Hi this is Module 23 of Applications in Engineering Mechanics. We've come quite a ways in the course. We've, we've, we done the review of my earlier course, introduction to engineering mechanics. We've looked at a number of different Structural Applications, Frames and Machines both plane and 3d Trusses or, or Space Trusses and also systems supported by cable system, cable support systems. We've looked at graphing the internal Shear Forces and Bending Moments for beams. And now we're at the final block of instruction, where we look at the Friction or Effects of Friction on Static Equilibrium. So for today's learning outcomes, I'm going to describe this concept of Coulomb friction. And how and where friction acts on a rigid body. we're going to graph the conditions for coulomb friction in situations where our rigid body. Does not slip and where it experiences slipping and then finally we're going to explain the condition for Coulomb friction when a rigid body is about to experience impending tip. So first of all the con, concept of Coulumb friction which you hopefully have seen before in the physics background that you have for this course. if I have a, a body [SOUND] sitting by itself no forces acting left or right the, the weight is down at the mass center. And we see that the, the, the resultant normal forces acting up through the center of the body to balance that weight for us. Now, if I come along and I push on the body, then we see that the, from, from the equilibrium equations that the normal force is going up the migra away from the center. Hence at that time we also get a friction force which is tangent to the surface down here, and it's going to oppo, oppose the impending motion. And that friction force if you recall from your earlier physics days, is a function of both the surface material and the normal force. And the way that we account for the surface material is through something we call the coefficient of friction, which is given the symbol mu. So here's, here's the situation with impending slip. I start off with no force being applied, my normal force is in the center as I apply a force to push this. What I'll see is my, my normal force migrates and I, I gain a friction force. And that friction force gets larger and larger depending on the force P that I push on the rigid body. And so if I start with a, a, a push of let's say 1 Newton and increase it to 2, 3, 4, 5. Eventually I'm going to get to the point where I have no more friction available to stop the system from moving. And so let's say that's at 5 Newtons for our thought experiments and then all of a sudden it's going to break free and it's going to start to, to slide. And the friction will go down slightly at that, at that point. So let's look over here on this graph. As I pushed with one, zero, one, two, three, four, all of a sudden I got to my max friction. Which was equal to the coefficient of what we call static friction times N. And then, once the system breaks free, once that rigid body starts to slide, we find experimentally, that the friction goes down slightly, and that value is mu sub K times N. Where mu sub K is the kinetic friction constant for sliding motion. And so what we do is we idealize this actual experimental graph to show it like I, I've shown over here on the left. We have a no-slip zone, and a slip zone. In the no-slip zone, the friction can be anything from zero up to the maximum value. it can achieve use of S times N and then it breaks down once it starts slipping and we just made this more sharp curve where the friction drops down to kinetic friction coefficient times the normal force. So that's, that's how we understand impeding slip. Now let's look at Impending tip. There will be cases when the friction is large enough so that, the friction back is large enough so when I push on a, on, on, on, the body with a force P, it will actually start to tip. And so at that point, once it tips, the normal force has migrated all the way over to the corner of our body. And fa, fi, the friction must be in the no-slip zone, so it's gotta be somewhere in between zero and the maximum friction we can, we can achieve, and the end obviously must act on the body. So here, we can find we'll find as we do example problems, at what point, if we have enough friction, will the body experience impending tip. And we'll do all this in future modules, as we look at actual real world examples and I'll see you then.
