 Okay, this is a redo video. I made this quite a few times and there was some plans that the video didn't turn out well and you couldn't see the top so I'm going to redo it. And I'm not positive exactly what everything was on there but I'm going to just make up my own stuff. It was about friction. So friction is a complicated thing but we can actually model it pretty easily. So let's look at an example. Suppose I have a block. Let's say this is a one kilogram block just to be just to make it easy and it's just sitting there. Well if it's sitting there at rest then the acceleration has to be zero so that I have these two forces MG the weight pulling down and then I have the I'll call it the normal force the surface pushing up and those two forces have to be equal such that the net force is zero and it stays there. Okay now what if I push on this with my finger one Newton so f equals one Newton x hat. I'm pushing that way but it stays there it doesn't move so I have a block and I'm just pushing there it doesn't move. Well that says that the net force has to still be zero and how does that work? Well then I'm going to have to have there has to be a frictional force I'll call it f friction and it would have to be negative one Newton x hat. You'd have to be pushing that so that the net force in x direction zero. Now what if I change that and I push a little bit harder so I push with two Newtons. If I push with two Newtons and it still doesn't move then that means that the frictional force has to be has to get larger too it has to come up to two Newtons. So that's one of the things about static friction. In static friction is the case where the two surfaces are interacting and they're not sliding. It turns out that the static friction force does whatever it needs to do to make the thing not move up to a point. If I push this with 80 Newtons this is probably going to start sliding. Okay so the static friction force the model for the magnitude of the static friction force I call it f to the f it's going to be less than or equal to some coefficient of static friction times the normal force. So the harder these two things are pushed together the greater the frictional force could possibly be. It could be smaller. The mistake to make is to say oh it's equal and if I put that up here I could get some force let's say 10 Newtons and I'll only push two Newtons if I have a 10 Newton friction force and a two Newton pushing force then it's going to accelerate this way and that would just be really weird to push on a block and have it accelerate back the other way because of friction. It doesn't do that. Okay so this is our model for friction. Once things start to slide, once they start to slide it turns out the model for friction says this is static. Once it starts to slide the friction force becomes equal to some other coefficient times the normal force and this we call kinetic friction. Now the interesting thing here is that does it depend on the surface area in between these two? This model says no. Okay so this model doesn't work for every single case. There are some cases where it does depend on surface area but this model says no. Does this model right here say the faster you go the more friction there is? Not according to this model. This just depends on how hard they're pushing together. Okay so this is just a model that works in a lot of cases but not every case. This is the one you'll see in introductory physics because you can you can work with it. Okay but it's friction is a complicated thing in reality and this is just a simple model for it. Okay let me let me look at an example calculating the coefficient of friction. Let's say I had an experimental method where I took a plane and I kept on raising up the angle and had a block on there until I got to the angle when it just started to slide. Okay so that that point where it's just if I it's just the verge of sliding if I tilt it up a little bit more it's going to slide. Okay so what if it's at that point where it's the maximum static friction force possible? What would the free body diagram look like? Well I have the gravitational force MG now what when you're drawing a free body diagram think about what's touching the object and what long range forces are in the object. The only long range force I have here is gravity. What's touching the object for the block it's just this plane. A plane can exert two forces. It can push on it this way just like this one did it pushed up we call that the normal force and here normal means perpendicular that's perpendicular to the plane and then it can also exert a frictional force parallel to the plane. In this case the frictional force is going to be in whatever direction it needs such that the object doesn't slide so in this case the frictional force would be this way. I mean if I was pushing really hard this way the frictional force would would change directions because they would say I don't want it to slide it doesn't really say anything okay but it it always opposes the desired change it wants the frictional force is such that it tries to make the thing not move and again I'm saying it's like it's person and it's not. Okay so there's my free body diagram these two forces are from the plane and that's from gravity let's go ahead and and but it's at it's at an equilibrium and they called out the x direction and the y direction why would I do that well there's two reasons to choose an axis one this way I only have one vector that's not one force it's not either the x or the y direction so I find one component if this block were accelerating down the plane this would be a good choice too because then I'd have the acceleration in either the x or y direction that's really important it makes things a lot easier you don't have to do it but it makes it easier. Okay so in this case the acceleration in both the x and the y direction is zero you can do a little geometry and see this is the complement of theta so this is the complement of the complement of theta that's also theta so I'm going to have the components let me just draw the components of the weight I have that at the y component and that is the x component so in the x direction I can say f net x equals zero because the acceleration zero so I have negative the friction force and then I have part of weight so here's my triangle I want the opposite side of that triangle so if this is the hypotenuse mg the opposite side is going to be plus mg sin theta can I messed up last time with okay you can see that want to make sure I didn't get it out of the range okay so now I have one equation right there let me go ahead and say I'm at the point with the greatest frictional force so instead of that I can say the frictional force equals mu s times in so I get zero equals negative mu s the static coefficient of friction times in plus mg sin theta and let's experimentally determined what that theta was okay and I want to find me why I can't right now because I don't know in even if I knew him in theta I don't know in so let's go to the y direction f net y is also equal to zero so I have in going in the positive y direction and then I have part of the gravitational force this side right here so it's going to be the cosine of the angle times mg so this is going to be the normal force minus mg cosine theta now I think I like this example for two reasons well let me let me go ahead and solve for n in equals mg cosine theta reason number one is all too often people say oh x direction cosine y direction sine and that's not true look here's the y component using the cosine you have to look at the triangle to figure that out don't just fall in the trap of saying x is cosine it's not good the other thing I like is here n equals mg cosine theta the other trap is to say n equals mg that is true sometimes but that's not always true you have to figure it out okay but now let me put this in up here this I can move add mu s in to both sides I get mu s in equals mg sine theta and then putting in for in I get mu s mg cosine theta equals mg sine theta the mg is on both sides I can divide both sides by cosine theta and I get mu s equals sine theta over cosine theta which is tangent theta so if I just measure that angle theta I don't even know need to know what the mass is I can get the coefficient of static friction okay let me check the time that's that's 10 minutes I have some other frictional examples and I'm pretty sure this is what I did before but I think I think I'll just stop right there that's a pretty straightforward problem and you can make it more complicated if you want