6. Intro to Forces (Dynamics)

Vertical Equilibrium & The Normal Force

# The Normal Force

Patrick Ford

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Hey, guys. So early on in this chapter, we took a look at all the forces you might possibly see in your problems, and one of those forces was called the Normal Force. So we're gonna go through a little bit more detail about this normal force and I'll show you how it works. Let's check it out. The whole thing here, guys, is that whenever you have two surfaces in contact, if one surface is pushed up against another in any direction, then that surface is gonna push back with the force called the normal. Now there's different symbols letters that we use for the normal force. One of the ones you might see it as a letter end. You might see a little end. You might even see uh, f n with your professors. Uh, there's lots of different ways to write it, But here, a clutch. We're going to use a capital end. That's just what I'm used to. So what this normal force means is actually kind of like a fancy engineering term, but it really just means perpendicular, so that just means 90 degrees to the surface. So what we saw in a previous video is that if you have the weight force, that's w equals mg. Pushing down that is, pushing this block against the surface to the surface pushes back, and that's going to be upwards with a force called the normal. But obviously like to do is use my finger and thumb to figure out the direction you point your thumb along the surface like this, and then your finger points in the direction of the normal. Now it doesn't necessarily always have to be up. You can actually push a block against the wall like this with an applied force, you have surfaces in contact and the surface pushes back with the normal force. So you take your thumb like this and your finger points in the direction of the normal pushes back like that. And if you have a block against a ramp or an incline or something, you have the weight force that pushes down. It's w equals mg, and then your normal force is you're just gonna tilt your thumb like this in your normal points that way. Now, the most important thing about this normal force, you absolutely need to know, is that unlike W equals MG the weight force. There's no magical equation to solve For the normal, you always calculate that normal force by using f equals m A. So what we're gonna do here is we're going to use a familiar example that we've seen before. We're gonna do some variations so I can show you how this works. So we've got this 2.4 kg book that is going to rest on the table and we want to calculate the normal force. So we've already seen with the free body diagram looks for that we've got the W which is equal to mg, which, by the way, you can calculate because you know, the mass, which is 2.4 And if you do 9.8, this w is going to equal 20 Newtons and it's actually gonna be the same throughout all of our problems here. So we have w equals 20 w equals and then w equals 20 right? So it's the same way because the same mass throughout. Now, in this case, we've got a normal force and it's going to point up. We've already seen that. So we want to calculate what that is So now that we've got our free body diagram, we just have to use f equals m a. Right. So you've got f equals m a here. And so we got our other forces, which is the normal plus our wait for which is downwards RMG. This is equal to mass times acceleration. We'll just like we did in the previous video we have to do is extract from the problem that this book is resting on the table. So what that means here is that this box is at equilibrium or this book is at equilibrium. The acceleration is equal to zero and therefore the forces have to cancel. So that means that your normal force minus your M G is equal to zero. So what that means here is that your normal is equal to mg and that's just Newtons. So you have n equals 20 here. Now, we're gonna talk about this last bullet point in just a few minutes here, but I just want to go ahead, go ahead and move on with the next problem here. What we got is the weights. But now we're going to push the book with an additional 10 Newtons are gonna push the book downwards. What that means is that in our free body diagram we have to write another force which is going to be F and you know this is going to be 10 downwards. Now, here we've got two pushes downwards, which means the surface has to push upwards just like it did before. So we have a normal force like this. We want to calculate that. So we have to use f equals M A. So f equals m a. Now here we got a normal force and then these two forces point downwards. So they're gonna have to pick up a negative science. This is gonna be negative F plus negative mg. And this is equal to m A now, just like we did in the last problem. This book is still at equilibrium, right? It doesn't go flying off the table. It doesn't go crashing through the surface. So we have to do is extract from the problem that the book is still going to be at rest on the table. So a is equal to zero and all the forces will cancel just like they did before. So now we just have another force to consider. So here, once you move everything over to the other side, you're gonna have N is equal to MG plus f because remember, this is going to be zero. So what happens is now we've got our MG, which is 20 and our normal forces 10 So near now are normal. Force is going to start. Our apply forces tend to our normal force is going to be 30. All right, so that's our normal force right here and for this next one same thing. But now we're going to pull the book up with 15 Newtons instead of pushing it down. So now, instead of our applied force being downwards, it points upwards. So here we've got an F, and this is equal to 15. Now, if you take a look here, what happens is we got this 15. You're trying to pull the book up with 15, but the way force is stronger, it's still 20. So that's the way force winds. There's still gonna be some some weight downwards. And so the surface is still going to have to push back upwards with the normal force. So that's our normal. And we're gonna calculate that using f equals m a. So here we've got our normal force, but now are applied. Force also points upwards, so it stays positive and RMG is going to be negative. And this is equal to a now, just like the previous two examples this box is still this book is still going to be an equilibrium, right? All the forces still have to balance out because it's still your Basically, your force isn't strong enough to lift the book off the table, so it's still gonna be some normal force and all the forces are going to have to cancel. So this is a is equal to zero. So now we've got here is we've got N in which you move m g to the other side. You're gonna have to subtract f So this is going to be 20 minus 15, So you're gonna end up with a normal force of five. So we know here that this end is equal to five. And finally, for the last problem here, we're going to double our force, and we're gonna pull this book up with 30 Newtons instead of 15. And so now what we want to do is calculate the acceleration. So here we've got is we're going to double that applied for us and our f is going to be instead of 20. So now what happens to this normal force? Well, unlike this previous example that we did here are force now is strong enough to overcome the force of gravity. The weight force of 20. If you're pulling with 30 but gravity is only 20 then you're pulling force winds. So what that means here is that this book is actually gonna go flying upwards with some acceleration. So what happens to the normal? Well, unlike before now, there's no surface push. So that means that the normal in this case is equal to zero doesn't exist anymore. So to calculate this acceleration, we just use f equals m A. So here we have an applied force of 30 and now we've got mg downwards, and this is equal to mass times acceleration. And unlike the last three examples here, we can't just go ahead and assume this is zero. Because we know again that this box is gonna go flying upwards. So here we've got our 20 and here we've got our negative Sorry, 30 and are negative. 20. And this is equal to 2.4 times a. So you work this out and what you're gonna get is that a is equal to 49 m per second squared. So what happens is we know that this box or book is going to fly up with 4.9. So let me just recap all of these different scenarios here. So when you have the book that is just resting on the table, that means that there's no other applied forces. And in this case, what we saw is that your normal force was equal to mg. So in these cases, if there's no other applied courses and is equal to mg and the second one, we push the book down. So if you're pushing the book down, which means you're applied forces along with MG, then your normal force has to basically balance out both forces. And we saw that and is greater than mg. It went from 2030 here. We pulled the book with the book up, but not enough to lift it. What that just means is that are applied force of 15 was less than RMG of 20. And in this case, what we saw is that our normal force was only five Newtons. So in this case, it turned out to be less than mg. And then finally, if you pull it with enough force to lift it, which basically means you're 30 was greater than the 20 then That means that your normal force is equal to zero. There's no more surface push anymore. All right, So do you have to memorize all these situations? No. But you should always remember that you are you Are you going to calculate and by using F equals m A. These are just some of the results that you might see, So hopefully that makes sense. That's about this one, guys, let's move on.

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