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

2

Problem

A large warehouse is 100 m wide, 100 m deep, 10 m high: a) What is the total weight of the air inside the warehouse? b) How much pressure does the weight of the air apply on the floor?

A

(a) 1.2×10^{4} N; (b) 1200 Pa

B

(a) 1.2×10^{5} N; (b) 120 Pa

C

(a) 1.2×10^{5} N; (b) 1200 Pa

D

(a) 1.2×10^{6} N; (b) 120 Pa

3

concept

Pressure In Air and In Liquids

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Hey, guys. So in this video, we're gonna look into how pressure works. If you have an object that is surrounded by air as opposed to if you have an object surrounded by a liquid such as water, let's check it out. All right, So imagine that you are next to the ocean. Okay, So your next next to the ocean. And if you're next to the ocean, remember that the pressure of the air molecules around you let's make air molecules green. The pressure that the air is going to exert on you at this level next to the ocean is gonna be one A T m, which is the standard atmospheric pressure at sea level. Okay, so if you're out in the open, you have air molecules around you, and that's what happens now as you go up in height. As you go up in heights, the pressure will change, and the easiest way, I think, to to to, um to remember what happens to the oppression whether increases or decreases is just to think that if you go up in air, there's going to be less air above you. So if you are here, you can imagine there's a column of air molecules on top of you. But if you're here, there's a smaller column of air molecules on top of you. So because there's less air on top of you, the air pressure will be lower. It will decrease. Okay, remember, air pressure. Um, air pressure decreases. Air pressure comes from the weight of air molecules on top of you. So if there's less air on top of you, there's less of a wait so the air pressure decreases, Okay, because there's less weight pushing down on you. Now, the air density the air density is going to is going to decrease as well, and number two follows from number one. So here you have a ton of air molecules on top of you and the air molecules up here push down against the air molecules down here so the air molecules down here arm or switch together because there's all this weight on top of them. Okay, so you can think that this is this is low density, and this is higher density off molecules. Okay, the molecules arm or spread out up there because they're not being squished by the weight of the molecules. on top of them. So if you just remember that e think if you think about it in terms of what's on top of you, you don't even have to memorize that. As you go up in height, your P air goes down and then your row goes down as well as you go up in heights. Okay, now here's what's even more important for you to remember is that the density of air is very low as it is. So both of these changes air very insignificant. In fact, most of the time we're going to ignore changes in pressure and density of air. Okay, so this first example deals with that Which of the following is the best approximation for the atmospheric pressure? Pierre at 100 m above sea level, So remember changes are Onley significant over large distances, and I should say, for very, very large distances, such as how high and airplanes flying. So 100 m is not a very large distance, even though it be pretty tall. Um, but it's not significant. Therefore, the answer is that the atmospheric pressure here is basically gonna be the same as it is at sea level. Okay, so it's the same because there's very little different. It's approximately the same cool. So if you're not sure which which pressure to use, you should be using 1. 80 m which, of course, is this number right here. It's 1.1 I made 1.0 just because I was rounding on def. They don't tell you you can use that number. So it's a little bit different if you have liquids, however, So if you were an object or under a liquid submerged in a liquid, um, the pressure differences will be much more pronounced. They're gonna be much bigger, different differences in pressure, even for a little bit of a distance, because liquids have much higher density than air. Okay, so but now, in air, we moved up in our pressure changed. But if you are in water, you're going to move down. Okay, so here the pressure depends on your height, and here it depends on your depth. Okay, Now, we just used H for both of those, Um, but the idea is that the pressure will increase as you go down here. And everyone knows that if you start swimming, uh, If you start going underwater, the deeper you go, your year start to feel a lot of pressure. And that's because the water pressure increases as you go down in heights or depth. Okay, it increases and it increases because there's mawr liquid above you. So before, if you went up, it would go down because there's less air Now. If you go down, the pressure will go up because there's mawr stuff on top of you. There's more liquid on top of you, so there's more weight pushing down. It's the same logic as before. The difference here is that changes are significant even for small distances, right? And if you're swimming and you just go a little bit lower underwater, you can tell those differences are pretty significant. Water density does not change much, so we're always going to assume that water this density is constant because the changes are very insignificant, even for very large distances. So you can pretty much assume you could even assume that I never even mentioned this and just pretended. Water density is always the same, always cool. And in the last point here, is that the pressure in the liquid, um such as water. But it really many liquid depends on this equation, or it can be calculated according to this equation is this is a very important equation and it tells us that the pressure at the bottom off a column. So let's draw a little beaker here and let's say we have Let's say we have some liquid and there are two lines that are important here. The highest point here, Okay. And the lowest point of the liquid here. So the pressure at the bottom right here pressure at the bottom is going to be equal to the pressure at the top, which is this plus row. This is density of the liquid G gravity and H h, which is the height difference between these two or the depth of the liquid. Okay, so I can calculate the pressure at the bottom if I know the pressure at the top. And if I know the h Okay, we're gonna use this equation quite a bit. Now you should know that the pressure at the bottom is called the absolute pressure. The pressure at the top is called the relative pressure, and the pressure difference between these two is called the gauge pressure. Okay, gauge pressure is the difference between the two pressures. How much greater one is than the other. And the idea is that this pressure here is relative to the top. Pressure, the pressure, the bottom depends on the pressure, the top. That's why this one's called relative. So sometimes you see questions that will throw these terms that you so you should know what they are. Let's do an example real quick, and then we'll be done with this. So it's as suppose you are 1.8 m tall and your hearts located 1.4 m from your feet. So I'm gonna draw. I'm gonna draw a person here pretty big s so that we can do this. And your heart, Let's say, is over here. And your total height is 1.8 m and your heart is 1.4 m away from your feet. So it follows that your if this is 1.4, this is 1.8. This gap here, heart to top of your head must be the difference between those two, which is 0.4 m. So that's you. Um, it says the blood pressure near heart is 1.3. So right here the pressure at your hearts is going to be, um, is going to be 1.3 times 10 to the fourth, but scow and we wanna know that way. Want to calculate the blood pressure at the top of your head? So we want to know the blood pressure here. Pressure of head. And we wanna know the pressure at the bottom of your feet. Pressure feet. And guess what? We're gonna use this equation highlighted in green right here to figure this out one at a time. So the first one we wanna know what is the pressure of your head? Okay. Blood pressure of your head. This here, by the way, is the density of blood. So I'm gonna right here that row blood is 10. 60 on. We're gonna use that number. All right, so check this out. We know this here. This is our known, and these are our unknowns. So for both of these questions were the same thing we're gonna set up in equation with a known pressure in an unknown pressure. And if you look at this known pressure and this unknown pressure. We know we know this distance right here, which means we can set up in equation between these two guys. So if you set up in equation between these two guys, it's always gonna be that P bottom equals P top plus row G. H. And the H is the gap between them, which is 0.4. So I know P bottom. I'm looking for P Top, and this is just because this is at the bottom, This is at the top. It's that simple, right? This is the guy at the bottom that's at the top. So I know I want P top. I know the density 10. 60. I know gravity. We're gonna use 10 actually, for gravity. We're gonna use 98 because I wanna be more accurate. Since we're dealing with the human body here, um, and H h is going to be the distance between top and bottom, so this is very important. H is the distance between top and bottom, which in this case is 0.4. So let's set this up. I can write that P bottom is 1.3 times 10 to the fourth equals P top, which is what we want. Plus row 10 60 gravity 9. h, 0.4 for the sake of time. I'm not including units here, but all the units Air Standard. Which means my pressure will have standard units at the end by scout. So if I move this around, you end up with P Top equals 1.3 times 10 to the fourth minus right. This goes to the other side minus, and I have it here. Um 10 9804 And this is gonna I'm rounding here 00 p a. So let me write this here. This went from 1.3 times. 10 to the fourth. If I want to rewrite this with a 10 to the fourth, I'm gonna do this kind of quickly, but it would look like this 0.88 times 10 to the fourth. Okay, you can validate that if you would like. Let me get out of the way. All right. And I want to do that so that we can write all of these answers with a power of four. Let's do part beat. So, for part B, we want to know what is the pressure? Um, of blood or blood pressure on your feet. So again, we're gonna set up in equation P bottom equals P top plus row G h. But now we're talking about this interval here. Okay, So this green Heights was this height right here. But now the blue height has to do with this height right here. And perhaps obviously, this is now for this equation. Bottom is the feet and top is the hearts. Okay? Just to be very careful here. When I did this, the bottom was the hearts in the top was the head. But this is all sort of relative, right? So now that I'm writing another equation for a different interval for this height here bottom and top change. Okay, so be careful there. And we are looking for P bottom, whereas before we were looking for P top. Okay, be careful. If you're careful, it's gonna be easy. So let me write this over here. P bottom p top is the heart. So 1.3 times 10 to the fourth plus road 60. Gravity 9.8 and H is 1. 1.4 m all the units, air standards. So I'm gonna get the answer in Moscow. And if you do all of this, you get 27 500 27 500. Or if you want to write it in terms off a power of 10 to the fourth, right, you can write. This is 2.75 times 10 to the fourth, Pascal 275 10 to the fourth. But scout, let me get out of the way. And last thing I do is put it over here that this is 2.75 times 10 to the fourth Moscow. So I want to quickly show you these answers. This is 100.8. This is 1.3 and this is 2.75 And the important point to make here is that as you go down, you have mawr and more pressure. And that's what you should have, because at the bottom of your feet you have all the weight of the blood and your entire body pushing down on you. So the lowest blood pressure should be all about the top. The Onda, the highest blood pressure should be all the way at the bottom um, Now, this is a little bit simplistic. The human body is a little more complicated than that, but this is good enough for physics. Approximations theory. Last last point I'm gonna make here is that this equation actually technically works for air pressure. But we're not going to use it most of the time because most of the time we're just going to ignore changes in air pressure. Okay, so if I tell you that you are on top of a building that's 100 m tall, you're not going to calculate the pressure up there because it's not gonna be very different from atmospheric pressure. You can try it and you'll see that it's a very small difference. So we tend to think of this equation as an equation for pressure in liquids, even though it would work for air. It's just that air pressure changes are very, very subtle over small distances. Cool. That's it for this one. Let's keep rolling.

4

concept

Calculating Pressure in Liquids

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Hey, guys. So in this video, I'm gonna show you how to calculate pressure at different points within the liquid using to common examples. Let's check it out. Cool. So, first, remember that the pressure in the liquid changes with depth. As you go down in a liquid, the pressure is going to increase, and the exact calculation is used is done using this equation the pressure equation. You should also know that in between two liquids, whenever to liquids, touch or two materials, they don't have to be liquids whenever to matures touched. We have something called an interface. So, for example, over here in this little cup beaker, uh, this line right here, where these two things touches called interface. There's another interface here, and I want you to see if you can figure out where it goes. And hopefully you're thinking that the other interfaces over here, and that's true. So this is the interface between air and the yellow liquid. Those are two different materials, and then there's an interface between yellow and blue liquid. Now, technically, there's an interface between, like down here between blue liquid and glass. Those are two different materials, but you're never gonna use that. So just forget about it. What's important about interfaces that at these points, the pressure of both materials is the same. So what does that mean? So imagine you have a molecule all the way at the bottom of the liquid here, blue molecule and a molecule all the way at the top. These two molecules, you're gonna have a different different pressures because they're different heights. And the molecule at the bottom is gonna have a greater pressure in the molecule at the top because he has more stuff on top of it. Now what? This what this over here saying is that the top most molecule, the one that's like all the way at the top, has the same pressure as the bottom most molecule in the yellow liquid. I do it right here. But imagine this is a yellow molecule. Okay, so this has some consequences. But I want you to remember that the pressure is the same. The first consequence is that everywhere a liquid touches air, the pressure of the liquid equals the pressure of the air. So what does that mean? So if you look at the molecule, all the way at the top of the Yellow column. This is all the way. The topic the top most molecule. It is right under air. Therefore, the pressure at the top of the yellow is the same as the pressure of air, and this is gonna be very useful. So let's do example one to see how this might work. So it's, I suppose the density of a particular beer is 10 50. So density Rho is 10 50. This is using the the standard units. I don't have to do anything weird and we want to know what is the gauge pressure at the bottom of a solo cup if it is field filled with beer to its very top. So I have a solo cup. Looks something like this. Um, it's not a perfect straight cylinder, but here doesn't make a difference. And it just has beer. I'm gonna make beer blue, um, has beer all the way to the tops. It's got 12 centimeters. Hike 0.12 meters and it's got beer everywhere on Do we wanna know what is the gauge? Pressure gauge pressure. Okay, Now, almost every time you asked for a pressure on do you have a height, you're going to use the pressure equation right here, which combines links, pressures with heights. Okay, so let's write this real quick. So we're gonna say because we have ah, height and I wanna pressure. I'm gonna write that P bottom equals Pete Top plus row G h okay. And P bottom is down here. This is the P bottom, and Pete Top is the top of the liquid peat top. Now, because the top of the liquid touches air because it interfaces with hair. The pressure at the top here will be the pressure of air. Or more precisely, the atmospheric pressure, the standard atmospheric pressure, which is one a t. M. Now, if you remember, we can't really use 1 18 and we have to use the Paschal version. So the pressure at the top is 1.1 times 10 to 2/5 Paskowitz, Just a no number. You're supposed to memorize that plus row G bitch. Now, before we get further here, I wanted to talk about this, but you may have noticed that the question says that we want the gauge pressure and this is a little tricky and I did this on purpose. I hope you remember that. What gauge pressure means is this right here? Okay, so let me make that yellow as well. Meaning we don't want the pressure at the bottom. That's not what we want. We want the pressure difference. So I don't want p bottom. I just want I just want row G h. Okay, so I was almost going the wrong way. I wanted to talk about how the pressure at the top was gonna be the pressure of air. So you made that made that connection. But this question, actually, once just the gauge pressure. Which means you don't even use p top. You just use row G h. Okay. Ro is density, which we have. It's 10 50 gravity. I'm going to use 10 instead of 9.8 to make things a little simpler. And the heights is points 12 m and all the units air standards of the pressure will come out in Moscow and you multiply everything. The answer is 12 60. But scow, this is the engage pressure here. Quote. Let's do another example. And on the second example, we have two liquids on top of each other, which is kind of common. So you're going to get something like this with two liquids and the first liquid here, It says it's blue. So I got some blue liquid here and the second liquid is yellow. So I'm just gonna sort of do this and I'm gonna put a little line here. Cool. And it says, uh, the blue liquid you pour six centimeter column of blue liquid so you pour liquid essentially until it reaches a six, uh, centimeters of heights. That's what it means by six centimeter column. So this height here is 0.6 m, and the the density of blue liquid is 1200 standard units, and then you add a four centimeter column, so of yellow liquid. So this is four centimeter column, and the density of the yellow liquid is 800. Also standard units, and this is on a 12 centimeter beaker. So this entire thing is 12 centimeters. So 0.12 m. By the way, if you look at this quickly, you got 6 10 64 So that's 10 which means there's sort of a two centimeter gap here. I don't know if we're gonna need this. Let's right here. Just in case. Cool so the liquids don't mix. This is very important. If they look liquids, Miss mix, this would be a mess. And you you wouldn't be able to solve it like this on we went to calculate the absolute pressure at the blue yellow interface. So there is blue here. Just make this blue. Andi, I want to know what is the pressure here? So part A is asking for this. What is the pressure in the blue yellow interface? How do we do this? Well, there's two ways we can set this up. We can set up an equation that goes from here to here. And then we would use the Six Centimeter Heights. Or we can set up an equation from here to here, and then we would use the Four Centimeter Heights. Okay, so we have a choice there, but we don't really have a choice. Because if you have an unknown pressure, this is my unknown pressure. I have to couple it with a known pressure. I don't know the pressure here. I also don't know the pressure here, but I do know the pressure at this point. The pressure at this point because the top of the yellow liquid touches air. The pressure at the top of the yellow is the same as the pressure of air or the atmospheric pressure, which is 1.1 times 10 to the fifth. So therefore, I have to use the top interval to calculate this. Okay, so let's do that. We're gonna say that now. We're using this piece here, the top someone to write that P bottom. The equation is always the same. Equals P top plus row. G h. Now, when we do this, um, this is the density because we're talking about this interval here this interval, this height of liquid. Um, the density here is the density of yellow. And it's the height of the yellow column. And P bottom means means blue yellow interface. And Pete Top is air. I hope you see this. I'm just doing this slowly so we don't screw this up. Bottom is over here. So this is the interface between the two, which, by the way, is what we want. And top is where we touch air. Okay, so let's calculate it. Just a matter of plug and stuff in. We already know that the pressure of areas 1.1 times 10 to the fifth. The density of yellow is 800 gravity. I'm gonna round it to 10 just to make life easier. And the height here is 0. meters. Okay? And if you do all of this and I have it here, you this piece here is this entire thing here is just 3 Not much. Okay? And if you do this whole thing, you end up with 101 3 20. Which if you were to round 22 significant figures or three significant figures, you would basically end up with this number. In other words, there's negligible difference here. And that's because it's on Lee Four centimeters, which is a tiny column of air or liquid. But that is the pressure in that middle point. This blue, this thick blue line over here. Quote for part B. Part B asks us. Read out of the way Part B asks us for the gauge pressure. Remember? Absolute pressure means p bottom right right there. Between those two gauge pressure, it's just a difference. So if I'm asking for the gauge pressure from the blue and yellow interface. It's just I hope you see it. It's just this part here. It's how much higher is the pressure of blue relative to the pressure directly on top of it. Okay, so when I say pressure gauge, we're just saying, um is the pressure gauge between between these two these two things here. So it's between blue and the gap between between the air and the blue over here. So it's the pressure gauge across the yellow is gonna be row yellow G, height, yellow. And we already did this the entire thing here. If you multiply its just 3. 20 ph Just asking how much higher is the pressure of the blue line relative to the water on top of it? Okay, so this is related to this, uh, and see is about a new point. We want the absolute pressure. So we want the absolute pressure you can also think of this is P bottom right at the bottom of the blue liquid. So all the way at the bottom of blue. Hm. Cool. And again, we're gonna use the P bottom equation. So P bottom equals p top. Plus row G h. But now we're going to set up a new interval from here to here, right across the six centimeters. Why? Because I know this pressure. I now know this pressure over here. And to find this pressure, I'm going to write an equation from here to here. I hope that makes sense. So when I write p bottom, this is all the way at the bottom of blue. The P top is gonna be the blue yellow interface. This is going to be we're gonna go through. Think of it as you start at the top of the liquid, you're gonna go through the liquid, you're gonna go through the blue liquid, and the heights will be the height of the blue liquid, which is six. I'm doing this very slowly so that hopefully everyone can follow that. So, um, P bottom is what we are looking for. Pete Top would just calculated it's this number right here, Tank. So 101 3 20 Plus the density of blue, which is 1200 gravity, which I'm going around us 10 and the height of blue right here. 60.6 And if you do all of this. You get that? The answer is 102 040 busk out. Very similar. Not a big difference, but a little bit higher pressure than before. Okay, so if I want the pressure at the bottom of the second liquid, I confined the pressure in the middle, right? So I started the top. I know this one. I can find the next one, and then I can find the next one. Now, if you didn't want to do this one at a time, let's say this question asked you directly foresee which sometimes they'll do that. It was just gonna say, Hey, find the bottom, the pressure all the way at the bottom. Can you do this in one step? And the answer is yes. So or you could have done this in one shot. You could have said the pressure. Let me rewrite this just to make this a little bit cleaner. Let's say you have a liquid here. You have another liquid here and let's call this pressure a pressure. Be in pressure, see? And by the way, if this is a rare pressure, is the pressure of their because it's touching air But if you have a situation like this, which is what we have, we could see the pressure. See, Is the pressure a plus plus row G H for the first liquid? Let's call that row one G H one. So we're adding that tiny pressure plus the next column of air or a column of liquid row G H. But now it's gonna be the density of the second liquid, plus the heights of the second liquid here. Okay, so this is one. This is two. If you were to do this, you would get something like this. Pressure of air, which is 101000 plus the first density. Which up here was 800 gravity. 10 in the first hype, 0.4 Then we do the same thing for the second column. So 1200. Let me get out of the way. 1210 in the heights is 12100.6 If you do this, you would end up with the exact same answer. And you can try it if you want. You end up with the same exact answer here. So point I wanna make here. That's very important. Is If you have two columns or three columns or four columns of liquid on, do you want to find the pressure at the very bottom? You can just keep stacking. Row G. H is for every column you have, and that is a faster way of solving this. If you have to do it in one step, Cool. That's it for this one. Let's keep going.

5

Problem

The deepest known point on Earth is called the Mariana Trench, at ~11,000 m (~36,000 ft). If the surface area of the average human ear is 20 cm^{2}, how much average force would be exerted on your ear at that depth?

A

2.22×10^{5} N

B

2.22×10^{7} N

C

1.11×10^{8} N

D

2.22×10^{9} N

6

Problem

A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m^{3} liquid and 10 L of a 6,000 kg/m^{3} liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s^{2}.)

A

3.20×10^{4}

B

3.52×10^{4}

C

1.33×10^{5}

D

1.36×10^{5}

7

Problem

A wooden cube, 1 m on all sides and having density 800 kg/m^{3} , is held under water in a large container by a string, as shown below. The top of the cube is exactly 2 m below the water line. Calculate the difference between the force applied by water to the top and to the bottom faces of the cube (Hint:calculate the two forces, then subtract. Use g=10 m/s^{2}.)