Hey guys, so in this video, we're going to keep talking about buoyancy and I'm going to show you the 3 common cases that are going to cover pretty much every possibility. Let's check it out. Alright. So an object floats or sinks depending on its density compared to the liquid density. So if the object is denser than the liquid, it's going to sink. And if the object is less dense or lighter than the liquid, it rises to the top. So whoever is denser is going to be lower, okay? So the first situation is referring to this case right here. This here is sort of a secondary case that I want to talk about. It's sort of an exception. In here we have this object that floats above water. So part of the object's above water and this is the part of the object that is underwater and you can just tell by looking at the picture that the volume under is less than the volume total. So for example, let's say that the volume total is 100 and there's maybe 40 60 here. The volume under 60 is less than the volume total 100 because some of it's above water. Pretty straightforward. What about the forces? Well, if the object is floating, it just sits there, it is at equilibrium, right? Because it's just sitting there floating which means the forces cancel. And the forces are Fb going down and and I'm sorry. Fb going up. Fb is always going up. And mg going down. So it must be that Fb equals mg so that they can cancel each other out. And that's what happens there. What about the density? Which one of these two densities is greater? The object or the liquid? So think about it. I actually just mentioned it and hopefully you got it, that the density of the liquid is greater and that's why the object floats because the object is lighter. So one of the, one quick way to look at this that I like is to just look at the top of the objects and the top of the liquid. And because the liquid, the top of the liquid is lower than the top of the object, I think of it as being heavier, therefore it is denser. So liquid is lower, so it has a higher density. Okay. Now these three things here apply to this picture. And this here is just a different slightly different situation. Sort of an exception that I want to talk about. So here you have this object that that's in the middle here. It's floating with a cable. Right? So think about this. What do you think would happen if I if I cut that cord? Right? It must be that the object would ride up because if the object was too dense to sink, it would just sink. The reason it sits there, it's because the the the cord is holding it. So what's happening here is that you have a tension pulling it down. And then you'll have mg also pulling it down. And then you'll have a buoyant force pulling it up. It's still at equilibrium. It still sits there. But now you would write that the forces going down, mg+t, equal the forces going upFb. The reason why I have this next to the other one is because in this situation, you also have this be true. That the object is less dense. Even though it's underwater because it's only underwater because of the tension, right? If you were to cut this, it would look a lot like this. Okay. So whenever you see a block being held underwater, you have to think what would happen or there's some tension or something like that. You have to think what would happen if I cut that tension and then you would know, okay, well here it goes to the top, which means that it is less dense than the liquid. Cool. The second situation is kind of trivial because it's very similar to this one. Here, the object is floating, but instead of above water, it floats underwater. Right? So how does this happen? Well, this happens if you have an object and you put it underwater and you release it and it stays there. So in this case, the entire volume underwater is the entire volume of the objects. It is 100% underwater. In this case, we also have equilibrium. Okay. Because the 2 forces are gonna cancel. Fb and mg cancel. So they're still at equilibrium. Now what's special here, the difference between these two situations, 1 and 2, is that the density of the object is equal to the density of the liquid. Okay? These two situations are exactly the same. So if you have an object that's entirely underwater, it sinks if it is denser, it's going to rise to the top if it's less dense, and if it does neither, if it stays in the middle, it's because its density is exactly equal to the density of the liquid. Now, how do you get this versus this? The difference is that in the first case, I manually, I grab this object and I brought it just under the waterline and I release it there and because the densities are the same, it stays there. On the second case, you just brought it lower and you released it. Okay? So these are identical situations. If an object floats entirely underwater and it doesn't sort of peak out outside of the water or the liquid and it doesn't sink, it is because the densities are exactly the same. Okay? So this is a simple case but still important to know. Now, number 3. What happens, if the object sinks? Well, what causes an object to sink is the fact that it is heavier. So in this case, you can see here the object is entirely underwater, so So the volume underwater is the same as the total volume. Fb does not equal mg. Fb does not equal mg. The reason why it sinks is because mg is actually going to be greater than Fb. Okay? This is still at equilibrium. It just sits there. But now there's a third force. So you're going to have mg down. You're going to have let me draw this bigger. You're going to have mg down. You're going to have an Fb that's smaller. And because of this, this object is going to be let me move this up. This object is pushing against the surface, so the surface pushes back with a familiar force called normal. And it's not going to be that big. They're both essentially going to add up to cancel the mg. And here you can write that the forces going up, Fb + normal equals the force going down mg. Okay? So there are 3 forces here, just like what we had here. So here, we're going to say that the density of the liquid, or the density of the object rather, is greater. The object sinks because it's heavier, it goes all the way to the bottom, and now it pushes against the floor, so you have a normal force. Okay? So these three things have to do with this situation here. And here we have something very similar. This is sort of an, a side case, kind of like this one where you have a cable. Now look here, this is not sitting on the floor. It has a cable. But think about this, what do you think would happen if you cut the cable? Right? It must be that this object is not lighter than water. Otherwise, it would already have bubbled up to the top and the string would have been sort of loose. Right? If it stays there with the string taut with a tight rope, it's because it's trying to fall. It's trying to sink. So if you were to cut that cable, what would happen is that it goes down and that's because the density of the object is greater than the density of the liquid. So the forces here are you have a bigger mg than you have an Fb, just like in the picture next to it. But now you have the help of a tension pulling you up. And the way you would write this is very similar. Force is up top, Fb + T equals mg. It's the same thing but now instead of the tension, instead of the normal force pulling you up, you have the tension pulling you up. Okay? And by the way, both the normal and the tension in this situation can be referred to as can be referred to as the apparent weight. Okay? So I'm going to put here also known as, in these problems, apparent weight. So if you see a problem with attention or something sitting maybe on top of a scale or something, and I ask you for a parent weight, that is asking for normal or asking for tension depending on which one you have. Cool? So that's plenty of talking. I wanna give you a shortcut and then we're gonna go solve this. There's a shortcut that says that the density of an object is the percent under times, times the density of the liquid. Okay? And I'm going to show you how to get to this equation, but I really just wanna start this example here. Cool. It says a block of unknown material, floats with 80% of its volume underwater. So let's draw that real quick. Bucket of water. 80% is under. Remember, the volume under is what you want. This is 20 but this is the useless one. Right? You want the volume under. Okay. What is the density of the object? And I'm actually going to calculate this really fast using this equation. The density of the object is the percent under times the density of the liquid. And this object is 80%. Remember 80% means point 8, times the density of the liquid. We're underwater so this is a 1,000 which means I can quickly figure out that the density of the object is 800 kilograms per cubic meter. It should make sense that the density of the object is less than the density of water. That's why it's floating up top. Okay. Now that's how you can very very quickly calculate this using the shortcu...
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Buoyancy & Buoyant Force
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