We want to talk about friction today and we want to limit ourselves here to dry friction or cool on friction. We're not talking about anything lubricated here. Friction is another force. We treat it like a point force acting tangent to the surface in an opposite direction from how motion would occur if there were no friction. This is another of the three kinds of ways we can model of surface. We can model of surface as a frictionless thing so there are no tangential forces or as a completely rough surface where you can have as much tangential forces you need to prohibit motion along a surface or as friction. Here motion might occur but it might not. That's what we need to know about. Friction depends on the surface nature so if it comes from irregularities in the surface or some sort of molecular attraction between the two surfaces it does not depend on the area of the contact. So if you have two great big things in the touching at one point tiny point or one huge surface it doesn't make any difference. The big point here is that it is limited in magnitude. This comes in all with this word might. So if you have block here and you're pushing on it with a force P the friction force acts tangent to the surface opposite the way it would move if there were no friction and you obviously have a normal force. If you plotted these two so you have a how is F changing as P changes at the first part there one to one because the sum of the forces and I give you F equals P but we know that if you're pushing on something sooner or later it will move. Sooner or later you get to F max. F max is equal to some constant times N. This constant is called the coefficient of static friction. Mew S. After that friction is only one value it comes in at mu sub k times N. That's the coefficient of kinetic friction. This is true F equals mu N only at this one point at the very top of this curve. So those of you who learned in friction that F equals mu N this is only true if motion is impending. Let's blow up this free body diagram a little bit more puts some distances on it. So if I say my box is 2B wide and the P is pushing at a height H the N cannot act right under the weight. It has to act somewhere on this side of it. As P increases this X value is going to increase as well. Anything it can to keep this in equal and grim. So let's look at what these equations are. That some of the forces on X just tells you P equals F. That some of the forces on Y tells you N equals W. That some of the moments if you take it right under the weight tells you the N times that X is equal to P times H. If there's no X if N acts right under the weight you can't have a P to maintain equilibrium. As P increases this X has to increase as well. Until you get to a certain point when this N has moved over this way as far as it'll go and it can't go any further then you have your tipping condition. If X equals B tipping occurs. We also have the possibility now that it could slip. We could get past our maximum friction force then we'll have slipping. These are not both going to happen. One of them is going to happen the other one won't. So how do we handle this? We draw the free-body diagram and write equations of equilibrium for our case. We're going to assume that it's not going to tip. We're going to assume it's not going to slip and then you have to come back and check did it slip did it tip. If rotation can occur so if your box is stuck into a corner where it can't possibly tip over then you can treat it like a particle and you don't have to worry about this. The friction angle is called feet. There are a lot of different ways to define a force you can say it's magnitude direction, Cartesian form or magnitude along the line. When we're talking about F and N we're talking about a Cartesian form something perpendicular to and along the surface. But this all makes up simply the reaction of the surface. If you add them together we call that the resultant R and the angle is usually called feet. So tan phi where phi is between N and R tan phi is F over N. This gets to be useful when you've got only a couple extra forces. So if you have a blocks lagging down and inclined of its own accord or that kind of thing then we can use a force triangle with this resultant R. At our magic top point of the graph where I have impending motion tan phi is going to be F max over N or tan phi S equals mu S. This phi S is called the angle of static friction or if you're talking about a block in an inclined we call it the angle of repose. Oops! What about this? I have four cases here of looking at my graph. I can look at it where it's zero. I can look at it somewhere along in here. I can look at it at the top or I can look at it past where it has gotten to the flat part. Let me put this here so it doesn't fall over. So here's my free-bodied diagram. Now I want to let P be at some sort of angle. If P is at some sort of angle theta how does this whole system change as theta changes? If theta is 90 so you're pushing straight down that's I have no friction that's living at this origin here. F can be zero and will be in some cases or tan phi is equal to zero or you can have friction but no motion and not even close to it. Now I get from my some of the forces and x f equals p cosine theta or p x. Tan phi is still up over n by definition but I don't have f max equals mu times n. I'm not equal to that until I get to motion and pending. When I get to motion and pending f is equal to p x still because of the some of the forces and x but now it's equal to f max from U S times n. This is my angle of static friction phi s where I have tan phi s equals mu s. L or I could live out here on this part of the graph where I have f is equal to p x but now this is f sub k or mu k times n or tan phi k. All the s's become k's that's how that works. So those are my four possibilities. The other two things you got to remember is that friction or one thing. The friction has to be relative motion. So if you're looking at the friction between a surface and you draw the free body diagram of one side or the other friction is going to oppose how the block moves relative to the rest of the world if it were staying still. So I can consider the red block as if the green block were staying still or the other way around. When you draw the free body diagram of both of them you have to use equal and opposite forces on each side and by that I mean the same level and opposite in the arrows in the other direction. So if I look at the red block the red block is moving up relative to the green one. That means that friction is acting down and the normal force has to be there. No you cannot have a friction force without a normal force because f max equals mu times n. So if there's no n there's no f. So this is my relative motion of the red block. The green block has to have equal and opposite things on the other side. So if f is going down f is going up. If n a is going to the left n a is going to the right on the green block. And how does that work? If you look at the green block the green block is moving down relative to the universe. That means friction is acting up relative to the universe. If you picked this up and superimposed it back on top of this these forces would be internal if you considered it all together and these have to go away. So when you look at the free body diagrams of both sides you have to make sure you're using equal and opposite reactions. In the next video we'll look at the steps you've used for solving some of these equations and a couple examples. Thanks.