Lec 18 Friction I

0:41 Let us move on to our next chapter on Friction. See, in common usage of the word friction, even in the relationship when we say if there is friction, we use it in a negative connotation; we are not using in a positive connotation. If you ask the question whether friction is a bane or a boon, you find friction is needed in certain applications. Even for you to walk, you need friction. I have shown, it on a glass floor if somebody walks, you have to walk very carefully. That is what you see here. Without friction, you cannot walk. And, if you go to your simple ‘atta chakki’; this is driven by belt drives, and these belt

1:34 drives employ friction. So, in such applications friction is beneficial. Friction is also beneficial in another application that deals with braking system. So, when you apply the brake, because of the friction, the wheel comes to a stop. So, there are many applications where friction is needed for our own good. There are also many other situations where friction is undesirable.

2:22 You know, lots of money is spent on lubrication. This is the IC engine which is used in automobiles; and you have millions of automobiles, they all use oil to minimize the friction between the cylinder and the piston. And, you also have several applications of journal bearing where oil separates metal-to-metal contact between the shaft and the bearing. And, if you go and see a machine in the workshop, you would see lot of oil is used to lubricate

3:12 the systems involved. And, here you also have a system where this is pumped like this, and you have a worm and worm wheel; that assembly is literally flooded with oil to remove the frictional effects. This is one example. You also have another example; this is a quick-return mechanism of a shaper, is literally in oil. It is a pool of oil here. We will also have an occasion to solve this quick-return mechanism when we see dynamics. So, in all these applications, you find, you need to minimize the effect of friction. So, you achieve this by having a medium of oil to solve your frictional issues.

4:07 And, we have also seen earlier when we studied support conditions; when I have a pin-joint, it restrains translation in two directions. And, you have two reactions; the force is unknown and the direction is unknown. So, you have essentially two unknowns. We also saw frictionless thin bearings; here again, the direction as well as the magnitude are not known - you have two unknowns. Extending this, you have in the case of rough surfaces in contact; the rough surfaces are shown highly exaggerated, you have two forces, a normal force and a frictional force.

4:59 In all problems dealing with friction, one of the challenges is to find out what is the actual direction of the frictional force. And, from the laws of dry friction when the motion is impending, it is possible for you to write the frictional force from the equations of friction. In all other cases, you will have to determine these forces only based on the free body diagram of the component under consideration, which we will emphasize and see later also. And, what are the classifications of friction? It can be broadly classified as external and internal. In external friction: I will have static friction, I will also have dynamic friction.

5:50 And, internal friction: I have fluid friction as well as solid friction. What do you call as external friction? The interaction between surfaces of two solid bodies in contact; this can be static friction or dynamic friction. In static friction, the surfaces are at rest, but there is a tendency for relative motion. See, only when there is a tendency for relative motion, frictional forces come into play. Until then, frictional forces do not come into play. And, in dynamic friction, the surfaces are in relative motion.

6:41 See, in earlier books you would also find the term called kinetic friction. The current practice is to do away with kinetic friction, and embody all that what we have discussed under the ambit of kinetic friction as dynamic friction. That is the new terminology that is accepted. And, before we get into the details of external friction, let us have some brief discussion on fluid friction as well as solid friction. This is developed between fluid elements when adjacent layers in a fluid are moving at different velocities.

7:26 This is possible only when you have the metal-to-metal contact is completely separated by your lubricating oil. And, what is interesting here is, the frictional force developed is proportional to the relative velocity between the layers, and the fluid’s viscosity. It is also interesting to note; in your course related to physics, you are already exposed to certain aspects of friction, and you might have also heard the frictional force is proportional to the normal reaction. From Newton’s third law, you have also learnt force is proportional to the acceleration;

8:16 related to the acceleration. So, in case of a dry friction, you find the frictional force is directly proportional to the acceleration. In the case of fluid friction, it is proportional to relative velocity. And, we would see later, in the case of solid friction the frictional force is related to displacement. This is very very interesting. And, fluid friction is useful in problems of flow through pipes or orifices, bodies immersed in fluids, lubricated surfaces and so on. This is also called viscous friction. And, you know fluid friction appears as frictional drag, which is seen in the design of automobiles.

9:04 And, India is also going in for a high-speed train. If you look at the stream lined body contour of the engine; this is essentially done to minimize the frictional drag. And, also in the case of sports, if you look at the cycling in Olympics; the participants are competing with each other, and they can have an edge over the competitor if he or she wears an appropriate clothing. The dress is designed based on frictional aspects, and if they reduce the frictional drag from that, they may have an edge of the order of 0.1 seconds compared to the competitors.

9:56 And, another interesting aspect is; in the case of vibration studies, you use the damping as viscous damping. And, this is also used in aerodynamics; the frictional drag in the, as frictional drag in aerodynamics and as viscous damping in vibration studies. And, this is what you see here; in the vibration study, I have a spring and dash-pot. And, dash-pot has viscous fluid. And, you find the amplitudes reduce rapidly because of the viscous damper. And, this is the case of a shaft running in a journal bearing, completely separated by

10:41 a fluid film. And, this develops a maximum pressure slightly to the left. This is where it develops a maximum pressure; there is no metal-to-metal contact, fluid completely separates it. In such a case, in well lubricated applications; you have to employ only fluid friction for analysis. That is what is again seen here. I have the lubricating oil is pumped on to this; you find this is the contact point where you have a flood of viscous oil. So, this has to be analyzed based on fluid friction.

11:30 You also have the other application. This is the quick-return mechanism of a shaper; this is almost in a bath of the oil. In fact, it is a very big subject by itself. Tribology is the name of the subject. And, you have engineers who are trained on how to circulate the viscous oil to all the components in the engine. And, with space application, how to handle microgravity; zero gravity applications are also becoming very important. You also have journals that deal with wear. So, it is not a trivial aspect.

12:17 One has to handle friction very very carefully. And, it is also surprising, when solid materials are subjected to cyclic loading, one comes across the impact of solid friction. Energy is dissipated internally within the material; that is why it comes under the category of internal friction. For example, if you put an oscillating spring in vacuum, it comes to rest on its own. The moment you put it in vacuum, you make sure that there is no frictional drag because of the surrounding air. So, that is eliminated. When there is no retarding effect visibly, you imagine if you disturb the spring, it

13:04 would continue forever. It does not happen. Even in vacuum, this spring comes to rest. And, the energy dissipated per cycle is independent of the frequency over a wide range of frequencies, and is proportional to the square of the amplitude of vibration. So, it is interesting to note, frictional force is proportional to the displacement. This is what I mentioned to you also earlier. In one case, frictional force is proportional to displacement; in another case, frictional force is proportional to relative velocity. In the case which you normally come across, frictional force is proportional to the accelerations.

13:52 So, you have all the three possibilities. And, this spring comes to rest after a long period of time. And, in vibration problems, material damping is usually included as equivalent viscous or Coloumb friction. Either it is related in terms of fluid friction, or it is related in terms of dry friction, to simplify the analysis. See, even in friction, experiments have played a very very important role in understanding the concepts. Let us get on to dry friction. Suppose, I have a block and I have a force F 1 acting on it.

14:41 Are frictional forces developed? Frictional forces are not developed. In the absence of an external force to cause a tendency for relative motion, no frictional forces are developed. Only when a force which tries to dislodge; when there is a relative motion possible between these two surfaces, you have frictional forces developed. And, frictional forces are developed, and the object continues to remain at rest until the force applied reaches a threshold value. This is a common experience.

15:26 I have a table in front of me. Suppose, I want to push this table; common experience is you go and try to push it. After you apply sufficient amount of force, suddenly you find the table picks up an acceleration. And, it also becomes easier for you to push it further. And, when F reaches the maximum frictional force, the object will be on the verge of sliding. And, this is what is put in the graph. It is plotted between applied force and the frictional force. It remains linear. As the applied force is increased, frictional force is also increased.

16:13 It cannot indefinitely increase. It reaches a maximum value dictated by the frictional coefficient between the surfaces. And, this happens; reaches a maximum value when the motion is impending. That means, if the forces are slightly increased further, the block or the object will tend to move. Under this situation, the block is at rest. Suppose, I increase the force; you also plot between-. Relative motion starts when I increase the force, dynamic friction comes into play and

17:01 frictional force is reduced. This is a common feeling; experience. If you take a; if you have to push a table, you find at some point in time, you have reached the maximum force. Then the block or the table whichever you are trying to push picks up an acceleration. Why it picks up an acceleration? There is a drop in the force. That is documented in the form of a graph like this. There is a reduction. After that, it remains constant. It is also an idealization. Frictional force is independent of relative velocity, up to a limit. Beyond that, there are changes, it drops down. And, in this situation, the block is in motion.

17:50 It is always desirable that you plot these graphs as two graphs as it is shown in this slide, because, the first graph is between applied force and the frictional force, second graph is between relative velocity between contacting surfaces and frictional force. Many books simply combine these two as one graph, which is strictly not correct. And, what are Coloumb’s laws of dry friction? Though they are attributed to the scientist Coloumb, the first two laws are formulated by another scientist called Amonton. And, these are based on experimental observations.

18:37 They are empirical laws. And, the law states - magnitude of the frictional force is directly proportional to the normal load between the surfaces, for a given pair of materials. What you need to understand is; the coefficient of friction is always given for a pair of materials. It is not given for one single material. Between the two materials, what is the coefficient of friction. And, what is said here is; magnitude of the frictional force when we mean, we mean the maximum static frictional force. And the second law is; this maximum static frictional force is independent of the area

19:25 of the contacting surfaces, which is known as an apparent area for a given normal load. It is a very subtle point. Because, normally you associate when you bring in your intuition, if I have a larger object, it has a larger surface, you may think that it would offer larger resistance because of friction. This is not so. We will also see some of the details as we go by. To these two laws, Coloumb added a third law which says, magnitude of the frictional force - when we say this, we always mean the maximum static frictional force when the object is at rest. And when the object is moving, kinetic or dynamic frictional force; is independent of

20:16 sliding velocity. This is an experimental observation. We also have situations where this is violated. And, what happens in such a case? The first law may be expressed simply as the frictional force is less than or equal to mu s N. Please note down the mathematical inequality written here. Normally, people write this, equal to mu s into N. But, you should recognize from the way we have learnt, what happens when the frictional forces are developed. In the initial stages, the frictional forces are dictated by the conditions of equilibrium. And, it reaches a threshold value when the motion is impending.

21:08 When there is impending motion taking place, only at that condition, I have f equal to mu s into N. This is the coefficient of static friction, that is why the symbol s is used. And, N is the normal load. And, you should note here; when I want to denote this as a force, these are written in terms of italic font. One may confuse this with the Newton as the force unit; that is always written as a normal font without this italic. So, see the distinction. And, you know, it depends only on the two contacting surfaces.

21:54 I have one surface shown as in this color, another surface in this color. Suppose, I apply a smaller load here, and I apply a larger load here. The experiments reveal, even if the load is varied by a factor of 10 power 6; the force is shown by a thin arrow indicating 1 gram of load, and this is shown by a very thick arrow indicating one ton, separated by a factor of 10 power 6, the coefficient of static friction between the surfaces in both the cases remain same. They do not have a change.

22:40 And, this is based on experiments. Without experiments, one can never appreciate this concept. Intuitively, you may feel, more frictional forces would be developed; but the coefficient of static friction, that remain same; that does not change. So, that you will have to make a distinction; mu s is independent of the normal load. And, another aspect is; experiments also reveal that mu s remains constant even when area of contact is varied by a factor of 250 times.

23:26 What we normally see is only an apparent area, that is nothing but the area that we measure macroscopically. And, I show an example here. I have the surface, on this I have an object supported on a knife edge. I apply a force to displace this. And, I have another situation where the block is resting on one of the edges. The third situation where the block is resting on an edge like this. In all the three cases, the coefficient of static friction remains same; it does not change at all. The experiments reveal, even if the apparent area is increased by 250 times, there is no

24:13 change observed. For all practical purposes, we can take that this is independent of the area of contact, and also the load that is acting on the object. In a similar vein, we also find coefficient of dynamic friction is nearly independent of sliding velocity. And, what is the best way to find out the coefficient of static friction? We would see a demonstration, and we will also see that by an animation. See, one of the simplest experimental methods to find out the coefficient of friction is the inclined plane. In this, you make the plane made of one material or you put the material for which you have

25:04 to find out the frictional coefficient as the base. Then you have a sample; in this case, I want to find out for the same material. I have a block made of this, I put it on this, and slowly increase the orientation. And, find out at what angle the block slips. Student: 22. What is the angle? Student: 22. 22 degrees, ok. Now, I have the same block. Instead of putting it like this, let me put it this way. The surface area is less. And, this also happens more or less at a similar angle. So, this indicates that surface area has no role to play in determining the coefficient

25:54 of friction. And, if I have to find out for another material; I have this, it is aluminium. I put the aluminium here, and raise it; and slowly raise it. And, you have to see at what angle this slips. It slips at this angle. Student: 26. This is happening at an angle 26. And, what you have to appreciate here is; you have to appreciate that the motion is impending, only at a stage where this is about to slip. If I slightly raise the plank, it will start slipping. So, you have to correctly identify that portion; that position and you have to employ that

26:41 for applying your frictional laws. When I say frictional force is proportional to mu into N; it happens only when the motion is impending. That is very important to see. The first case, I have Perspex on Perspex, the frictional; it is very very smooth. I have a smaller angle, that is about 22 degrees. And, for aluminum, between aluminum and Perspex, it is found to be 26 degrees. So, now I have this animation, and you find the block is sliding. I will repeat this animation again. And, what is drawn here is; I have the free body diagram of the block - weight is acting

27:33 downwards, friction is opposing the motion and your normal force is shown slightly displaced. It is a good practice to put in this way. And, from this experiment, if you measure the angle at which the block is about to slide, you call that as angle phi s which is known as the friction angle. Based on the equilibrium equation, this is related to the coefficient of static friction as mu s equal to tan phi s. I will repeat this animation. The important point what I want to see is; if I displace slightly at this stage, the block slides.

28:19 So, you have to understand what is the meaning of impending motion. Only when slight angle is modified, the block is going to slide - that moment is impending. You know, in the game of tug-of-war, when you are pulling the rope, when the rope is about to slide out of your hands; that is the time the motion is impending. And, you should know how to identify whether the motion is impending or not. You understand whether the motion is impending only when the actual slipping takes place. But, we are talking about the situation where slipping has not taken place; but any slight

29:06 modification would precipitate sliding of the objects concerned. So, that is what is illustrated in this. And, when you look at the mathematics, I get the expression mu s equal to tan phi s. This is not dependent on the mass m or the force of gravity g; acceleration due to gravity g. It is not a function of these two. And, in fact, if you go and see in many places where they store sand or where they store some of the construction materials, or also in the places where they have grains in large

29:55 markets where they put it in a pile; depending on the material that you have, they will automatically form a cone of a particular angle. And, this is also known as angle of repose; that is dictated by the friction. This is also known as angle of repose. And, you again see, what is the meaning of impending motion. When I slightly change it, the block begins to slide. So, the situation just prior to this is the condition for impending motion. What happens at higher relative velocities?

30:42 When the block is in motion, it is dictated by the coefficient of friction, which is known as dynamic friction indicated by the symbol mu with the suffix d. At very high sliding speeds, for metal-to-metal contact, mu d falls with increasing velocity. This is what is observed. What is the consequence of it? This phenomenon is observed for poorly lubricated or unlubricated surfaces, that may lead to frictional oscillations called stick-slip. In fact, in some of the movies where they want to show a very eerie condition, in midnight you would enter into a bungalow where there will be a door which will be oscillating like

31:31 this and generating a creaking sound. You feel the situation is very uncomfortable for you to feel. The creaking sound what you hear is mainly because of the phenomenon called stick-slip. So, it is seen even in simple doors if they are poorly lubricated. And, what happens when the objects under consideration are well lubricated? Friction coefficient mu d increases with increase in sliding velocity and minimizes the frictional oscillations. So, it is always desirable that you should have well lubricated surfaces. So, normally that is what you will do.

32:17 If there is a creaking sounds from your door, you take a drop of oil and put it; you essentially lubricate it. You do not even need to study mechanics to do this. You are not comfortable with the sounds, so, you simply put an oil and manage the situation. So, from a scientific perspective, you have to lubricate it well so that you can increase the coefficient of the dynamic friction so that you minimize the frictional oscillation. And, how do I select the appropriate frictional laws? Three possible states of the surfaces are identified. One can be dry; greasy or partially lubricated; film or completely lubricated.

33:03 For the first two cases when it is dry or partially lubricated, laws of Coloumb friction are applicable; that makes our life very very simple. On the other hand, when I have a film that completely separates the metal-to-metal contact; even though I do not see visibly here, there is a film available in between the two; it is very very small in thickness with a very high pressure. In such cases, you have to apply laws of viscous friction for the analysis of the problem. So, in dry friction or Coloumb friction, it is essentially external friction phenomena,

33:55 you have both static and dynamic friction. In dry friction, maximum frictional force is proportional to the applied normal load; the concept is re-emphasized. And, this maximum frictional force occurs only when the body is just about to slip. That is a key point to note. For any frictional problem, you cannot simply replace the frictional force as mu times N. Only when you investigate and find out relative motion is possible, or motion is impending, then only you can say frictional force equal to mu times N. And, you will also have to note that dynamic frictional force is always less than the maximum

34:45 frictional force when the body is just about to slip. And, you know, this is very useful to study wedges, power screws. Power screws are nothing but wedge wrapped around a cylinder. And, you have a square threaded screw which is used in many mechanical engineering applications. Partially lubricated bearings; you have an important application of brakes, clutches and belt drives. In all these cases, you can apply laws of Coulomb friction and get your parameters calculated. And, you know, it is better that you learn the concepts by solving a simple problem.

35:34 I have a block of 2 a by 2 a, weighing 200 Newtons. And, in this case, you will have to find out, for different forces F 2 starting from 0, 50, 90, 100 Newton; find out the condition of the block, and also determine the reaction forces. And, it is given in the problem statement that the coefficient of static friction between the block and the floor is 0.3 and the dynamic coefficient of friction is 0.25. You can note clearly here, the mu s is greater than mu b. Please ponder about this problem, and we will try to solve it in the next class.

36:23 So, in this class, we had a brief idea about what are the classifications of friction; we classified as external and internal friction. In external friction, you have it further classified as static and dynamic. In internal friction, we looked at fluid friction as well as solid friction. And, the interesting point I brought into focus was; in one case, frictional force is proportional to displacement; that is what happened in solid friction. In the case of fluid friction, frictional force is proportional to relative velocity. And, in the case of dry friction, frictional force is proportional to the acceleration. And, I have cautioned, in problems dealing with friction, you should recognize that frictional

37:14 forces develop only when there is tendency for relative motion. Further, in initial stages, the frictional forces are dictated by the equilibrium condition. The frictional forces increase as the external forces are increased. It reaches a maximum value when the motion is impending. Only at that condition, you can replace a frictional force as mu times the normal force. Thank you.