Everyone, so now that we've seen the basics of density, a lot of problems in this chapter are going to involve one of these materials: water, saltwater, blood, air, or even oil and wood. So what I want to do in this video is go over some very common density values that you'll see throughout the chapter, and also some conversions because it will help you balance between the different types of units that you'll see expressed for density. So I'm going to go ahead and show you how to do that, and we'll do an example together. Alright, let's check it out. Some very common density values and units that you'll need to know. Let's check it out. The first one, probably the most common that you'll see, is going to be freshwater. Freshwater has a density of 1000 kilograms per meter cubed. Now, what that means here is that for every 1 meter cubed of volume, it has a mass of 1000 kilograms. Alright. Now, oftentimes, I kind of struggle to visualize that. So the best thing I can come up with is if you've ever moved, so you packed up your house or apartment or whatever, and you've had to put your clothes in one of those big wardrobe boxes, ones that one of those ones that kind of goes up to your waist. That's a box that is about 1 meter or about 3 feet length width and height. So basically what this means is if you were to empty it out and you were to fill it with purely water all the way up to the top, this volume here, it would weigh or it would have a mass of about 1000 kilograms of water. Alright, Here's a person for reference. A person is, I think, with the average height of a human is like 1.8 meters or something like that. Alright? Now there's other ways to express this density. 1000 kilograms per meter cubes can also be rewritten as 1 kilogram per liter, and sometimes we use this. We use liters for volume because it's a little bit more readily identifiable as a volume, and it's also more useful for everyday objects. Like if you go to a store and you pick up a 2-liter bottle of water or soda or something like that, that 2-liter bottle is going to be about 2 kilograms. That's how much mass it has. Alright, Now, the last sort of that's the second sort of pair of units or the other way you might see density. The third one is grams per centimeters cube. This is one that's usually used by chemists because they're using very small amounts of liquids and solids and things like that. Alright, so the centimeters cubed would be like if you had a box, but instead of it being 1 meter in length, width, and height, it would actually be 1 centimeter in length, width, and height. So it would be about the size of like a pencil eraser at the end of a wooden pencil. All right. So this is 1 grams per centimeter cubed. All right. So these are the units for freshwater and they're really important because they basically can help you jump between some different ways that you might see density expressed. What I mean by this is if you see a 1000 kilograms per meter cube, you know that's going to be 1 kilogram per liter. Now, if you had a 1030 kilograms per meter cube like you have for saltwater, which is a little bit denser than water, then basically according to the same pattern, all you have to do to convert to the other one is just move the decimal place back by 3 units. Right? So see how we move the decimal place back, and then it just turned into a one. We do the same exact thing for saltwater. So this would be expressed as 1.03 kilograms per liter and this would also be expressed as 1.03 grams per centimeter cube. Notice how we have 1 and then we have 1 as well. Alright. Now for whole blood, it would basically be the same thing instead of 1.03, we'd have 1.06, and then so on and so forth. So we're taking advantage of these conversion factors, which I want to go over really quickly here. There are 2 main ones that you need to know. 1 centimeter cubed is equal to 1 milliliter, and then 1 meter cubed is equal to 1000 liters. This conversion factor is actually how we got from this unit, these pairs of units, meters cubed over to liters. All we did was we just divided by 1000, and that's why we went from 1000 to 1. All right, so these are the 2 important conversion factors. Now there's one more thing I want to mention here. Sometimes in your problems, you are going to be given that you're dealing with water from a lake or a river or house water or tap water or something like that. That's an indication that you're dealing with freshwater. And if you're dealing with seawater or the ocean, or you're out in the middle of the ocean or sea or something like that, you can usually use this density. If you're ever not sure, the default water is always going to be freshwater. You can always default and use those numbers. Alright, and now the last thing I want to talk about is air, which is at sea level. If you're never not at sea level, the problem will tell you. If not, you can always assume that you are, and it has a density of 1.2 kilograms per meters cubed. Alright. Now, this isn't a typo. You'll notice that this number is way smaller than all of these other numbers here, and that's not a typo. It's because air is actually 800 times less dense than water, and that makes sense, right? We're standing in the air. We can move through it and all that stuff, and that's not very dense. Now the last one is oil and wood. Sometimes you might see these in a problem as well. Basically, these are going to be slightly less dense than water. Usually, they'll probably tell you what the density is, or you'll be able to figure it out, but a good rule of thumb is it's about 800 kilograms per meter cubed. You might need to know that, not sure, but it's a little bit less than the density of freshwater, which is 1000. Alright? So that's really all there is to it, guys. So let's go ahead and take a look at an example. Alright? So we have 500 milliliters of some kind of liquid, and we're told that it's 2.2 grams per centimeters cube, right? And we want to figure out how much does it weigh. So remember, we're not looking for mass, that's the mass. How much it weighs is going to be w and remember the w is equal to mg. So if we want to calculate w and we can just assume that g equals 10 for just to make the calculations a little bit simpler, really what we're looking for in this problem is what is m? Alright, so that's the whole game here. So how do we figure out m? Well, according to our equation for density, we know that m is going to equal rho times the density. Right? That just comes from the definition of density, mass over volume. Okay? So, we're going to have mass is equal to now what's the density of this liquid here? So we've got 500 milliliters, but remember that's a volume. Right? Milliliters, liters, that's all volumes and then we've got this number over here. This is grams per centimeters cube. This is a mass divided by a volume. So even though the problem doesn't explicitly tell you that's the density, you can figure it out from the units and sometimes you'll have to do that, right? So this is going to be the density. This is 2.2, and remember, you want to put this, you want to rearrange this so that you have your units as fractions. So we have grams per centimeter cubed. Now we're going to multiply by the volume, which is 500 milliliters. Alright. So can we cancel out the units and multiply? Well, actually, we can't because we have grams per centimeter cubed and then we have milliliters. Right. So we can't convert, we can't multiply those things and hope that they'll cancel. So how do we get rid of this? We are going to have to go up and look for our common conversion factors. Remember, there are 2 of them. One of them converts centimeters cube to milliliters. The other one is meters cube to liters. Alright? And really this is just, you're just off by factors of 10. Right? A centimeter cubed is actually 1,000,000 times smaller than a meter cube, and that's why you have this as 1 milliliter and this is 1000 liters. Right? So it's all really powers of 10. So with this conversion factor in particular, this one tells us that 1 centimeter cubed and 1 milliliter are actually the same exact thing. There's no difference between a centimeter cubed and a milliliter, and that's why sometimes you'll see this in glass vials or something like that. So even though this says centimeters cubed, this actually is also the same thing as a milliliter. Centimeters cubed or milliliters, it's equivalent. They're the same exact thing. So actually, you can cancel those things out because you don't have to insert a conversion factor. So once you multiply this, what happens is your milliliters cancel, and you're only left with grams on the left side. So be very careful with what units you are left with. So this is going to be 1100, but again, be careful because some of you might be tempted to put kilograms there. 9 times out of 10 when you make a mistake in these problems, it's going to have to do with the units and, you know, you stick at kilograms or you multiplied by grams or something like that. So just be very careful and follow your units. Alright? So this is 1100 grams, but remember when we plug into our equations for mg, we have to have this mass in SI units, which is kilograms. So this 1100 grams is 1.1 kilograms, because we're just shifting the decimal place. So now this is the number we plug back into our weight equation. And so last but not least here, we're going to have that the weight is equal to 1.1 times we're going to use 10 just make a little bit simpler, and this is going to be 11 Newtons. So that's the weight of 500 milliliters of this liquid here. Alright, so there we have it folks. That's for this one. Let me know if you have any questions.