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 going to 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 2 surfaces in contact, if one surface is pushed up against another in any direction, then that surface is going to push back with a force called the normal. Now there are different symbols, letters that we use for the normal force. One of the ones you might see is the letter N. You might see a little n. You might even see, an FN with your professors. There are lots of different ways to write it. But here at Clutch, we're going to use a capital N. That's just what I'm used to. So what this normal force means is it's 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=mg pushing down, that is pushing this block against the surface so the surface pushes back, and that's going to be upwards with a force called the normal. What I usually just 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 could actually push a block against a 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 and pushes back like that. And if you have a block against a ramp and your normal points that way. Now the most and your normal points that way. Now the most important thing about this normal force that you absolutely need to know is that unlike W=mg, the weight force, there's no magical equation to solve for the normal. You always calculate that normal force by using F=ma. So what we're going to do here is we're going to use a familiar example that we've seen before and we're going to do some variations so I can show you how this works. So we've got this 2.04 kilogram book that is going to rest on the table, and we want to calculate the normal force. So we've already seen what the free bond diagram looks like 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 2.04. And if you do 9.8, this W is going to equal 20 newtons. And it's actually going to be the same throughout all of our problems here. So we have W equals 20, W equals W equals 20. Alright, W equals 20. Right? So it's the same weight 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. And so we want to calculate what that is. So now that we've got our free body diagram, we just have to use F=ma. Right? So you've got F equals ma here. And so we got all the forces, which is the normal plus our weight force, which is downwards, our mg. This is equal to mass times acceleration. Well, just like we did in the previous video, what 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 0 and therefore, the forces have to cancel. So that means that your normal force minus your mg is equal to 0. So what that means here is that your normal is equal to mg, and that's just 20 newtons. So we have n=20 here. Now we're going to talk about this last bullet point in just a few minutes here, but I just want to 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. We're going to 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 we know this is going to be 10 downwards. Now here we've got 2 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=ma. So F=ma. Now here, we've got a normal force. And then these two forces point downwards, so they're going to have to pick up a negative sign. So this is going to be negative F+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 0 and all the forces will cancel just they do before. So now we just have another force to consider. So here, once you move everything over to the other side, you're going to have m is equal to mg plus F because remember this is going to be 0. So what happens is now we've got our mg which is 20 and our normal force is 10. So now our normal force is going to, or sorry, our applied force is 10. So our normal force is going to be 30. Alright. 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've got this 15. You're trying to pull the book up with 15, but the weight force is stronger. It's still 20. So this the weight force wins. There's still going to be 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 going to calculate that using F=ma. So here, we've got our normal force but now our applied force also points upwards so it stays positive and our mg is going to be negative and this is equal to m a. Now just like the previous two examples, this box is this book is still going to be at equilibrium. Right? All the forces still have to balance out because it's still you basically, your force isn't strong enough to lift the book off the table. So it's still going to be some normal force and all the forces are going to have to cancel. So this a is equal to 0. So now what we've got here is we've got n, and once you move mg to the other side, you're going to have to subtract F. So this is going to be 20 minus 15, and so you're going to end up with a normal force of 5. So we know here that this n=5. And finally, for the last problem here, we're going to double our force and we're going to pull this book up with 30 newtons instead of 15. And so now, what we want to do is calculate the acceleration. So here, what we've got is we're going to double that applied force and our F is going to be 30 instead of 20. So now what happens to this normal force? Well, unlike this previous example that we did here, our 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 your pulling force wins. So what that means here is that this book is actually going to 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 0. It doesn't exist anymore. So to calculate this acceleration, we just use F=ma. So here we have an applied force of 30 and now we 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 0 because we know again that this box is going to go flying upwards. So here we've got our 20 and here we got our, negative sorry, 30 and our negative 20, and this is equal to 2.04 times a. So you work this out, and what you're going to get is that a is equal to 4.9 meters 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 forces, n is equal to mg. And the second one, we push the book down. So if you're pushing the book down, which means your applied forces along with mg, then your normal force has to basically balance out both forces. And we saw that n is greater than mg. It went from 20 30. Here we pulled the book with the book up, but not enough to lift it. What that just means is that our applied force of 15 was less than our mg of 20. And in this case, what we saw is that our normal force was only 5 newtons. So in this case, it turns out to be less than mg. And then finally, if you pull it with enough force to lift it, which basically means your 30 was greater than the 20, then that means that your normal force is equal to 0. There's no more surface push anymore. Alright. So do you have to memorize all these situations? No. But you should always remember that you're already are you gonna calculate n by using F equals ma. These are just some of the results that you might see. So hopefully, that made sense. That's it for this one, guys. Let's move on.
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6. Intro to Forces (Dynamics)
Vertical Equilibrium & The Normal Force
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