then it can lead to lubricated friction. The force which resists the fluid motion across the biological body’s surface is skin friction [1,2,3]. Fig-1 depicts that friction is a force that resists an object’s motion, causing it to slow and halt.

Fig-1 Depiction of Friction

2. History of Amonton’s friction laws:

Amonton’s laws of friction are categorized as the classical version of friction laws which have highly been accepted by the engineers dealing with friction [4]. Guillaume Amontons has earned his name in the field of physics and chemistry as a physicist and inventor of instruments. He is also accredited as the pioneer theorist who studied the concept of friction in detail and presented laws of friction. In the field of tribology, Da Vinci, Amontons and Desanguliers along with Euler and Coulomb are recognized as researchers, who not only contributed to the theoretical dimension of the tribology field but also provided the analytical and practical version of the concepts which form the foundation of the modern tribology [5].

Many of the fundamental rules of friction, like the proportionality between normal and limiting friction forces, are believed to have been formulated by Leonardo da Vinci [6]. For generations, however, the study of friction and wear remained mired in obscurity, with only speculative theories to explain the fundamental mechanics. Laws of friction were being rediscovered in the year 1699 which were first introduced by Leonardo Vinci. Despite facing a lot of scepticism, Coulomb analysed and verified these laws in the year 1781 [4]. Understanding the physical principles underlying friction was a key area of research in the 20^thcentury. Frank Philip Bowden and David Tabor demonstrated that the real contact area among surfaces is indeed a very small proportion of the apparent contact area at a microscopic scale [7].

3. The five laws of friction:

3.1 The first law of Amonton’s states that for any object which is under motion the friction is proportionate and perpendicular to normal load.

The friction force rises proportionately as the normal force increases. This is the reason why pushing heavy items is more difficult than pushing light objects. The below figure (Fig-2) depicts that the normal force acting on the object is equivalent to its weight if it is lying on a horizontal surface.

Fig-2 Normal force

3.2 Amonton’s second law states that friction of an object is determined by the characteristics of the surface it comes into contact with.

For example, the friction coefficient is affected by the nature of the contacting surfaces. Certain surfaces, such as rubber on pavements, have a higher coefficient of friction. Others, like ice on steel, have a lower coefficient of friction.

3.3 Friction exists regardless of the area of contact as long as there is one.

Consider 2 objects of same weight lying on the ground as shown in Fig-3. The increase in contact area is countered by a comparable drop in pressure for objects of the same mass i.e., 50N. As a result, regardless of the object’s contact area, the frictional force will stay constant.

Consider turning a box so that very little of it is in contact with the floor. This wouldn’t have an effect on the normal force as the box’s weight remains constant, hence the normal force remains constant, even though the contact area changes.

Fig-3 Friction and Contact Area

3.4 The Coulomb’s Law of Friction states that the amount of the relative surface velocity has no effect on the kinetic friction exerted between the contact surfaces of two dry objects. Velocity has no effect on kinetic friction.

3.5 The static friction coefficient is higher than the kinetic friction coefficient.

For 2 bodies which are in contact the friction laws are elucidated as:

• If there is any slipping or relative movement with respect to one another between these 2 contacting bodies then there’s presence of Kinetic friction which is given by the formula:

f_k = µ_k N

where,

f_k = Kinetic friction

µ_k = Kinetic friction coefficient

N = Normal reaction force

• Kinetic friction acts in opposite direction with respect to the relative velocity of the body. If X and Y are two bodies and X is moving over Y towards right then kinetic frictional force on X would be towards left.
• When the bodies are stationary in relation to one another, the friction between them is static friction, which is always less than or equal to kinetic friction. It’s vital to understand that, unlike kinetic friction, the value of static friction isnot constant. The amount of force applied to the body determines the value of static friction. Assume that the maximal static friction for an object on a particular surface is 10N. When 5N of force is applied to the object then the value of static friction remains 5N and the object would be at rest. When the applied force on the body exceeds 10N then the body begins to move.
• The kinetic and static frictional forces are independent of the contact area as long as the Normal Reaction force is constant.
• When the body is almost about to move, the peak of static friction is obtained. Limiting friction refers to the friction that occurs at this point. Limiting friction is usually somewhat higher than kinetic friction and is calculated as follows:

f_max = µ_s N

where,

f_max = limiting friction

µ_s = coefficient of static friction

N = Normal reaction force

4. Limitations of Laws of friction:

Laws of friction have gained some importance in the modern world in order to solve many tribological and engineering problems [4]. The limitations of laws of friction are that with the development of nanotribology field, the validity of Amonton’s laws is questioned [8]. Many researchers reported failure of the laws at nanoscale and new models are being develop to help engineers in solving various problems.

Reference:

1. “Laws of Friction.” Wikipedia, 3 February 2022, https://en.wikipedia.org/wiki/Friction
2. Beer, Ferdinand P.; Johnston, E. Russel, Jr. (1996). Vector Mechanics for Engineers (Sixth ed.). McGraw-Hill. p. 397. ISBN 978-0-07-297688-5.
3. Ruina, Andy; Pratap, Rudra (2002). Introduction to Statics and Dynamics (PDF). Oxford University Press. p. 713.
4. Popova, Elena; Popov, Valentin L. (2015-06-01). “The research works of Coulomb and Amontons and generalized laws of friction”. Friction. 3 (2): 183–190. doi:10.1007/s40544-015-0074-6. https://link.springer.com/article/10.1007/s40544-15-0074-6
5. Gao, J., Luedtke, W. D., Gourdon, D. R., &Israelachvili, J. N. (2004). Frictional forces and Amontons’ law: from the molecular to the macroscopic scale.
6. Engineering Tribology by Gwidon W. Stachowiak and Andrew W. Batchelor
7. “History of Science Friction”. tribology-abc.com. 21 February 2022, https://www.tribology-abc.com/abc/history.htm
8. Popova, E. and Popov, V.L. (2021), The legacy of Coulomb and generalized laws of friction. Proc. Appl. Math. Mech., 20: e202000062. https://doi.org/10.1002/pamm.202000062
9. HOWELL, H. The Laws of Friction. Nature 171, 220 (1953). https://doi.org/10.1038/171220a0.