Density

Alright, so, liquids and gasses are types of fluids, types of fluids. So liquid is a fluid and a gas is a fluid. So we're going to use the term fluids to refer generally to both liquids and gasses. And the reason we do this is because liquids and gasses behave very similarly in a lot of different situations. So instead of saying liquids and gasses, liquids and gasses all the time, we're just gonna say fluids, which refers to both both things. Cool, so density is the first big concept you have to understand and you may remember density from chemistry class, the density of the material has to do with how tightly packed the molecules are. So, for example, here you got the same sort of volume, this sort of blue um cup. And it's got these little green balls here, they're not very packed together. So what I'm gonna say that this is low density and here they're very tight together. So this is going to be high density. Okay, so the more compressed things aren't the higher density you have density in physics is given by the letter, by the greek, letter wrote row, which is a little p a curvy P and if you remember, it's simply mass divided by volume, mass divided by volume. So mass in physics is always kilograms and volume is a three dimensional length. So it's going to be cubic meter since kilograms per cubic meter. Remember if you have the three dimensions of an object like a rectangle or something, then the volume of a rectangle would be the width of the rectangle times the height times the depth. Right? And sometimes you see length instead of one of these three measurements. And because each one of these guys is a meter, you got to meet him in the meter. You have cubic meter. Cool. Now sometimes you are given the density and you're given these dimensions, right? So you're given density rho and you're given the three dimensions. Whenever you're given the three dimensions, you're able to find volume. And if you have row and volume, if you have rho and volume, then you're going to be able to find the mass. And that's because of the equation rho equals mass divided by volume. Therefore if I move the v up here, I hope you see that right away, you get m equals rho volume. So let's put this this over here, mass equals rho volume. Alright. And they try to trick you with this but it's very straightforward um It's just a play on this original definition here of density. Sometimes you see something that says that objects have the same material in density problems. This usually means that they have the same density. Okay, so if you have a if you have two pieces of wood and we say it's the same kind of wood, you can also infer that they have the same, you can conclude that they have the same density. Cool. And then the last quick point I would make in the world. One example is if you have liquid in a container to liquids or more liquids. Two or more liquids in a container. The liquid of the higher density will be at the what do you think? Top or bottom? Higher density liquid will be at the bottom. Okay. The high density liquid will be at the bottom and you can think of this as higher density being heavier. Now I'm putting this in quotes because it's not necessarily heavier. It's gonna be heavier depending on whether you have more or less volume of it. But on a per molecule basis it is heavier or or per small area or per small volume. It is heavier. Therefore it's gonna go to the bottom because liquids can sort of move around. So you might have seen something like this where they put all kinds of different things and you can see them becoming very different sort of a heterogeneous mixture here. Um And honey is all the way at the bottom which means honey is the highest density out of all these things that are here. Cool. So we'll see some stuff like that later. Let's do a quick example here. Um What is the total weight of of air molecules inside a large warehouse? And I give you the dimensions here. So I want the total weight of air. Right? So air does have a weight. And so first let's start with wait wait remember is just MG Mass times gravity. And I know gravity I'm gonna use here just for the sake of keeping this simple, I'm gonna say gravity is approximately 10 m/s square. So I'm gonna use 10. So if it's asking me for weight and I know gravity, all I really need is mass. So this question is really about finding the mass of air in this space. Now, I'm given this right, so you can sort of draw this, it's 100 wide, 100 deep. So it looks something like this not to scale. Okay, so this is 100 m here, 100 m here And 10 m high. Whenever you're given three measurements, you can right away find the volume. vol is just those three measurements together, multiplied 100 times 100 times 10. And here you can just count the zeros or five zeros. So this is 10 to the fifth and I got meter times meters times meters so cubic meter. Right? Or you can write it out if you want 12345. So it's 100,000 cubic meters. Okay, now I have the volume. I have the density right here. So I can find the mass because remember density is mass over volume, I have the volume. I have the density. It was given right here. So we can just find the mass which is the equation I showed you just a few moments ago. So roe V and then you're gonna multiply the two row is going to be 1.225 kilograms per cubic meter. I highly recommend you put the cubic meter down here right? Like don't put it over here, if you put it in the bottom, it's going to be easier to play with it Times The volume, which is 100,000 Q B commuter. And then notice what happens here right away. This cancels with this. And you just got this big multiplication. The mass therefore is going to be if you put this in the calculator, you're going to get 00. You're left with kg. A little bit of dimension analysis here. Cool, are we done? No, because we're getting mass so that we can plug it in here and get the weight. But that's the last step I'm gonna do here. Weight is mass times Gravity. And I just have to multiply those two. We're gonna use gravity as 10. So we just have to add an extra zero here. And the unit for weight, since it's a force is Newton's. So this is a million newtons of weights. Cool. So the air in this entire thing is actually pretty heavy. If you would put that entire air on top of you, it would crush you in a very small amount of time. Alright, cool. Let's do this example here. If you want you can pause the video and give this a shot yourself. I'm gonna keep rolling here. It says the density of whole blood. So whole blood means it's all the different parts you have of your blood plasma. Everything else is nearly this now in physics, whenever they see a value is nearly or approximately, we're just going to use that value. So density is rho of whole blood is 1.06 kg per leader. I'm gonna write it like this, notice that it didn't say kilograms per cubic meter instead of said per leader. Um and these two are not equivalent but they are related and we'll talk about this in a future video. So we're just gonna leave it like that for now. And then it says, how many kilograms are in a pipe pints of whole blood. So ask me how many kilograms kilograms is the units for mass? If I say how many kilograms I'm asking for the mass. So what is the mass? And then I'm given the volume here, the volume is 4 73 mL. Now you can't really use milliliters, you're supposed to use leaders, but let's leave it alone for now, let's not sort of prematurely convert units here. Alright, so this is very straightforward. I have three variables that are related by this equation by the definition of density, which is mass over volume. I want to know mass, I have the other two, I just have to move things around this question is a little bit more straightforward than the other one PV or Rovi And this is 1. kg per liter times of volume, which is 473 millie leaders can't really do this without changing either leaders into milliliters or milliliters into leaders. Hope you remember this is very straightforward. One leader is 1000 mL, so I'm actually just gonna scratch this and put 1000 milliliters right here. Middle leaders will cancel and then you're left with kilograms, which is what you want. So all we gotta do here is multiply this big mess. And if you do that, you get 1.6 times 4 73 Divided by 1000. And this is gonna be in kg. And if you do this in the calculator, you get 0.5 or one kg. That's how many kilograms. Or how much the mass of the mass of blood, of whole blood. If you have one pint of it with this density, cool, that's it for this one, let's go to the next one.

Hey, guys. So in this video, we're gonna talk about some values of dense that you should know as well a specific gravity. Let's check it out. All right. So you should know certain values and units for density. So you should know that fresh water is 1000 kg per cubic meter. What this means is that if you have a cubic meter, a cubic meter of water, right, so you fill it out with water. That's gonna have a mass of 1000 kg, which is over £2000. Okay, so pretty heavy stuff. So 1000 kg for every cubic meter and you could also rewrite This is 1 kg per leader. That means that every kilogram every leader of water has a mass of kg or 1 g per cubic centimeter. That means that 1 cc tiny little amounts off water is 1 g of water. Cool. So if you remember these, you got to benefits one. You know the numbers for water, but you also can use this as a way to convert stuff. So, for example, if you know that 1000 kg per cubic meter is 1 kg per leader, and then I give you 1.2 kg per leader. You can immediately convert that and say, Well, if one here is 1000 here, then 1.2 of this must be 1200 of the other 10. So this allows you to make some quick conversions by remembering what the ratios are. Now you have fresh water and you have salt water, and this is pretty straightforward. But just in case I have here any time that the question refers to a lake, a river or house water meaning water coming out of the faucet or whatever it's going to be fresh water and fresh water is the default water. If you're not sure if it's fresh or salt, it is fresh, okay, and it's 1000. It's the easiest number out of all of these to remember. Salt water is water. You put some salt in it and its water from the ocean right Seawater. One way to remember this is Imagine if you have water and you pour some salt on it. Now it is denser, therefore, it's a little heavier. That's why it's 10 30. Okay, just a little bit heavier. Whole blood. Whole blood is when you have a plasma and all the other crap it's in your blood. Andi, that's gonna be 10. 60. Um, air air is 1.2. Now, this is not a typo or some weird mistake. Air is, in fact, 800 times. This is 1000. This is 1.2. This is about 800 times lighter than water. And that makes sense right? There is much lighter than water. If you have a huge box with a bunch of water, that's gonna be very heavy. If you have a huge box, let's say a cardboard box and it's got a bunch of air in it. It's not going to be very heavy. It's also why, when you look at the horizon, you see water at the bottom right? If you're looking out of the ocean and air at the top because air is lighter, so it is on top. It's pretty silly, but that's how it it's cool. You should know that oil in wood are usually going to be slightly lighter than water. Ah, lot of the measurements for oil and would end up being a about kg per cubic meter instead of 1000 so it's a little bit lighter. Those are pretty popular in fluid problems, and the last thing I want to talk about before we do an example is I want to give you an idea of what these measurements are so you could have a volume as something like Centimeters, um, Centimeters Cube or are cubic centimeters your cubic meters, which are lengths right? But then it's cubes. It's a volume, or you can have it in terms of leaders or milliliters, which are more readily identified as being volume. And I want to give you a sense of what these things are. So a cubic centimeter, a centimeters, like tiny like this, right? It's less than half an inch. Eso a cubic centimeter is a tiny little cube, and that's 1 mL of water, right? Eso It's this guy right here. Okay, this is 1 cc or one mil. Leader of water. Now this is what's one middle leader of water. Looks like it's a tiny amount of water. Two liters of water is your big water bottles, right? And this is what one cubic meter looks like. So here's a dude this guy. The average person is probably, I don't know, 1.8 m. Right? So you would have a box of one cubic meter box would be about Go about halfway up to where you are. And it would be this big box here and that this would have 1000 liters, 1000 liters of, um of water or whatever. Right? So the idea here, one point that I want to make is that one cubic meter is gigantically bigger than the cubic centimeter. It's actually a million times bigger. Cool. All right, let's go. A problem here? A quick example. How much does 500 mL? That's a volume. So volume equals 500 mL of a 2.2 g per cubic centimeter. So what is this? Well, this is a mass and this is a volume mass over volume is our is our density. So the density, it didn't say density. You have to figure out by by the units there. It's 2.2 g per cubic centimeter and I wanna know how much does that liquid weight? In other words, what is the weight of that liquid which is mass times gravity now we know gravity. We're gonna use 10 here just to make life easier. We know gravity. So really, this question is asking us for mass if I confined and mass. If I can find the mass, I will find the weights. How do I find mass? Well, if I have V and road density and I want mass, I can just use the density equation. Density is mass over volume. Therefore, mass is Roe V, and the row is 2.2 g per cubic centimeter. Remember to always draw, always write it in the bottom. So it's easier to see times the volume when she's milliliters. Okay, so there's all kinds of problems here with the units that we're gonna have to try to fix. Um, this here is a volume this year is units of volume as well, but they're not necessarily compatible with each other. Or at least they're not the same exact thing, right? Milliliters and cubic centimeters. So can we convert one into the other? And if you remember this piece here, if you remember, that 1 cc is in fact, one millimeter. Then you know that these two are equivalents. They're not the same, but their equivalent so they could be canceled. And then you're left with two times. 502 times, 500 which is, um, 12.2. So it's 1100 g. Um, but we cannot leave this Ingram's We have to turn it into kilograms. So this is just gonna be divided by 1000. So it's gonna be 1.1 kg just some quick, um, to mention analysis there or really just conversion using the metric system. Right? So 1.1 kg. Are we done? Not really. That's the mass. So we can find a wait. Wait is mass, which is gonna be 1.1 kg times gravity between meters per second squared. So this is going to be 11. Newton's 11. Newton's cool. So that's it for That's one for that one. Now let's talk about specific gravity real quick, and some professors will talk about specific gravity. Someone's If you've never heard this. If you've never seen this in class, you could skip it. But specific gravity. Um, it's just a term that's related to density. It is density relative to water. It's kind of a silly idea, but you should know it if your professor cares about it. So the definition of specific gravity SG So the specific gravity of something is the density rho of that's something divided by the density of fresh water. And by the way, the density of fresh water is 1000. So I can simply rewrite this and say that specific gravity of something is density of something divided by 1000. That's it. Just take density divide by 1000. So, for example, what is the specific gravity of fresh water? Well specific gravity of fresh water. You have specific gravity off fresh water is the specific gravity, Um is the I'm sorry it is the density of freshwater because this guy here goes on the top. So this matches up with this right? The dense, the specific gravity of axes, the density of X So the specific gravity of fresh water is a specific density of specific water. Divided by the definition of the equation is that the bottom is always a fixed number, which is the density of fresh water. So this is kind of silly because it's just one, because specific gravity is relative to, um to freshwater. The specific gravity of fresh water is one because it's the same. Okay, so what the heck is this used for? Well, if you know that the specific gravity of something is true, that means that it's because it is twice as dense as fresh water and you would immediately know Oh, that means that the density is 2000. If the specific gravity of something is 20000.7, it means that it's 70% of water, which is 1000. So this would mean that the density is 700. Okay, it's a little silly. They could have just left it at density. But there's this other term you should know. Um let's do an example here. It says, What is the volume off a wooden cube? So I wanna know what is the volume of a wooden cube with a specific gravity of eight. So the specific gravity is eight that weighs 16,000 Newtons. So if the weight is 16,000 Newtons, what is the volume? Okay, so can we do anything here? So where am I gonna get the volume from? Well, their specific gravity, which is related to the idea of density, and that weight is related to the idea of mass right? There's equations that connect these true, So if you have volume density and mass, you can put them together under density equation. Density is mass over volume. Therefore, if I move some things around, volume is mass over density. So if I can find the mass and if I can find the density, I confined the volume, so let's see if you can do that. So first, let's try to find the density. So the specific gravity of something is the density of that something divided by 1000 so I could just move things around. Finding the density of something is a specific gravity, which is 0.8 times 1000 which will give us 800. It's very similar to what I did up here, right? The 0.7 became 700 a point. It becomes 800 so I got the density. So let's see if we can find mass. So wait, remember, is mass times gravity and if I know the weight but I want mass, I could just move things around. Mass is weight divided by gravity, so it's 16,000 divided by we're using 10. So this is 1600. So now we can plug stuff in the mass was And the density? I'm sorry. The density was 800 the mass was 1600. Got that backwards? There The mass is and the density is 800. And if you do this, this is simple and made the numbers easy Here it means that the volume is true now. What are the units? The units are cubic meter. Why? Because we had standard units. This was 1600 kg. Okay, 1600 kg Because we were dividing because we're dividing Newton's by meters per second square. So we're using standard units and then you get a standard unit. And here this is was This was kilograms per cubic meter. OK, so long story short. Whenever you're using standard units, you get standard units. The standard unit for volume is cubic meter. So you get a cubic meter. So the answer here is to That's it finished one. Let's get going