WEBVTT physics/high-school-physics/selhorst-jones 00:00:00.000 --> 00:00:05.000 Hi, welcome back to educator.com, today we are going to be talking about friction. 00:00:05.000 --> 00:00:09.000 At this point, you have got a really strong grasp on the basics of Mechanics. 00:00:09.000 --> 00:00:15.000 Force = mass × acceleration, we have talked about it in two dimensions, you have got a really good idea of how Newton's laws work. 00:00:15.000 --> 00:00:22.000 But so far, we had to pretend that friction does not exist, as if something that we could not really deal with. 00:00:22.000 --> 00:00:24.000 But no more, now we are finally going to tackle friction. 00:00:24.000 --> 00:00:32.000 You have got enough understanding about mechanics, you will be able to understand how to use friction in our work. 00:00:32.000 --> 00:00:37.000 First, let us get a sense of how friction works in two dimensions. 00:00:37.000 --> 00:00:42.000 Imagine you have got a plank of wood that you are pushing along at a constant speed. 00:00:42.000 --> 00:00:47.000 Here is some floor, here is some plank of wood on that floor, and we are pushing it along at a constant speed. 00:00:47.000 --> 00:00:57.000 First thing to notice, is that in real life, we are used to the idea that if we want something to move, (since everything experiences friction), you have to push on it if you want to keep a constant speed. 00:00:57.000 --> 00:01:04.000 It is not going to have that constant speed unless you push on it, because friction is going to sap the energy out of it. 00:01:04.000 --> 00:01:11.000 So, for the first time, we are saying that we need a constant force to keep that constant speed. 00:01:11.000 --> 00:01:19.000 Up until now, if we had any force at all, we would have had an acceleration automatically, because we have been talking about being on a frictionless surface. 00:01:19.000 --> 00:01:26.000 It would be a small acceleration, but we would have had some acceleration because we would have had some force, unless all the forces are cancelling out. 00:01:26.000 --> 00:01:32.000 Now, we are going to have all the forces cancel out, because we have friction cancelling out the forces we are putting in, so we can have a constant velocity. 00:01:32.000 --> 00:01:38.000 With that out of the way, we have got this plank moving along at a constant speed, because we are putting in some force into it. 00:01:38.000 --> 00:01:44.000 Now, which would be easier to push, which would take less push, which would take less force for pushing on the plank? 00:01:44.000 --> 00:01:53.000 The plank was on a floor that is made of wood, or the plank on a floor made of rubber, which one of these will stick together more, which one will have more friction? 00:01:53.000 --> 00:01:56.000 Just like you would expect, the wood. 00:01:56.000 --> 00:02:00.000 The wood is going to stick less, and the rubber is going to stick more. 00:02:00.000 --> 00:02:03.000 If we want to make it easy for ourselves, we are going to want that wood floor. 00:02:03.000 --> 00:02:07.000 What if we were to put the plank on a piece of ice? 00:02:07.000 --> 00:02:08.000 It is going to make it even easier. 00:02:08.000 --> 00:02:12.000 Different pairs of materials have different connections. 00:02:12.000 --> 00:02:26.000 They behave differently with one another because of material science and chemistry and stuff that we are not going to really talk about, but friction is a pretty complicated idea that we will experience in lots of further courses and there is lots of cool interesting things to learn about it. 00:02:26.000 --> 00:02:31.000 But in our case, we just know that, if we have different materials, we are going to have different frictions. 00:02:31.000 --> 00:02:37.000 Different PAIRS of materials, that is an interesting thing to keep in mind, it is not just one material, it is the pair of it. 00:02:37.000 --> 00:02:41.000 If we had a rubber plank on top of that rubber floor, we would have experienced even more friction. 00:02:41.000 --> 00:02:45.000 An ice plank on top of an ice floor, it would have been the least of all. 00:02:45.000 --> 00:02:50.000 It is the pair together that gives us the friction between them. 00:02:50.000 --> 00:02:52.000 Let us talk about another thing for our intuition to deal with. 00:02:52.000 --> 00:03:00.000 Imagine that, that same plank of wood is on a wood floor, but this time, we are going to put some sack of sand on top of it. 00:03:00.000 --> 00:03:11.000 So, we have got some sack on top of it, and there is going to be some amount of sand, it is either going to have 10 kg of sand, or 20 kg of sand. 00:03:11.000 --> 00:03:13.000 Which one is going to be easier to push along? 00:03:13.000 --> 00:03:21.000 The 10 kg sack or the 20 kg sack, which one is going to have more friction reacting with that? 00:03:21.000 --> 00:03:30.000 More friction force for us to overcome, the 10 kg sack push on the plank or the 20 kg sack push on the plank? 00:03:30.000 --> 00:03:32.000 Which one would you expect? 00:03:32.000 --> 00:03:34.000 It is just like you would expect, it is the 10 kg sack. 00:03:34.000 --> 00:03:42.000 More pressure means more friction, harder we push on something, the more the friction that we have to overcome. 00:03:42.000 --> 00:03:47.000 The lighter something is, the lesser friction that we have to overcome. 00:03:47.000 --> 00:03:54.000 Assuming the same object, and the same material for the incline, which of the following three situations will be the easiest to push? 00:03:54.000 --> 00:04:00.000 It is similar to the pressure idea, now we are going to start talking about the normal force. 00:04:00.000 --> 00:04:06.000 In all of them, gravity ('g') is pointing straight down. 00:04:06.000 --> 00:04:08.000 Which one of them would be easier, which one of them would you expect to? 00:04:08.000 --> 00:04:10.000 Just like you would expect, the steepest incline. 00:04:10.000 --> 00:04:12.000 Why is that? 00:04:12.000 --> 00:04:16.000 We can explore that idea by looking at two extreme scenarios. 00:04:16.000 --> 00:04:20.000 The exact same object and the exact same surface, but very different orientations. 00:04:20.000 --> 00:04:24.000 One of them is a horizontal orientation, the other one is a vertical orientation. 00:04:24.000 --> 00:04:27.000 Which one of these is going to have more friction going this way? 00:04:27.000 --> 00:04:34.000 Here is our friction force, here is our friction force, which one is going to experience more? 00:04:34.000 --> 00:04:36.000 The one that is sitting on it. 00:04:36.000 --> 00:04:37.000 Why is that? 00:04:37.000 --> 00:04:49.000 That is because, this one has 'mg' down here, so it has got the pressure (the normal force) pushing that amount. 00:04:49.000 --> 00:04:53.000 How much does this one on the right, how much is the force normal? 00:04:53.000 --> 00:05:12.000 We have got 'mg' down here, but there is nothing this way, so our normal force, FN = 0, because there is no pressure, no interaction, nothing holding it against the wall to cause friction to happen. 00:05:12.000 --> 00:05:15.000 If you push really hard on something, it is going to have more friction. 00:05:15.000 --> 00:05:21.000 If you do not have any push between the things at all, there is no way for the materials to interact, there is no friction between them. 00:05:21.000 --> 00:05:24.000 If we have no normal force, we have no friction. 00:05:24.000 --> 00:05:29.000 If we have a lot of normal force, if we push really hard on it, we are going to have more friction. 00:05:29.000 --> 00:05:56.000 If we were to instead, come along and push crazy hard on this, then we are going to have a resultant normal force that is equal and opposite, we are going to have this normal force because it is not going to blow through that wall, assuming the wall is able to withstand that much force, we might actually to able to arrest the power of gravity, arrest the acceleration due to gravity, the force due to gravity will be canceled out because we will be able to make a really large friction by pushing really hard. 00:05:56.000 --> 00:05:59.000 You can test this out in a real quick demonstration. 00:05:59.000 --> 00:06:06.000 If you take just a normal book, and you go up to a flat wall, and you just put the book up the wall, and you take your hand away, of course the book falls to the ground. 00:06:06.000 --> 00:06:10.000 It is like you would expect. 00:06:10.000 --> 00:06:20.000 If you were to put the book up against the wall, and push really hard with the flat of your hand, not under it, because then you would be holding it up, it would not be friction, it would be just direct force applied through your finger tips. 00:06:20.000 --> 00:06:32.000 But instead, if you were to push really hard against it, you will be able to keep it in place, because you put so much pressure on it, the friction of the book against the wall is going to be able to overcome the pull of gravity. 00:06:32.000 --> 00:06:37.000 It is going to beat out gravity, and it is just going to stay still. 00:06:37.000 --> 00:06:50.000 Just like you would expect, from all this talking, friction is not just weight, it is about how hard the object is pushed, it is about the pressure between the object and the surface, the two materials, the interaction, it is the normal force. 00:06:50.000 --> 00:07:09.000 For those of you having trouble with calculating the normal forces on inclines, I would recommend you to refer to the 'Newton's second law in multiple dimensions lecture', it will give a good explanation. 00:07:09.000 --> 00:07:25.000 You need to calculate just how much of the gravity is perpendicular and parallel to the surface. 00:07:25.000 --> 00:07:31.000 To sum up, friction is based on the interaction between the materials involved in it, and the normal force of the object on the surface. 00:07:31.000 --> 00:07:38.000 What kind of materials do we have, how hard the pressure is, the two things, the normal force. 00:07:38.000 --> 00:07:51.000 If you want to turn that into an equation, that's going to become the friction = μ × FN... 00:07:51.000 --> 00:08:13.000 μ is a Greek letter, and it is the coefficient of friction between the two materials, and it is spelled 'm-u', it will change depending on what the materials are, and it is going to vary a lot depending on specifics, and we have to determine it experimentally. 00:08:13.000 --> 00:08:19.000 There is no easy formula for determining what it is going to be. You just have to go into a lab, get it, or look it up in a table. 00:08:19.000 --> 00:08:35.000 Even in looking up a table, it is going to vary, because depending on the specific condition of the object, whether it is dirty, clean, if it is wet, if it has grease on it, if there is a layer of air, if it is operating in vacuum -- what things are happening between it, it is going to vary a lot. 00:08:35.000 --> 00:08:42.000 So, it is basically up to you to figure it out in a lab, or to be able to look it up in a table where it has some very, very similar situations to the way you are doing it. 00:08:42.000 --> 00:08:45.000 Or, it is given to you precisely in the problem statement. 00:08:45.000 --> 00:08:52.000 So, figuring out μ can be a little difficult, but normally that's what the problems will be about, or it will be given to us in the problem. 00:08:52.000 --> 00:09:08.000 Once again, going back to the equation, friction = μ, the coefficient that represents the interaction between the two materials, times the force, the normal force, fn. So μ × fn. 00:09:08.000 --> 00:09:16.000 One thing to keep in mind, is that we do not have to worry about the area touching it. 00:09:16.000 --> 00:09:27.000 If we had a block of mass 'm', and we had a table of mass, 'M', but the same material on the bottom. 00:09:27.000 --> 00:09:35.000 Same material here, same material here, same surfaces, it is not about the cross-section, the area touching the ground, it is just about the pressure. 00:09:35.000 --> 00:09:37.000 Why is that? 00:09:37.000 --> 00:09:43.000 That has to do with the way friction works, it is what is happening on a really microscopic thing. 00:09:43.000 --> 00:10:00.000 If we have a lot of area, the pressure per square area, the force per square area, is going to wind up being much smaller in the case when we have got that large surface. 00:10:00.000 --> 00:10:28.000 So, same pressure, but it is going to be extended over a large area, whereas in the table example, where we have got just the little weak contacting, it is going to be the same pressure, but it is going to be over a small area, so the total effect is going to be the same, either a small force per area, but over large area, or a high force oer area, but over a small area, the total effect of the pressure is going to be the same. 00:10:28.000 --> 00:10:35.000 So you do not have to worry about the cross-section, you just have to worry about the interaction between the materials. 00:10:35.000 --> 00:10:37.000 One last thing: Friction is a force. 00:10:37.000 --> 00:10:41.000 We know forces come in vectors, so what direction does friction come in? 00:10:41.000 --> 00:10:47.000 It is not going to go in the direction of the normal fore, that is why our equation in our previous page was not in vectors. 00:10:47.000 --> 00:10:51.000 Because it is upto us to figure out what direction friction is going to go in. 00:10:51.000 --> 00:10:53.000 Friction always opposes the movement. 00:10:53.000 --> 00:11:05.000 Whatever direction it is moving in, keep in mind that it is the velocity , not the acceleration, whatever direction it is currently moving in, it is the opposite direction that the friction is going to point. 00:11:05.000 --> 00:11:16.000 Friction always is fighting current motion, so the velocity, whatever the direction of velocity is, the opposite of that direction, is the direction that our friction is going to move in. 00:11:16.000 --> 00:11:20.000 So with this point, we have got a pretty good understanding of how force works. 00:11:20.000 --> 00:11:22.000 We have got this interaction between μ and the normal force. 00:11:22.000 --> 00:11:25.000 Let us consider these two diagrams here: 00:11:25.000 --> 00:11:32.000 We have got, the block is the same in both diagrams, and the surface it is resting on is the same on both diagrams. 00:11:32.000 --> 00:11:36.000 Let us assume that F1 and F2 are both big enough to move the block. 00:11:36.000 --> 00:11:47.000 But also that, F1 and F2 are equal in magnitude, they are the same number of newtons. 00:11:47.000 --> 00:11:54.000 If F1 and F2 have different orientations, but same magnitude, which block will accelerate faster? 00:11:54.000 --> 00:12:16.000 If we break down our forces into components (we can do that since force is a vector), we look at the vertical amount in F1 and the horizontal amount in F1, and over here, the vertical amount of F2, and the horizontal amount of F2. 00:12:16.000 --> 00:12:32.000 We see that the thing that is actually do the motion here, is this right here, it is going to be the actual horizontal motion is going to stem from the horizontal component of our force. 00:12:32.000 --> 00:12:39.000 If we were instead looking at what the normal force is now, we need to figure out what the normal force is going to be. 00:12:39.000 --> 00:12:41.000 Both these cases, we still have gravity to contend with. 00:12:41.000 --> 00:12:42.000 We have not dealt with gravity. 00:12:42.000 --> 00:12:49.000 So there is the force of gravity, and over here, it is going to be the exact same force of gravity, so force of gravity on both of them. 00:12:49.000 --> 00:12:54.000 How much does the normal force has to be to cancel these things out. 00:12:54.000 --> 00:13:09.000 Before when we were talking about the force of gravity and the normal force, they were going to be equal to one another (in the horizontal case), because the only thing creating the normal force is gravity. 00:13:09.000 --> 00:13:23.000 But in this case, if you push through an object, and the object does not blow through the table, then that means that the table has to resist both the object's force of gravity, and in addition, the force that you put into the object. 00:13:23.000 --> 00:13:33.000 So, the table, the surface has to resist both the forces, that has been put into it by ourselves, by the problem, and the force that is put into it by gravity. 00:13:33.000 --> 00:13:44.000 In the first case on the left, it is going to have to fight both gravity, and the amount of the force, the normal force is going to be FN over here. 00:13:44.000 --> 00:13:45.000 What about over here? 00:13:45.000 --> 00:13:56.000 In this case, we have already got this component over here, is going to cancel out this component over here, so the normal force over here, is just going to be this little smidgen, down here. 00:13:56.000 --> 00:14:05.000 In F2's case, we lift off some of the effective weight, what the normal force has to be is much smaller. 00:14:05.000 --> 00:14:22.000 So which one of these is going to have a higher friction, this one is going to have a much smaller friction because it has got a much smaller normal force. 00:14:22.000 --> 00:14:26.000 But over here, we have got this huge normal force in comparison, so we have got this giant friction. 00:14:26.000 --> 00:14:41.000 We have got the same equal force horizontally, so we know that the giant friction is going to wind up sapping more of the acceleration and so, F2 is the more efficient, easier way, it is going to cause more acceleration. 00:14:41.000 --> 00:14:46.000 F2 will accelerate the block faster, because it will have the smaller FN. 00:14:46.000 --> 00:14:54.000 So it is really important to pay attention to the interaction between the force of gravity, then also the forces that we are putting into our object. 00:14:54.000 --> 00:15:02.000 One more thing to talk about, is the idea of, an object being still, at rest on a surface, and an object moving along on a surface. 00:15:02.000 --> 00:15:07.000 Which one of these will take more effort, more force from us? 00:15:07.000 --> 00:15:15.000 Just start a refrigerator moving, sliding on a floor, just start that refrigerator up, or keeping an already sliding refrigerator go away. 00:15:15.000 --> 00:15:32.000 If we want to just, just start it moving up in addition to creating motion requiring some amount of force from us to get that started, there is actually going to be this little thing, if you have to sort of like, unstick it, we have to pop it off of where it was already located. 00:15:32.000 --> 00:15:41.000 It might seem like a trick question, but it really is not, it really cannot take more force to start something moving than to just to fight kinetic friction. 00:15:41.000 --> 00:15:44.000 Kinetic friction is going to be different from static friction. 00:15:44.000 --> 00:15:48.000 The friction of when it is moving, is going to be different from the friction when it is still. 00:15:48.000 --> 00:15:49.000 Why does this happen? 00:15:49.000 --> 00:16:09.000 That is a really complicated thing, it is something for future classes in chemistry, more physics, friction is something there is still doing lots of research into, so it is really complicated for right now, but it is definitely something interesting, but we do not have time to talk about it right now. 00:16:09.000 --> 00:16:16.000 The exact reason is lots of complicated, but it suffices to say that on a microscopic level, the two surfaces interact differently between one another. 00:16:16.000 --> 00:16:33.000 They are going to wind up interacting in a different way when they are going to be still, and when they are already moving against one another, slight differences happening microscopically , and sometimes major differences as we will see in some of the numbers that we are going to see soon. 00:16:33.000 --> 00:16:46.000 Static versus kinetic, if we are going to be able to talk about two different kinds of friction, kinetic- the moving kind, and static- the still kind, we are going to have to use a different coefficient for each one. 00:16:46.000 --> 00:16:57.000 So, μ is now going to split into two different categories: static is going to be μs, kinetic is going to be μk. 00:16:57.000 --> 00:17:00.000 So, we have got μstatic and μkinetic. 00:17:00.000 --> 00:17:09.000 One thing to keep in mind: In almost all cases, μs is greater than μk, 00:17:09.000 --> 00:17:32.000 There are a very few special cases where this is not going to be true, but as far as we are going to deal with in our course, it is almost always true, sometimes they will be equal and there is really freaky materials where μk is larger, but it is beyond this course, it is not something we are going to have to worry about. 00:17:32.000 --> 00:17:41.000 If you get really interested in material science, it might be the kind of thing you have to deal with in graduate school, but not something that you have to worry about in high school physics. 00:17:41.000 --> 00:17:44.000 Applying kinetic friction is pretty easy. 00:17:44.000 --> 00:17:56.000 If we just want to have friction on an object, it is just going to be, μk × FN, until the object stops moving it is going to be in the direction opposing the current motion. 00:17:56.000 --> 00:17:58.000 What about static friction? 00:17:58.000 --> 00:18:00.000 That is a little bit different. 00:18:00.000 --> 00:18:11.000 If we have an object sitting still, and we push on that object, we have got an object like this, and it is giant, and a guy comes up, and he pushes on it, lightly. 00:18:11.000 --> 00:18:30.000 It is going to be able to defeat him, but it is not going to go back with all of the friction, you know, if you have to push this lightly, if it is going to be able to cancel out this lightly, and this lightly, and say it is able to cancel out all the way up till this big, it is not going to react with the static friction force in the opposite direction of this big every time. 00:18:30.000 --> 00:18:33.000 It is going to cancel out whatever is put into it. 00:18:33.000 --> 00:18:39.000 Static friction is going to be able to cancel out up to the amount of force, up to it is maximum amount. 00:18:39.000 --> 00:18:45.000 So the maximum static friction, static friction resists an object starting to move it, until it gets surpassed. 00:18:45.000 --> 00:18:56.000 Until we get to that really extreme case, we are always going to have the case that static friction is going to oppose however much force is put into it. 00:18:56.000 --> 00:19:17.000 It is not going to put in more than that, it is just going to oppose the amount put into it, until we suddenly get to the point where we are able to equal and then surpass static, just that equal point is the razor's edge of flipping over into kinetic friction, at which point the object lurches forward, unsticks, starts to move, and then kinetic friction comes into play, and in almost always μk will be less than μs. 00:19:17.000 --> 00:19:20.000 So we have some slight acceleration, if we kept up a constant force. 00:19:20.000 --> 00:19:26.000 The static friction cancels out the force that would cause acceleration, but it never exceeds them. 00:19:26.000 --> 00:19:39.000 That gives us, the maximum static friction = μs × FN, but keep in mind that it is the maximum static friction, not more than that, but just the maximum. 00:19:39.000 --> 00:19:53.000 It is the top amount that it can be, we are not going to see that every time we put any small force into it, it is going to be the top amount, that is μs × FN. 00:19:53.000 --> 00:19:56.000 What is some basic examples of μs and μk? 00:19:56.000 --> 00:20:14.000 These are some approximate values, this table here, keep in mind that these can vary depending on the specific situation, the condition of the materials involved, wet, greasy, air between them, perfect vacuum, there is certain material properties that can happen. 00:20:14.000 --> 00:20:26.000 For the most part, these are going to remain the system, but it about the whole system interacting together, so it is really something that has to be experimentally determined, or given to us in the problem statement, or something we are solving for from the problem statement. 00:20:26.000 --> 00:20:34.000 Take a look at these, these give us some idea how these things work. 00:20:34.000 --> 00:20:48.000 Notice, μs and μk can change very greatly, the difference between cast iron when it is moving and when it is static, is vast, it is almost a tenth of what it start off as. 00:20:48.000 --> 00:20:55.000 But rubber on concrete, it is not much of a change, it is still a change, but it is not giant. 00:20:55.000 --> 00:20:58.000 Ice on ice, once again, pretty large change there. 00:20:58.000 --> 00:21:17.000 Teflon on Teflon, Teflon starts off with a very low friction coefficient, but it stays the same whether it is moving or whether it is still, Teflon is the stuff that goes on to non-stick frying pans. (Teflon is actually a brand name, no one ever recognizes the chemical name, unless they learned it before in chemistry.) 00:21:17.000 --> 00:21:41.000 This gives us some idea of what it is, we start to see that μs is almost always larger than μk, sometimes they are equal, and like I said before, there are few freaky cases where μk is larger. 00:21:41.000 --> 00:22:04.000 It really can vary what it is, we see massive changes from 1.1 to 0.04, we can have even higher than 1.1, grip of a rock climbing shoes on rock is going to be even larger than 1.1, μk can get very small, μs can get very small, really depends on the situation. 00:22:04.000 --> 00:22:21.000 You have to get it in the, either the problem statement, for most part we see numbers between 0.2 and 1 as the very highest, but for very slippery objects, we will see even lower, it has to do with what we are getting in the problem, and the specific materials we are working with in our case. 00:22:21.000 --> 00:22:23.000 One special thing to talk about, is wheels. 00:22:23.000 --> 00:22:25.000 How do wheels work! 00:22:25.000 --> 00:22:33.000 So, you might think at first at wheel are going to have kinetic friction between the road and themselves, because they are moving. 00:22:33.000 --> 00:22:36.000 Not actually true. 00:22:36.000 --> 00:22:42.000 One special thing to note is that, when a wheel rolls along a surface, it is going to use its static friction, not the kinetic. 00:22:42.000 --> 00:22:46.000 Now, why is that? 00:22:46.000 --> 00:23:02.000 When the wheel is rolling, at the moment of contact, consider this sort of like flash forward thing, you have got some point here, and then that point is here, and then that point is here. 00:23:02.000 --> 00:23:16.000 At the moment of contact, when it is right here, when it is on the ground, it is actually still because it gets laid down, and then it gets picked back up, it does not move relative to the ground until it is off of the ground. 00:23:16.000 --> 00:23:23.000 If we have got this perfect circular wheel rolling, the wheel is not actually going to wind up having any friction on the ground. 00:23:23.000 --> 00:23:28.000 In reality, the contact patch just moves slightly, but we are talking extremely small rolling resistance. 00:23:28.000 --> 00:23:33.000 For instance, 0.001, that sort of scale, very small. 00:23:33.000 --> 00:23:40.000 So for our purposes we can pretend that there is no friction from a rolling wheel, if it is able to stick to the ground. 00:23:40.000 --> 00:23:45.000 Static friction is what you use for a wheel. 00:23:45.000 --> 00:23:49.000 Notice, this does not mean that a car is being slowed by friction to the wheel. 00:23:49.000 --> 00:24:00.000 Static friction can be very large, numbers like 1.0 for a wheel on concrete in dry conditions, but that does not mean that the car is taking all that out. 00:24:00.000 --> 00:24:12.000 In fact, because it is being put down , and then it is moving off, it never moves, it is never trying to be moved around, when it is on ground, it is like it is practically still. 00:24:12.000 --> 00:24:15.000 It is perfectly still from the point of view of the tyre at that moment. 00:24:15.000 --> 00:24:19.000 That piece, that dot, does not start to move away until it is off of the ground. 00:24:19.000 --> 00:24:23.000 Once it is off the ground, it can move around, because it is not going to have any friction. 00:24:23.000 --> 00:24:36.000 So the only thing that creates friction is that tiny contact patch, and because that tiny contact patch is picked up before it moves relative to the earth, relative to the road, it is not going to give us any frictional force on our car. 00:24:36.000 --> 00:24:44.000 So on the contrary, the fact that it is the static friction is what is going to allow the car to move smoothly, and experience practically no friction. 00:24:44.000 --> 00:24:57.000 I have included bearings, and good oil, it being able to have a good wheel system, you are going to be able to have a almost frictionless motion, and you will be able to have all the motion to the car translated easily as it is running frictionless. 00:24:57.000 --> 00:25:00.000 At least, that is what we would hope. 00:25:00.000 --> 00:25:04.000 In reality, there is going to be some slight friction, because nothing is perfect. 00:25:04.000 --> 00:25:06.000 But, it is going to be pretty darn good. 00:25:06.000 --> 00:25:11.000 It is going to be way better than if we just had a metal body on the ground, that we are shoving along. 00:25:11.000 --> 00:25:16.000 So, we will be able to experience effectively no friction, while it rolls along the ground in a straight line. 00:25:16.000 --> 00:25:30.000 When the car turns, and tries to change its velocity, either by accelerating, so it is going to have those contact patches spinning up, because they are going to be moving faster than they were before, and this is a little complicated to think about. 00:25:30.000 --> 00:25:51.000 But the acceleration, the force, it is the frictional force that allow the car to get that traction, which is why you sports cars, racing cars have really big flat large wheels, because they want a big contact patch, so they can get lots of force into the earth, where as cars that are trying for efficiency tend to have much thinner wheels. 00:25:51.000 --> 00:25:53.000 They are going to have less contact patch. 00:25:53.000 --> 00:26:05.000 If you want to be able to get a car that gets better fuel efficiency, you pump up the wheels a little bit heavier, because that will make them firmer, tighter, and will be able to have a less contact patch on the ground, which means they will have a little bit less friction. 00:26:05.000 --> 00:26:10.000 Remember these are very small numbers, if you are driving at 100 miles, it can have an effect. 00:26:10.000 --> 00:26:31.000 Or if you were to turn, that is when friction is going to come into play, normally you would have the wheel running like this, but then if we want to turn, the wheel is going to turn like this, but the motion of the car is going to be like this. 00:26:31.000 --> 00:26:34.000 So, normally your wheels are going like this, and we have effectively no friction. 00:26:34.000 --> 00:26:50.000 If instead we turn, the car has two choices, if it were to keep going in this path, then all of a sudden, friction will be breaking its contact patches with the earth, because that is not the direction wheel wants to roll in. 00:26:50.000 --> 00:26:52.000 Instead, it is going to go this way. 00:26:52.000 --> 00:26:58.000 So, if the car were to keep going this way, it would break friction, friction would fight it. 00:26:58.000 --> 00:27:02.000 So instead, it goes this way, which means that friction is going to wind up actually pulling this way. 00:27:02.000 --> 00:27:10.000 This is a little bit complicated to think about, but the force of the wheels, friction is the only thing that connects the car to the earth. 00:27:10.000 --> 00:27:14.000 The car and the road are connected through the friction of the tyres. 00:27:14.000 --> 00:27:21.000 So when you go into a turn, the thing that pulls you into the turn, is going to be the friction of the wheels on the ground, and it is going to be μs. 00:27:21.000 --> 00:27:34.000 This is a lot of explanation for something that does not seem to make sense, but if you want to be able to understand how a car rounds a corner, like we will in the section when we talk about uniform circular motion and force, we are going to be actually understand this. 00:27:34.000 --> 00:27:39.000 So this stuff actually matters, it is a little complicated to think about at first, but it will make sense. 00:27:39.000 --> 00:27:47.000 If something is going to be rolling, it effectively has, static friction, it effectively has no friction, because it is going to be putting in its contact patch, and lifting it up. 00:27:47.000 --> 00:27:58.000 But if it wants to have an acceleration, that contact patch only has to move relative to the ground, otherwise, the rotation movement of the wheel is going to change the speed that the wheel is moving along. 00:27:58.000 --> 00:28:03.000 So its going to require friction to be the interaction, the interplay between those two things. 00:28:03.000 --> 00:28:07.000 Let us finally start talking about examples for the normal basic friction. 00:28:07.000 --> 00:28:14.000 We have got a block of mass 10 kg, resting on a flat surface, horizontal force acting on it. 00:28:14.000 --> 00:28:19.000 It just barely begins to move, unsticks at the force F = 60 N . 00:28:19.000 --> 00:28:20.000 What is μs? 00:28:20.000 --> 00:28:22.000 First let us do a free body diagram. 00:28:22.000 --> 00:28:24.000 What forces are acting on it? 00:28:24.000 --> 00:28:36.000 There is Mg, pulling down, FN = Mg, (flat surface, nothing else pulling down, so they are going to cancel one another out.) 00:28:36.000 --> 00:28:41.000 Now we are going to work to figure out what the friction is, and we know that friction is going to pull this way. 00:28:41.000 --> 00:29:06.000 If μs, (we are dealing with static friction, the moment of unsticking, that razor's edge between staying still and just beginning to move, is going to be the maximum static friction). 00:29:06.000 --> 00:29:11.000 The force is going to be equal to the maximum friction, for it to unstick at 60 N. 00:29:11.000 --> 00:29:13.000 What is the maximum static friction? 00:29:13.000 --> 00:29:24.000 That is μs × FN = μs × Mg. 00:29:24.000 --> 00:29:26.000 What is F? 00:29:26.000 --> 00:29:30.000 F = 60 N. 00:29:30.000 --> 00:29:38.000 For it to just unstick, we know that the maximum static friction had to just be, barely on that razor's edge, where they are just equal. 00:29:38.000 --> 00:29:42.000 As soon as you surpass it, you flip it to motion, you switch over to kinetic. 00:29:42.000 --> 00:29:47.000 So, that precise moment when they are equal, is the moment of unsticking. 00:29:47.000 --> 00:30:10.000 Now, plug in our numbers, so, μs = 60 / Mg , we know 'M' and 'g', so, = 60/(10 × 9.8) = 0.61. 00:30:10.000 --> 00:30:16.000 So for this case, between this block and this block and this surface, we have got μs = 0.61. 00:30:16.000 --> 00:30:23.000 Once it starts to move, it still has that force of 60 N on it, and now it has an acceleration of 1 m/s/s. 00:30:23.000 --> 00:30:30.000 We know that the sum of the forces, = mass × acceleration. 00:30:30.000 --> 00:30:35.000 We know what 'a' is, we know the forces operating on it. 00:30:35.000 --> 00:31:05.000 The force, up here, = 60 N - μk × Mg = Ma = 10 × 1 . 00:31:05.000 --> 00:31:33.000 We get, 60 - 10 = μk × Mg, 50/Mg = μk , μk = 0.51. 00:31:33.000 --> 00:31:36.000 There is our answer for what μk is. 00:31:36.000 --> 00:31:42.000 Next example: For this example, we have got a block resting on a surface that can be tilted. 00:31:42.000 --> 00:31:52.000 We have got some tilt, θ on our surface, μs = 0.35. 00:31:52.000 --> 00:32:00.000 What angle θ will the block barely begin to slide, what is that instantaneous, that razor's edge, that break over point between staying still relative to the incline and suddenly starting to move along the incline? 00:32:00.000 --> 00:32:11.000 Notice, for this problem, we do not have the mass of the block, but it turns it we are not actually going to need it. 00:32:11.000 --> 00:32:18.000 So, we have got a block, it is going to weigh some 'm', so mg is the pull of gravity on it. 00:32:18.000 --> 00:32:22.000 How much of this is going to be perpendicular? 00:32:22.000 --> 00:32:30.000 The perpendicular force, is going to depend on what θ is. 00:32:30.000 --> 00:32:33.000 How much is the parallel force? 00:32:33.000 --> 00:32:34.000 That is also going to depend on θ. 00:32:34.000 --> 00:32:43.000 What is θ , we can figure it out by referring to that old lecture that I had on Newton's second law in multiple dimensions. 00:32:43.000 --> 00:32:54.000 We can also see that in the extreme case (90 degrees), then we have that this is going to be sin(90), so we would have all parallel. 00:32:54.000 --> 00:33:01.000 In the case of 0 degrees (other extreme), we would have cos(0) =1, so all perpendicular. 00:33:01.000 --> 00:33:15.000 So we see that θ has to go here, but we can also figure that out by other geometrical means. (This can be a real confusion down the road, so it is good to refer to.) 00:33:15.000 --> 00:33:20.000 And there is lots of problems that involve incline, so it is really important to have a good understanding of how this works. 00:33:20.000 --> 00:33:33.000 This is mg, so we have, the perpendicular force of gravity = mg × cos θ . 00:33:33.000 --> 00:33:35.000 How much is the normal force? 00:33:35.000 --> 00:33:46.000 That is going to keep it from bursting through the incline, so FN = Fg(perpendicular) = mg cos θ . 00:33:46.000 --> 00:33:48.000 What is the parallel force? 00:33:48.000 --> 00:33:56.000 The parallel force = mg sin θ . 00:33:56.000 --> 00:34:04.000 (we are able to do this because we have a right triangle, so these two things are perpendicular, so we use basic trig.) 00:34:04.000 --> 00:34:07.000 At this point, what are the forces acting on it? 00:34:07.000 --> 00:34:17.000 At this point, we have the parallel force going this way, mg sin θ = gravity parallel. 00:34:17.000 --> 00:34:21.000 What other thing is operating on it?, friction! 00:34:21.000 --> 00:34:23.000 Friction is going to be pulling backwards. 00:34:23.000 --> 00:34:28.000 We are going to be using static fricton, because the block starts off at rest. 00:34:28.000 --> 00:34:46.000 What is the moment of flip, is going to be when that maximum static friction, is just equal to Fg (parallel), that is the razor's edge, the moment of flipping. 00:34:46.000 --> 00:34:48.000 What is the maximum static friction? 00:34:48.000 --> 00:35:01.000 That is μs × FN = Fg (parallel) = sin θ × mg. 00:35:01.000 --> 00:35:22.000 What is FN, μs × mg × cos θ = sin θ × mg, (we get mg on both sides, that is why we do not need to know the mass, cancel on both sides.) 00:35:22.000 --> 00:35:31.000 μs × cos θ = sin θ , collapse it into one trig function by dividing by θ 00:35:31.000 --> 00:35:37.000 Since sin θ / cos θ = tan θ , we get, μs = tan θ. 00:35:37.000 --> 00:35:43.000 Now, we have done this in general, if you want to know what the angle is, we plug in numbers. 00:35:43.000 --> 00:36:06.000 We get, 0.35 = tan θ , taking arctan on 0.35, θ = 19.3 degrees. 00:36:06.000 --> 00:36:08.000 That tells us what this specific angle is. 00:36:08.000 --> 00:36:16.000 But it also tells us in general, if we want to do this for anything, that is a really easy to find out what μs is for any pair of objects. 00:36:16.000 --> 00:36:25.000 For any material on some surface, you measure the angle and just keep very slowly tilting it until it just begins to move. 00:36:25.000 --> 00:36:32.000 Really easy way to experimentally derive what μs is going to be. 00:36:32.000 --> 00:36:36.000 Example 3: We have a block against a wall, and it is sliding down. 00:36:36.000 --> 00:36:42.000 Between the block and the wall, μk = 0.2. 00:36:42.000 --> 00:36:49.000 How hard do we have to push against the block, to cancel out gravity, to give it a constant velocity? 00:36:49.000 --> 00:37:03.000 If we push in with some force here, what is the normal force?, it is just going to push back with the exact same amount, so FN = whatever force we put in, in terms of magnitude. 00:37:03.000 --> 00:37:05.000 What is going to be operating on this in addition? 00:37:05.000 --> 00:37:22.000 We got gravity pulling down by mg, friction pulling up by some amount that is going to be connected to μ, and the normal force. 00:37:22.000 --> 00:37:24.000 Are we moving, or are we not moving? 00:37:24.000 --> 00:37:32.000 In this case, we started off knowing that the block is sliding down, that means we will be using μk. 00:37:32.000 --> 00:37:33.000 What is the force of friction? 00:37:33.000 --> 00:37:41.000 Friction = μk × FN . 00:37:41.000 --> 00:37:52.000 That means, 0.2 × FN (FN is the amount that we push in, that is the amount the wall has to resist.) 00:37:52.000 --> 00:38:00.000 We get, μk × F . 00:38:00.000 --> 00:38:07.000 If we want those two things to cancel out, we want an acceleration = 0. 00:38:07.000 --> 00:38:24.000 That means that sum of the forces, is going to have to be equal to 0, because, ma = 0. 00:38:24.000 --> 00:38:29.000 That is the way we are doing it right now, is we know that we are in equilibrium, because there is no acceleration. 00:38:29.000 --> 00:38:36.000 It is going to have a velocity, it is sliding down, but we know that there is going to be no acceleration. 00:38:36.000 --> 00:38:47.000 The net of the forces, we have gravity, friction; we also have in the horizontal direction, the force that we are pushing, and the normal force, but they cancel each other out. 00:38:47.000 --> 00:38:59.000 We do not have to worry about that, because it is just staying parallel to that wall, so all we have to worry about is the things that can have an effect, in this case gravity and friction. 00:38:59.000 --> 00:39:10.000 Let us say that up is positive, so, frictional force - mg = 0. 00:39:10.000 --> 00:39:12.000 So, what is the frictional force? 00:39:12.000 --> 00:39:35.000 It is μkF - mg = 0, μkF = mg, so, F = mg / 0.2. 00:39:35.000 --> 00:40:13.000 In this case, we get, F = 5 × mg, so the amount of force that we need to push it, to keep a constant velocity or keep it still (then we use μs) is going to be dependent on the coefficient of friction. 00:40:13.000 --> 00:40:17.000 In this case, 5 × (force of gravity). 00:40:17.000 --> 00:40:24.000 Last example: This one will definitely require some thinking. 00:40:24.000 --> 00:40:27.000 We will start off thinking about the problem and then actually approaching it. 00:40:27.000 --> 00:40:32.000 It is a great way to approach a problem in general, think about it, then approach it, then actually do the math. 00:40:32.000 --> 00:40:38.000 We have got 2 blocks of masses, M1 = 2 kg, and M2 = 1 kg. 00:40:38.000 --> 00:40:44.000 They are sitting atop each other, they have μs = 0.7 between them. 00:40:44.000 --> 00:40:47.000 The bottom block is resting on a horizontal frictionless surface. 00:40:47.000 --> 00:40:52.000 What is the minimum force to keep the top block from slipping? 00:40:52.000 --> 00:40:59.000 First of all, if they are moving at the same rate, what does that mean? 00:40:59.000 --> 00:41:08.000 That means we have got some a1 acceleration, we have got some a2 acceleration, and they are both going to be moving in the direction of force. 00:41:08.000 --> 00:41:11.000 These are our accelerations, going this way. 00:41:11.000 --> 00:41:17.000 But, what about the fact that if they had different accelerations? 00:41:17.000 --> 00:41:34.000 If they had different accelerations, then one of them is either going to be sliding off the other, or sliding behind the other, there is going to be a difference in their relative velocities, which means that they cannot be staying together anymore, they have to be slipping, by the definition of slipping. 00:41:34.000 --> 00:41:46.000 That means, just to begin with, we know that the acceleration of the first block , has to equal the acceleration of the second block, so we can call them in general, 'a'. 00:41:46.000 --> 00:41:48.000 What else do we know about this? 00:41:48.000 --> 00:41:54.000 What keeps block 2 on top of block 1? 00:41:54.000 --> 00:42:02.000 Ther is nothing, no forces we are putting in externally, the only force that is keeping it there, is the force of friction. 00:42:02.000 --> 00:42:12.000 M1 is moving this way, that means that for them to stay attached, static friction wants them to stay in place, M2' friction is going to pull this way. 00:42:12.000 --> 00:42:21.000 So, we got friction moving this way. 00:42:21.000 --> 00:42:25.000 So, friction is going to be pulling block 2 over, what about block 1? 00:42:25.000 --> 00:42:38.000 Resultant force, so M1 is going to be reduced by that same friction, these will be equal in terms of magnitude, not direction. 00:42:38.000 --> 00:42:45.000 So, M2 is going to be accelerated by friction, M1 is going to be decelerated, or at least lose some fo its force to friction. 00:42:45.000 --> 00:42:48.000 That gives us an idea of what we are actually doing here. 00:42:48.000 --> 00:42:59.000 We have got these 2 blocks, they are pulled along, only the bottom one is being pulled along, and the way it is able to communicate with the top one, the way that it is able to cause it to move, is by using friction. 00:42:59.000 --> 00:43:04.000 The bottom one and the top one, they only communicate by friction, so friction has to be the way here. 00:43:04.000 --> 00:43:18.000 If we are able to put so much force, this makes sense, I am sure you have seen it, if you have got 2 books on top of one another, we yank the bottom book really hard, the top book will just fall down, whereas if you yank the bottom book really slowly, they will both slide along easily together. 00:43:18.000 --> 00:43:22.000 So it is going to be connected to the coefficient of friction, and the masses of the books. 00:43:22.000 --> 00:43:31.000 What is going to be the minimum force to cause the top block to slip? 00:43:31.000 --> 00:43:33.000 What is the maximum force to keep it in place? 00:43:33.000 --> 00:43:37.000 It is going to be the same thing, that razor's edge once again between slipping and not slipping. 00:43:37.000 --> 00:43:42.000 But, now we have got the understanding to actually approach this problem. 00:43:42.000 --> 00:43:46.000 Final thing, now we can actually do the math. 00:43:46.000 --> 00:43:49.000 Let us start looking at the two free body diagrams. 00:43:49.000 --> 00:43:52.000 In this case, we have got some force. 00:43:52.000 --> 00:43:54.000 What else is operating on it? 00:43:54.000 --> 00:44:00.000 We have got friction, from the top, what about its own friction? 00:44:00.000 --> 00:44:03.000 Does it have its own friction from the ground? 00:44:03.000 --> 00:44:16.000 No!, remember, we said that it is on a frictionless surface, so in this case, there is only one friction, there is just the friction between the blocks. 00:44:16.000 --> 00:44:18.000 What is μ;s? 00:44:18.000 --> 00:44:20.000 We know μs; what is normal force? 00:44:20.000 --> 00:44:23.000 How hard does M2 push in! 00:44:23.000 --> 00:44:42.000 M2 is going to push in with M2g, so, FN = M2g, because it does not burst through the box, it does not move through it, it stays on top of it, so the normal force has to equal M2g. 00:44:42.000 --> 00:44:45.000 With this in mind, we can start coming up with our formulae. 00:44:45.000 --> 00:45:17.000 Net force is, we know that, F - friction = M1 × a . (We can use vectors, but we do not have to be, because we understand the directions, because they have been dealt with.) 00:45:17.000 --> 00:45:20.000 So, F - friction = M1 × a . 00:45:20.000 --> 00:45:25.000 What is the forces on M2? 00:45:25.000 --> 00:45:30.000 Just friction, = M2 × a . 00:45:30.000 --> 00:45:34.000 With that in mind, we can start to figure out what is F going to have to be equal to. 00:45:34.000 --> 00:45:55.000 F - M2a = M1a, so, F = (M1 + M2) × a . 00:45:55.000 --> 00:46:03.000 That is how much force is necessary to give an acceleration of this, because it has to move both the objects, the whole system. 00:46:03.000 --> 00:46:08.000 We can sub that back in, we can now figure out what is friction. 00:46:08.000 --> 00:46:20.000 F/(M1 + M2) = a , plug that into this formula right here, 00:46:20.000 --> 00:46:47.000 We get, the friction = M2 × F/(M1 + M2), so, friction = M2 × F / (M1 + M2). 00:46:47.000 --> 00:46:53.000 Now we could sub these things in, we could figure out what are the actual numbers, what also is friction. 00:46:53.000 --> 00:47:21.000 In this case, friction = F / (1+2) = F/3, because that is the amount that it has to get, it is the share that the top block has to get, because it has one third the total mass of the system, so it has to get equal share for its mass, to be able to move it with the same acceleration. 00:47:21.000 --> 00:47:27.000 So friction has to be equal to F/3, for the acceleration to be the same between both the objects. 00:47:27.000 --> 00:47:29.000 What is the maximum amount of friction? 00:47:29.000 --> 00:47:43.000 Remember, that it is going to have maximum friction, (static friction, because we are static here), is going to be the maximum velocity without slipping. 00:47:43.000 --> 00:48:06.000 Once again, it is that razor's edge, so the minimum velocity for slipping is going to be that flip over point, the maximum velocity without slipping is going to be the same thing as the minimum velocity of slipping, if we just go an infinitesimal amount over, we are going to start to slip. 00:48:06.000 --> 00:48:11.000 So, the maximum static friction = the maximum velocity that we can move at. 00:48:11.000 --> 00:48:14.000 The maximum force, maximum velocity, maximum acceleration, 00:48:14.000 --> 00:48:26.000 ACTUALLY I SHOULD NOT HAVE SAID THE VELOCITY, THE MAXIMUM ACCELERATION, my apologies, you can of course have any velocity, it could be whizzing along in space, a million miles per hour, it does not matter. 00:48:26.000 --> 00:48:32.000 From its point of view, it is not experiencing any force, so it is about the maximum acceleration. 00:48:32.000 --> 00:48:35.000 So, maximum force. 00:48:35.000 --> 00:48:48.000 With all that in mind, it will slip at the moment, when, F/3 = max. static friction. 00:48:48.000 --> 00:48:50.000 What is max. static friction? 00:48:50.000 --> 00:49:11.000 μs × M2g, so, F = 3 × μs × M2g. 00:49:11.000 --> 00:49:36.000 Plug in numbers, 3 × 0.7 × 1 × 9.8 = 20.58 N. 00:49:36.000 --> 00:49:52.000 That is how much it is, to finally get the thing to just start moving, if we just barely see 20.58, that is the razor's edge, slightest bit f difference off 20.58, and it will just start to slip, because it will just exceed this maximum static force. 00:49:52.000 --> 00:50:09.000 Hope friction made sense, if you got difficulty in understanding how an incline works, definitely refer to Newton's second law in multiple dimensions, it will give you an understanding of how to deal with parallel and perpendicular forces, it is important to understand that when you are dealing with friction. 00:50:09.000 --> 00:50:11.000 Hope you enjoyed it, see you later.