6. Intro to Forces (Dynamics)

Vertical Equilibrium & The Normal Force

# Equilibrium

Patrick Ford

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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 gonna need to know how to solve problems where an object is said to be in equilibrium. So we're gonna be talking about what the equilibrium term means in this video. We're gonna do some examples. Let's check it out. The guys. The big idea here is if you have all the forces that are acting on an object, cancel out all the forces cancelled. 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 zero, and so therefore, your acceleration is equal to zero. Let's do a couple of examples so I can show you how this works here. So we've got these two equal forces that are acting on this box are pulling, and we know that this box is gonna be moving at a constant 5 m per second. So we know that vehicles five, it doesn't matter if it's moving left to right, So I'm just gonna point 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 boxes acceleration. So we want to calculate acceleration. We've got forces involved. We know we're gonna have to use some f equals m A. But first, we're gonna have to draw the free body diagram. So the first thing we would do is we will check for the weight force. But remember that this problem has, uh we're gonna assume that the boxes, no weights. We're gonna skip that one. We've already got. The applied Force is here and there's no cable, so there's no tensions. And then there's no two surfaces in contact, so there's not gonna be normals or frictions or anything like that. So our free body diagram is done, and now you 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 two applied forces, so we're gonna 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 the positive directions. I've got 10. And then that means that this one is negative. 10 because it points in the opposite direction, then equals Emma. So we know that the 10 and the negative 10 I'm gonna cancel it to zero. So this means zero equals m A. And what that means here is that the acceleration is equal to zero. And that's what we said it, Librium, was the forces cancelled out. So that means that the acceleration is equal to zero. So let me go ahead and actually make a conceptual point here. That's really important. So one of 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 zero. We actually solve the problem that the V that the velocity of the boxes 5 m per second equilibrium means that the object isn't accelerating, which means from Africa. Then you know a is equal to zero. So this box is just gonna keep moving at 5 m per second. All right, so it's an important conceptual point that you will need to know to make sure you remember that. All right, let's move on to the next one. So here we've got a 2 kg book and it's gonna rest on the table and it's going to stay at rest. And we're going to assume that the box does have or the books does have weights, and we want to calculate the forces that are acting on this book. So again, just like we did in the last problem, we 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 mg. And then we don't have any applied forces or tensions or anything like that. But we do have two surfaces in contact, unlike how we did in the first example. So we do have a normal force. It points perpendicular to the surface, which is basically just the table that it's worsening resting on. So this is our normal force. We don't know what that is. We don't 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 Emma. So we got f equals m A. Here. We know that the normal force is going to be up, so I'm gonna choose that to be positive. So I've got normal force and then my mg points down. So I've got minus mg, and this is equal to a well unlike what we did in the first example we have to do with 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 gonna be at rest and stays at rest. So what that means is that the acceleration is equal to zero. 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 zero, which means that we have end equal minus mg equals zero. And so when you move it to the other side, we have that m s and is equal to mg. So that means that both of the forces are going to be equal and opposite. We have two 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've seen 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 gonna start off from ethical dilemma. And there's basically going to be two different kinds of problems in some problems. You're gonna know by all the forces that they're going to cancel like we did in this first problem here, we had to equal forces. So, you know, on the left side of F equals M A that all the forces are going to cancel. That means, uh, some of the forces zero. And that means that the acceleration is equal to zero 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 gonna have to basically extract or learn from the problem that the acceleration is equal to zero, and so the acceleration is equal to zero. Then that means that you know the forces are going to cancel. It's basically two different sides of the same coin here. So if you know one, you know the other. If you know the forces canceled a zero a zero, then you know the forces canceled. So hopefully that makes sense, guys. But that's it for this one. Let's move on.

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