 It's summer. It's in Louisiana, and I'm wearing a sweatshirt. What do you think about that? It just shows how cold it gets in here. Okay, so let me show you a couple examples. I'll probably break them into different videos, but let me just start with Freedy body diagrams and forces. So this is my favorite example. I suppose I have a one kilogram book, and it's just sitting on a table, and and let me do the first thing and just sitting there, okay? So if something's staying at rest or moving at a constant speed, but but not changing its velocity, then the total force has to be the zero vector. So if I want to draw a free body diagram for this, what force is what I have on there? This was not too hard. But generally when you draw a free body diagram, think of it this way. What things are touching the book and then what long-range forces are in the book? Right now you're only going to see one long-range force, and that's gravity. The gravitational force can interact with objects without actually touching them. It's true for the other things too, but let's just make it simpler. Okay, so I have only one thing touching the box, the book, and that's the table, and then I have gravity. So if I want to draw a free body diagram for this, I could start with a dot. You could draw it on top of the picture too, but you could draw it as a dot too. I'm going to have gravity going down. I'll call that MG, where the vector G is pointed downwards, and MG is the weight of an object. And then I have the table pushing up. I'll call that, for right now, FN. N is the normal force, and normal means perpendicular in this case. So tables are going to push perpendicular to the table. That's the way they work. A lot of times I'll put that as just an N for the normal force. That's it. That's my free body diagram. Now, if this is at rest, then I would want to draw the length of this about the same as the length of that. But it's just a drawing. It's not perfect, so it has to be perfect. Another thing that may help is to have on here an X and a Y axis like that. Okay, just so I know which way is the X direction and which way is the Y direction. Okay, so let me just go ahead and use this to say, okay, if I know the mass of that block, what, how hard does the table push up on it? Or what even vector is that? Let's find that vector FN. Well, if it's at an equilibrium, then the forces have to add to zero. So I have FN plus MG equals zero. Now here it's important to say the zero vector. The zero vector equals zero X hat plus zero Y hat, and it is a vector. I can't have vector plus vector equals scalar. Okay, so it is important. Okay, so how do you add vectors? Well, you break them into components. So I can do this in the X and the Y direction. Excuse me, in the X direction, there's nothing interesting happening. In fact, nothing is happening at all. So in the Y direction, I can say, what's the Y component of that? It's called FN. What's the Y component of that? I'll call it negative MG. And here you see the difference. See here, this is plus MG, the vector, which is pointing down. In the Y direction, I need a new marker. I'll write this as FN, the scalar value, which is a component, minus MG equals zero. Those are all scalars now, because I'm just dealing in the Y direction. So I can solve for FN, which would be one kilogram times nine point eight. And here's, I like to call G, nine point eight Newtons per kilogram. And you can see the units work out to Newtons. So if I want to write the, the force FN as a vector, I could write it as zero X hat plus nine point eight Newtons, Y hat. I know that seemed all crazy complicated for such a simple problem, but it's important to start with the simple things and do them the correct way before you move on to complicated things. Okay, so let's go ahead and make it more complicated then. It'll be fun, though. Okay, how can I make this more complicated? What if I take my hand and I push down with five Newtons? So it's a book. I'm pushing down with five Newtons. What changes? Let's erase all this. Well, my free body diagram is going to change. So what, what changes? So I'm going to have to add an extra force right here. This doesn't change because this depends on the mass, the object, and G. G is a technically it should be called the local gravitational field, which didn't change. So how can I change this diagram? Well, I can add that five Newton force on there. Now there's two ways you could add that on there. I'll do it in red. I could add it right here. I caught F, H, force from the hand. Or if you wanted to, you could add it right there next to it. It doesn't matter. It really doesn't. I kind of like adding it right here because then you can see the total vector force downward. I can't stop there because if the book stays at rest then these vectors have to add up to zero and clearly they don't. So what has to change? Well, this can't change. I, I set that. This is on them that can change. So this has, this has to get bigger. How big? Well, it should be as big as this. About like that. F, N. Now we can do the same thing. Let's see if we can find the magnitude of that normal force. So in the y direction, this markers die in. Okay. I have F, N minus F, H because it's in the, if it doesn't write this as a vector, it'd be this. Let me write it like that. F, N plus F, H plus M, G equals zero. In the y direction, now I'm talking about the components of these vectors, not the vector. Okay. So it's plus the vector, which happens to be in the negative y direction. So when I go over here, it's a negative now and it's not a vector. Minus M, G equals zero. So F, N equals F, H plus M, G equals five Newtons plus 9.8 Newtons. So that's 14.8 Newtons. And then if I want to write this as a vector, F, N equals 14.8 Newtons y hat. Okay. So this is a pretty simple free body diagram. Pretty simple to solve for that. No angles and stuff to deal with. So we'll do that next, a more complicated one. But here's the cool thing. What if the table pushed with the force of 15 Newtons, just a little bit more? Then these forces wouldn't add up to zero and this block would start to change its motion that way. And before, if it didn't push exactly 9.8, it wouldn't stay still either. So it's the same table and it pushes different amounts. So why is that? I'm not going to tell you. I think I did say it in my book, but oh well. Okay, I'm going to stop there.