 Hi, I'm Zor. Welcome to New Zor education. I would like to talk about friction, friction. This is just one of the forces which we are dealing with on a day-to-day basis. So, the whole theory is really very, very simple. It's probably the problems related to this are much more important and that's why I would like to basically introduce the concept of the friction in this lecture and then have a couple of other lectures dedicated only to problems, because that's probably the most interesting and educational and developing. Okay, so this lecture is part of the physics 14's course introduced on Unizor.com. Now the website Unizor.com contains a course of mathematics, math 14's. Also, there is a US law for teens as well. The site is free. There are no advertisements. So, you're encouraged actually to watch this lecture from the website because it contains lots of very important detail notes for each lecture and exams for those who would like to get involved in a little bit more interesting way of studying. Plus, you have the functionality, educational functionality of this website. If you would like, for instance, to participate in the flipped classroom or study under supervision of a teacher or a parent, there is basically the functionality of the website which allows you to do this. Okay. Back to friction. Well, you know that if you would like to move a furniture, it's hard, right? Why? Well, because there is a friction. So, friction is not really something which you are kind of looking forward to when you're moving the furniture, right? Now, in addition, if you have certain machinery after a certain amount of time, the parts of this machinery are wearing out. Why? Well, because of the friction again. So, friction is not our friend in this particular case. If you are in a, let's say, space shuttle which returns to Earth and it goes through, it enters the atmosphere. At that time, friction between the body of the spacecraft and the air of the atmosphere. The friction is so big that actually your spaceship is heating up tremendously. So, that's just, you know, one of the very important factors why we don't like friction. Well, at the same time, I couldn't really stand on this floor if there is no friction. Friction actually keeps me in place. Friction is something which allows me to hold the glass of water in my hands because if there is no friction, it will just slip down. Friction is keeping the furniture in place, for instance. That's another furniture-related example. So, in these cases, friction is good. We couldn't live without friction. The closet probably would slip off our bodies if there is no friction. So, now, enough theory of kind of practical implementations and practical usage of theory. Let's go to the more physical aspect of it, more theoretical aspect of the friction. So, first of all, why does it exist, the friction? Well, the more or less traditional explanation is that if you have two surfaces, one and another, and they are really touching each other, well, they're not really smooth as I'm just putting in a picture. They have certain bumps here and there, and this one has certain bumps here and there. And when these bumps are catching each other, that prevents the movement. So, if you would like to move this object relative to this, let's say this is a floor, and this is a sofa. Well, these bumps are basically catching each other. They are in this position. And to move it, you have to really like a little bit, maybe even lift, and maybe some bumps will be crashed during this movement. I mean, it's kind of a difficult procedure. So, this is the reason why friction exists. Okay, now let's go back to a little bit more theoretical aspect of it and think about what factors contribute to this friction. And right now, let's consider so-called static friction, which means this object is touching this object, and I would like to move one relative to another. So, in the beginning, they are at rest. And now I would like to move. Now, if they are at rest, these bumps are already caught each other, right? So, to move it, I have to have some kind of a force to either jump over the bumps or maybe crash certain bumps, etc. So, which factors contribute to this force? I need to start movement, start the motion forward. Well, the most important factors are obviously the force. This thing pushes this way and this thing pushes back the reaction, force of action and reaction, because this actually contributes to this catching between the bumps, right? And also what's very important is the material these surfaces are made of. There are smoother materials and there are more rough materials. And obviously, in case of material of a rough structure, this catching is substantial and it's more difficult to move. Now, let's consider the most typical situation that we are on the horizontal plane. Let's say this is the floor and the floor is completely horizontal. So, what kind of forces exist here? Well, obviously, the pressure is a result of the gravitation, right? So, the weight of this guy is this guy onto the floor and obviously the reaction backwards are these two most important contributors to this pressure between these two objects. Okay, now, it has been experimentally established that for given two surfaces, for any pair of given surfaces, weight is actually the most important factor and the force needed to start movement to push from the position of rest forward depends only on this particular pressure or weight in this particular case and is proportional to this. So, the force which is needed to start the motion is proportional to the weight in this particular case. Now, in a more general case, we shouldn't really put the weight, we should really put some kind of force which acts perpendicularly to this surface, right? So, I will use the letter N which stands for a normal. So, the normal force against this surface. Now, why is it important? Well, because our floor can be tilted. In this particular case, force goes this way but it's not really the force, the full weight of this object which contributes to the pressure between these two items. I have to really make such a representation of my weight going normally perpendicularly to the surface and tangentially to the surface and only this component is actually contributing to this formula. Only this component would be N. Now, obviously, there is a reaction force. Now, this is the force needed for basically pushing it down. Okay, so now, let's just consider this particular problem in the following contents. I have this particular structure and let's say this angle is phi. What I'm interested is how big the angle phi should be that the object still doesn't really move, that its own weight is insufficient to move it or if you wish what is exactly the angle phi when the movement starts, right? So, maximum from all those angles when object still stands still or minimum from all those angles when the object slides down just on its own weight. How can I solve this particular problem? Well, again, since my force of the static friction depends on certain coefficient mu, which basically depends on the surfaces and let's consider I know this because I have to know what these objects are made of. Let's say it's a boot or a metal or something like this. They all have different coefficients of friction. Now, considering I know mu, let's just think about what is exactly the force of static friction according to this formula. Well, if this angle is phi, this angle is obviously phi as well, right? Because it's too perpendicular to two perpendicular. An angle between two perpendicular to the sides of the angle and obviously if this is w, this is the weight, then this is equal to w times cosine of phi. Which means my force of static friction which prevents movement is equal to mu times w times cosine phi. Okay, so this force is always against the motion, right? It prevents the motion. Now, what basically this is, this is the maximum force of the friction because let's consider I pull a little bit. Let's consider horizontal place. It's easier. And let's consider that I'm pulling something with certain force but it's very, very weak force. My object would not move, which means that my resistance, which is static friction, is equal to my force which I am applying to pull the object to the left, right? Now, as I'm increasing my force which I'm pulling the object with, object still is in the position of rest, in the state of rest, which means my static friction is increasing as well, right? Because the object stands still, it doesn't move, which means all friction and the force of pulling are supposed to be the same, right? And only if I'm overcoming this particular force of static friction then the object starts moving and that's exactly what this is. This is exactly what coefficient mu is related to. So, it establishes the maximum force of static friction or, if you wish, minimum of the force of pulling to start moving the object. It's either or, it's still the same thing. So, maximum of friction, it cannot go beyond this or minimum of the pulling force to start the motion from the state of rest. Same thing here, except here is the weight, it's just vertical and here the normal does not correspond to the weight. So, this is my normal, this is my force of friction and, okay, so the force of friction always against the movement. Now, my weight, this component of the weight, let's call it weight forward. Now, the weight forward is obviously weight times sine of phi, right? This is phi, this is phi and this is weight times sine of phi. So, this force goes this way and my force of static friction, this one, goes this way. Now, my question is, when exactly the object starts moving? Well, obviously when these functions, when these forces are exactly the same, which means that the maximum static force is equal to my component of the weight, which goes tangential to the inclined, at that moment, this is this pivotal moment. Before that moment, as I'm increasing this, for instance, if I'm increasing the angle, I'm obviously increasing this component. So, before that moment, object stands still, it does not slide down, but as soon as I have reached the angle when this force is equal to the maximum possible friction, static friction, then this is exactly the beginning of the motion. So, these are supposed to be equal to each other and obviously weight cancels out. So, I have sine phi is equal to mu cosine phi or divided by cosine I will have tangent phi equals mu and phi is equal to arc tangent mu. So, this is the answer, this is the angle starting from which, if I increase the angle, my object starts sliding down because my force will no longer be able to hold the object. This will become greater than maximum. So, this force of resistance has certain maximum and the maximum is this one. So, while my weight is such that its tangential component less than that maximum, then the friction will be sufficient to hold the object at the same place. As soon as I have exceeded that maximum, immediately I start moving. So, what's important here is that the static friction force is only as big as I'm trying to pull the object and start moving, but not greater than certain maximum value which is determined by the coefficient of static friction and the normal pressure between the surfaces. Alright, so this is all about static friction. Static friction is when we are trying to start moving the object. Now, I'm sure everybody noticed that if you are moving a sofa, if you ever move a sofa, it's more difficult to start moving than to continue moving. So, once it's already moving, it's kind of easier to move it further. Now, why is that? Well, there is a concept of, as I was saying, static friction and there is a concept of kinetic friction. So, kinetic friction is a friction between moving parts. And it's not the same obviously as friction between the parts which are not moving against each other. Now, why they are different? Well, let's go back to this theory of the friction related to these bumps. You see, if the objects are not moving against each other, the pressure which is applied from this to this or from this to that is sufficient to penetrate. So, bumps of the top part penetrate in between the bumps of the bottom part. As soon as they start moving, they don't really have time to go deeper. They are kind of sliding on the surface. They are definitely touching something. All these bumps are touching. But this is much more difficult situation to overcome than this. So, if they are just slightly touching each other and that's exactly the case when we start moving, then it's kind of easier to move further because these bumps are not deeply penetrating into each other. Now, does it depend on speed? Well, yes, but most likely it's not that much of a dependency. And in the problem which we will be solving, in most of the cases we will not really have this dependency. I mean, intuitively you would think that with the higher speed the tension, this friction between these two parts should be smaller because the penetration would be even less deep, right? More shallow. But at the same time if you think about this, these bumps are so tiny that even normal and relatively slow speed would still be sufficient for them to basically slide only on the tops of each other without any kind of deep penetration. But obviously it's an approximation and this particular law, it's not really 100% mathematically correct law. It's kind of an approximation and it's sufficient in our experience to have this approximation as long as we know the coefficient of static friction or in the case of kinetic friction, the coefficient of kinetic friction. So these are two different things. I mean, the state of rest is significantly different from state of movement as far as the friction is concerned. But one state of movement with one speed from another state of movement with another speed, they do not really differ that much and we usually ignore these differences. So we will have to deal with two different kinds of coefficients of friction. The static coefficient to start moving the object, which by the way we will rarely use in our problems, and kinetic friction. That's the friction of the same type actually. It's also the force of friction will depend on some coefficient of kinetic friction and the normal pressure. So the formula is exactly the same but coefficient between two different kinds of surfaces like between metal and metal or whatever else is probably different in case of movement than in case of starting motion from the position of rest. In any case, my point is that the old theory which I was just talking about is exactly the same. And if you already have a problem where the motion is kind of already occurring, then you obviously have to talk about the kinetic motion. If you have a problem, which by the way I think is a rare problem, when you have to start moving, then basically the problem is exactly the same. The only difference is the quantity of this coefficient has a different number basically. So it's one number of certain units per whatever in one case and a certain unit in another case. And by the way what's interesting about these things, this is the force which means it's a vector, right? Now what's the direction of this force? Well the direction of this force is against the movement. Now if there is some kind of a trajectory where our object is moving, then this force, since it's directed always, for instance this is my movement. Now my force of friction always against it, which means it's always tangential to trajectory. Now this is always perpendicular to trajectory. So this is not a vector equality. This is equality between the magnitudes of these vectors. So the correct would be either just don't use this bar on top, so just this, assuming that we are dealing with magnitudes of these vectors. Directions we do know this is tangential to trajectory, this is perpendicular to trajectory. Because obviously the tension depends on how you press the surface where you are moving, right? And as far as direction, so these are perpendicular to each other. And this is purely numerical, it's not vector equality. It's purely numerical equality because this particular two things are in perpendicular directions, right? Okay, that's basically it. Now I promised to solve a few problems that would be the subject of one or two next lectures about frictions. And other than that, that's it. I do suggest you to read notes to this lecture. There are quite substantial, quite details, you can read it like a textbook basically. And it's more or less whatever I was just talking about, but it's still nice to read it again. Okay, that's it. Thanks very much and good luck.