Hey, guys. So by now, what we've seen is that when you have a net force that pushes an object, it's going to accelerate in that direction. Well, you're going to need to know how to solve problems where an object is said to be in equilibrium. So we're going to be talking about what that equilibrium term means in this video, and we're going to do some examples. Let's check it out. So guys, the big idea here is if all the forces that are acting on an object cancel out. If all the forces cancel, then this object is at equilibrium. So what that means from your F equals m*a is that the sum of all forces is equal to 0, and so therefore your acceleration is equal to 0. Let's do a couple of examples so I can show you how this works here. So we've got these 2 equal forces that are acting on this box or pulling, and we know that this box is going to be moving at a constant 5 meters per second. So we know that v equals 5. It doesn't matter if it's moving left or right. So I'm just going to point to the right there. So we're going to assume that the box has no weight. And what we want to do is we want to calculate the box's acceleration. So we want to calculate acceleration. We've got forces involved. We know we're going to have to use some F equals m*a. But first, we're going to have to draw the free body diagram. So the first thing we would do is we would check for the weight force. But remember that this problem has, we're going to assume that the box has no weight. We're going to skip that one. We've already got the applied forces here, and there's no cables, so there's no tensions. And then there are no 2 surfaces in contact, so there are no normals or frictions or anything like that. So our free body diagram is done, and now we just have to write F equals m*a. So we've got F equals m*a here. Now what happens is we have all the forces involved. We know the 2 applied forces. So we're going to start from the left side of F equals m*a. We have all the forces, and I'm just going to make this the one direct direction, I've got 10. And then that means that this one is negative 10 because it points in the opposite direction. Then I equals m*a. So we know that the 10 and the negative 10 are going to cancel out to 0. So this means 0 equals m*a. And what that means here is that the acceleration is equal to 0, and that's what we said equilibrium was. The forces canceled out, so that means that the acceleration is equal to 0. So let me go ahead and actually make a conceptual point here that's really important. So one of the things we've seen here is that equilibrium doesn't mean that an object isn't moving. It doesn't mean that v is equal to 0. We actually saw from the problem that the v, that the velocity of the box is 5 meters per second. Equilibrium means that the object isn't accelerating, which means from F equals m*a, then we know a is equal to 0. So this box is just going to keep moving at 5 meters per second. Alright? So it's an important conceptual point that you will need to know to, you know, make sure you remember that. Alright. Let's move on to the next one. So here we've got a 2-kilogram book, and it's going to rest on the table, and it's going to stay at rest. And we're going to assume that the book does have or the books do have weight, and we want to calculate the forces that are acting on this book. So, again, just like we did in the last problem, we'd have to draw a free body diagram, but here, we actually do have to account for the weight force. So the weight force points down. This is W equals m*g. And then we don't have any applied forces or tensions or anything like that, but we do have 2 surfaces in contact, unlike how we did in the first example. So we do have a normal force that points perpendicular to the surface, which is basically just the table that it's resting on. So this is our normal force. We don't know what that is. We actually want to calculate the forces that are acting on the book. So now we've got our free body diagram. We just go into F equals m*a. So we've got F equals m*a here. We know that the normal force is going to be up, so I'm going to choose that to be positive. So I've got normal force, and then my m*g points down. So I've got minus m*g, and this is equal to m*a. Well, unlike what we did in the first example, what we have to do in this problem is we have to start on the right side of F equals m*a. Because one thing we know about this problem is we're told that the book is going to be at rest and stays at rest. So what that means is that the acceleration is equal to 0. It's going to stay at rest, and it doesn't accelerate or anything like that. So here we know that a is equal to 0, which means that we have n equal minusmg equals 0. And so when you move it to the other side, we have that n is equal to m*g. So that means that both of the forces are going to be equal and opposite. We have 2 times 9.8, and we get 19.6 newtons. So here, we have the magnitude of those two forces. We know that n is going to be 19.6 up and m*g is going to be 19.6 down. But just like the first example, what we see here is that the forces are going to cancel. You have the same equal forces just in opposite directions. So that actually brings me back to the point. The whole point of equilibrium is that you're going to start off from F equals m*a, and there's basically going to be 2 different kinds of problems. In some problems, you're going to know by all the forces that they're going to cancel, like we did in this first problem here. We had 2 equal forces. So you know on the left side of F equals m*a that all the forces are going to cancel. That means F is, the sum of forces is 0, and that means that the acceleration is equal to 0. Now in other problems, like we did in this problem over here is we actually have that this book is at rest. So in other problems, you're going to have to basically extract or learn from the problem that the acceleration is equal to 0. And so if the acceleration is equal to 0, then that means that you know the forces are going to cancel. It's basically 2 different sides of the same coin here. So if you know 1, you know the other. If you know the forces cancel, you know a is 0. If you know a is 0, then you know the forces cancel. So, hopefully, that makes sense, guys. But that's it for this one. Let's move on.