Pressure and Atmospheric Pressure

by Patrick Ford
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Hey guys. So in this video we're going to start talking about pressure and atmospheric pressure, both of which are huge topics in this chapter. Let's check it out. Alright, so pressure is defined as force divided by area force divided by area. So it's a measurement of how much particular force is spread out over a surface area and it has units of Newton per square meter. And that's because forces merging Newton's an area is measured in square meters. Now. They got tired of writing Newtons per square meters over and over again, so they decided to call this something. And this is called a bus cow pus cow named after Mr Plus Cow Abbreviated P A. And it just means that if you have one Pascal, we have one Newton per square meter. Let's look at a quick example here. So two identical wood blocks these two guys here one and two Um and it specifies here that they are they have 800 kg per cubic meter. Hopefully right away. You identify that this is density because of the units. It doesn't say that, but you need to know that. So the density which is row Greek letter row is kg per cubic meter. This is why we cover density earlier. And these are the dimensions of the blocks. So point to buy point to buy one. So if you notice this is alongside here, So this must be 1 m and these guys here will be the point. Choose meters and here it Z just oriented in a different direction. This is the long side. So this is gonna be 1 m and this must be point to heights and the depth here must be point to as well. Okay, so they're placed outdoors, meaning that there's a bunch of air around them and horizontal surface on horizontal surfaces. So the idea is that it's placed on sort of the surface here, the floor, something like that. We want to know the pressure of each block on the surfaces that they sit on. So the idea is that if you have a block and it sits on the surface, it is pushing against the surface and it's applying pressure. Why? Because there is a force over an area, and then whenever you have a force over an area, you have a pressure so I wanna know how much pressure is this block over here applying on the surface right underneath underneath it. So you might imagine that it looks kind of like that, right? If you draw sort of the three d version here on do you might imagine that there is the bottom here of this guy is also pushing against the surface against the floor and I want to know the pressure. So we're completing pressure pressure against the floor. Let's call that PF. How do we find pressure? Well, the equation for pressure is force over area. So let's right that it's the amount of force that the block applies on the floor, divided by the area theme area that they're touching. How much area is that? Is there between the two of them, which is just this area down here, the area of interaction. Okay, so So what is the force? This block pushes against the floor because it has weights because of gravity, right? So gravity pulls on the block down the earth, pulls down the block, the block pulls on the table or on the surface on the floor. So the force that's causing the block to push against the surface is mg. So I'm just gonna rename this two mg. And this happens a lot, by the way, that the force on a pressure problem is the weight force divided by the area. And I could just sort of start plugging in that the area here is gonna be 0.2 times 0.2. Okay, Obviously we know gravity is 9.8. For the sake of this problem to keep it simple, we're gonna use that gravity is approximately 10 m per second squared to make our lives easier. But I still have to find the mass. And once I find a mass, I plug it in and we're done. How do we find mass? You may remember that if you have density, which you do and if you have volume, which should do you confined mass? Because because density is mass over volume. Therefore, mass is density times volume. Now, please don't get the little P the little curvy Greek p, which is row confused. That's that's density. Don't get that confused with big P pressure. Okay, those are different things. It's unfortunately that they look so similar. So do I have pressure and volume? Yes. So that I can find I'm sorry. Do I have density C? I just did it. So I have density and volume. We do. So we're gonna be able to just plug all this stuff thio in and figure out the mess. So let's do that real quick. Mass is going to be density, which is 800 kilograms per cubic meter. Remember to always put units like this. It's easy to cancel times the volume. The volume is just the three sides multiplied. So 0.2 times 0.2 times 1.0. And because this is meter, meter, meter, this is cubic meter. And this is nice because cubic meter cancel here and we end up with the mass. The mass will be the mass will be, um I have it here. 32 kg. Now that I have the mass, I can plug it in here. 32 Gravity's 10. This is 0.4 And if you do this entire thing, you get that. The pressure is 8000. Now, the question is, what are the units here? Well, because I'm using the standard units. This is just gonna be Pascal. Now, if you don't, If you don't see that, just keep in mind that m g is because this is in kilograms and this is in meters per second squared. This mg here is in Newton's and this was meter and meter. So this is meter square. So Newton's per meter square gives you a pass cow. So that is the answer to this one. Okay, now I'm gonna do the second one in a different way So you can see another way that you could have done this. That is gonna be a little bit easier, and it's gonna be helpful later on. But this is sort of the most straightforward way. You could have done it without anything fancy. Okay, so let's do this a little bit different. And the first thing you might be wondering is isn't it just the same thing? Because it's the same block? Well, pressure is forced over area and while the forces the same because the masses the same because the same block right, the area is different. The floor is touching, is interacting with the surface underneath it via a much larger area. So the area that they are touching against each other is much bigger. And if the area is bigger, you might imagine that the pressure will be smaller. Okay, the pressure will be smaller. We're gonna calculate this a little bit different. So the pressure with the floor, it's still gonna be the force against the floor divided by the area and the force against the floor. By the way, it's still MGI divided by the area. But I'm going to show you something a little bit different now. So what is the area? The area is Are these two dimensions here? Right? These two dimensions here not all three of them, but just to which is the the with times the depth. Okay, so let's leave it there and in mass. Remember, we just did this here Mass is right here. Mass is density times volume, But what is volume? Volume is with times depth, times, height, okay, with depth and heights. So I can plug in this stuff in here, and I can say the m is gonna become a row. W d h don't forget that G over here divided by W times it deep. Okay. And this is the only time I'm gonna do this just to show you this is actually very helpful for you. W cancel d cancels and you're left with. You're left with that. The pressure against the floor is gonna be ro ro, not P. This is Ro. Be careful on. I'm gonna just move the letters a little bit here. Row G H row G H. So this is interesting because the pressure actually does not depend on the area. It only depends on how high this thing is. Why doesn't the pressure depend on the area? Well, as you have a bigger base, you have a bigger object. But that forces being distributed over a bigger area so it doesn't really matter. It only matters what the height of the object is. And that's good news. Because if you know this, this question is much simpler to solve because you can just plug a bunch of stuff in here. Let me move this up a little bit. So the density is 800. Gravity is 10 in the height is point to. And if you do this, if you do this, you get that. This is 8000 divided by five. This is gonna be 16 100 pascal 1600 plus cow and notice that this is a smaller number than the other number over here. And that's because even though it's the same mass therefore the same weight, it's distributed over a bigger surface area, so there's less pressure. Okay, so that's a quick example of how pressure works in two different ways. You can calculate it and even sort of showed you or derived, Um, this nice equation that you can use and this equation is gonna come back later. So that's good news. Okay, so now let's talk about something else. This is the last point. I'm gonna make you so and just like how you can have an object that is applying pressure against a surface, you can also have air molecules around objects applying pressure on them. A swell. So that is called atmospheric pressure. Atmospheric pressure is the pressure due to air molecules around you that are pushing against you or against a knob checked. Okay, so the idea is that a box will apply pressure on the floor, but then air molecules directly above will apply pressure on the objects alright, and that pressure has a standard value at sea level. So what does that mean? That means that the amount of pressure that the air exerts on you actually changes. If you go, let's say up a mountain. But if you're sitting hanging out next to the ocean, you know for a fact that that pressure has to be 1.1 times 10 to the fifth Pascal's. It's a standard value that we're always going to assume If they don't give us the pressure, we're going to assume that the pressure of air around us is 1.1 times 10 to the fifth Pascal, and this is the pressure of air. Sometimes I will refer to this as P air. Sounds funny, some French dude. So pressure of air Pierre. And that's the amount. Sometimes it gets simplified as 10 to the fifth person cow. But typically you do have to remember the 1.1 kind of annoying Um, Now they got tired of writing this over and over because it's a big number, and they decided to invent this thing called in 1 80 m. So 1 80 m just standards for 1.1 times 10 to the fifth It's sort of a shortcut because they got lazy. You can also have pressure in British units. So instead of Pasco, which remember pass Cowes Newton per square meter, you can have it in pounds per square inch. And you can also have it in terms off millimeters of millimeters of mercury, right, 7 60 millimeters of mercury. You see that in lab when you're doing chemistry? Okay, so you should know all these so you can convert between them. But remember that this is the standard units one. So this is the one that's gonna go into all your equations. So if I give you 7 60 millimeters of mercury, you have to you have to convert this into Pascal, Or if I give you any millimeters of mercury, you have to convert that into Piscotty. Alright, so let's do a quick example to drive this point home. So it says for the blocks above, calculate the force applied by the air above them, um, to their top surface. So we have these blocks. I'm gonna draw them both real quick, and I wouldn't know. I want to know the force applied by the air above them. So there's a bunch of air molecules everywhere, and I want to know how much force is the air applying to their top surface. So how much force is air applying here now? To be clear? Air is applying force to all sides of this block. The Bacca's well except the bottom because the bottom is touching the surface, right? But there's applying everywhere. But I just want to know how much force is applied to the top. So what is the force on the top for Part B? It's the same thing, except that it's laid out a little bit differently. So it looks sort of like this. And I want to know how much force is applied to the top surface over here. Have top. Cool. And so how are we gonna do this? We're gonna do this using the fact that we know what the pressure of air around you is. Most of the time, we can assume that pressure is going to be the pressure of air. Is that the atmospheric pressure, which is 1.1 times 10 to the 15th? And if we know that and we know the area, we can find the force let me show you. That's because pressure is force over area. And if I'm looking for force and I have the other two, I can rewrite that forces pressure times area. Okay, so the pressure will be the pressure of air up here, which is 1.1 times 10 to the fifth Pascal and the area is the area. If you remember the dimensions here, where 0.20 point two in the height was one. But if I want the top surface, I'm gonna use this in this measurement. These two measurements here. So 0.2 times 0.2 m times meters square meters. And if I multiply this, I get 4000 and 40 Newton's now notice how I use the standard unit for pressure. I use the standard unit for area. Therefore, when you combine those two, you're gonna get the standard unit. Newton's for force. I don't have thio sort of. Combine those two and figure out um do dimension Alice and figure out what unit gets left out at the end here. Because if I'm using standard units as an input, I'm gonna get the standard unit for the output So 4000 Newtons. You might be thinking, that's a lot of force and there is a lot of force. It's the equivalent equivalent of having something that is about 400 kg on top of you or roughly £880. Right and 20 by 20 is a square about this big. And if you have £800 on top of this, it's very heavy. Um and does that make sense? Air is very light. How come it's gonna be so heavy on top of you? Well, the reason it's so heavy on top of you is because there's a huge column of air that starts from right over on top of you all the way to the atmosphere, right? So, you know, thousands of, of or many, many miles above you. So it's a lot of air, so it's pretty heavy. It's upto a lot. You just used to it so it doesn't bother you. A tall Alright, so for the second one is gonna be very similar. But we're just going to use different numbers. So the force, remember, weaken, just start from here. Force is pressure Times area. The pressure is 1.1 times 10 to the fifth. And the area now is going to be the long one. The long dimension here, which is one and the one of the smaller dimensions, which is 10.2. So this is gonna be one times point to square meters. Okay? And this means that the pressure, this means that the pressure will be the pressure will be. I have it here. I'm sorry. The force will be 20,000 and Newtons. Now, Notice that the force here turned out to be much greater than the force here. Why? Well, because there's more air on top of you, right? That top base. The top area of this of this block is supporting a lot more air under on top of it. Therefore, it's Mawr Force. And you can also think of this as more weight. Essentially, what we're doing here is calculating the weight of air on top of you. All right, so that's how this works. Let's keep going