19. Fluid Mechanics

Buoyancy & Buoyant Force

# Intro to Buoyancy & Buoyant Force

Patrick Ford

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Hey, guys, In this video, we're going to start talking about buoyancy, which is the thing that causes objects to float or be pushed up when in a liquid, Let's check it out. All right, So if you have an object that is immersed in a liquid, the object will be pushed up by a force called buoyant Force. And buoyant force comes from the fact that the physical phenomenon responsible for this is called buoyancy right, which usually is associated with floating. Um, and because this is buoyant force with the B, we're gonna call this F B. Now. The reason this happened is because of a pressure difference between the top and the bottom of an object that's under a liquid. So let's say you have a box that is completely submerged completely underwater, and we know the water is gonna push on all sides, right? The water is going to apply pressure on all sides, and pressure is associated with with force. So if there is a pressure, there is a force. Now the force on the left will cancel the force on the right because they are at the same height for every force on the left. I can draw the equivalent force on the other side on the right. That will exactly cancel it. So the side forces don't do anything. But the top and bottom forces will be different because the top and bottom pressures air different. And we know that the deeper you go under liquid, the greater the pressure. So the pressure at the bottom over here at this point is greater than the pressure at the top. Therefore, the force with which the liquid pushes up on this box is greater at the bottom than it is at the top. And the difference between these two forces is the buoyant force. Okay, so you're always gonna have a stronger force up than a force down. So the Net buoyant force is going to be up cool. And so that's the number one thing opportunity to know, and you probably should memorize. This is our committee's principal. Um, he said he figured out that the magnitude of this buoyant force is the same as the weight of the liquid displaced. Okay, so you should memorize that quote because that could show up in some way. And it's important to know that it's a big principle in physics. Now, the problem is that this quote here doesn't really help you calculate this force. So I'm just gonna give you the equation. If you were to sort of translate this quote into physics equation, you would get that the buoyant force is the density of the liquid density of the liquid. Um, gravity 9.8 or whatever planet your own, um, in the volume, um, of the object that is underwater. So I'm gonna call it Roll Liquid G and V under. So there's two really important things here. Distinctions to make in this equation that the density that matters, the density that you should be looking into is the density of the liquid. Even though the object is inside. And this is the force on the object, the density that matters, the density of the liquid don't get that messed up. Okay, in the volume that matters is the volume of the object. But on Lee, the amounts of volume that is underwater. So it's the volume under water or under the liquid. Okay. Or the volume submerged of of the object that is submerged or immersed in the liquid. Okay, I'm just gonna call it under to keep these words simple. And it's not necessarily the entire volume. Unless, of course, you are entirely under. So let's think about this real quick. Um, the idea here is that the Maurer of the oven object is underwater, the stronger the fourth. And you might play this out in your head and just sort of imagine that if you're getting a piece of Styrofoam as you push it down under water, um, there's more resistance, there's more force pulling it up. And that's because the more volume you have, the more buoyant force you have. Okay, so that's that. And then one last thing I want to remind you because you're gonna be using this lot is the density of an object. The definition of density is mass over volume, so the density of the object will be the mass of the object and the total volume of the objects. I'm gonna write V I'm gonna write, actually, mass total. It's the entire mass sweeps. You won't go away. It's the entire mass of the object divided by the entire volume of the objects and the reason I'm being careful. That distinction is because you have volume under which isn't necessarily the entire thing. And you have volume total, which is the entire thing, and we're going to be using these two equations all the time to solve these questions. Okay, the last point I wanna make and we're gonna do an example here is that almost every single buoyancy force a problem is just a force problem. So it's just a good old f equals. They made problem. We could have done this right after you learn. If it was in May. In some ways, um, and also that most of the time it's gonna be even simpler than Africans in May, because most of the time the objects will be at rest meeting the velocity zero. And there will be, um, in equilibrium, which means the acceleration is zero and the Net force zero. So it's really an f. Some of our forces equals zero problem. Most of the time, just equilibrium forces. They're just gonna cancel coal. So let's do a quick example here. So it says when an object of unknown mass, so we don't know the mass and volume unknown volume. We don't know the volume great is fully immersed, fully immersed. Let me draw that. Fully immersed means you're entirely underwater. Remember I told you there's two kinds of volumes, right? There is volume under, and there's volume total because you are fully immersed. This means that volume under equals volume total. Okay, uh, in a large water tank and released from rest, it accelerates up. So when you release the object that's going to accelerate up on, Bennett says, once the object reaches equilibrium, 30% of its volume is above water. So here's the object it's going to, um, eventually it stops up there. So when you release, it accelerates up. Eventually it stops, and 30% of the object is above water. Okay, Now, if you remember on this equation here, the only two volumes that matter are the total volume and the volume under so 30% above doesn't do anything for us. What you really care about is the volume under. So you're gonna change that into 70% under. That's one of the things that you have to do in these questions is you always want to know the volume under. That's what matters. Okay, Now, with just that information, we want to calculate the density of this object. So what is wro object? Cool. Now again, all these questions they're going to start with f equals m A. Equals zero because you are at equilibrium. So I'm going to write that the some of our forces equals zero. And remember the way to solve force problems has always been to draw free body diagram and then write f equals in May. So let's draw everybody diagram. What's going on here with forces? Well, this object is here, so there has to be an mg pulling it down. And the new thing here is that because it's under liquid, it's going to be pushed up by a buoyant force and FB is always going to be up. Okay, let me write that here. Just so you have it always up because as, um because the density down here is stronger as you go lower quote. So if the system is the equilibrium of the objects equilibrium, it means that the forces cancel so you can simply write that f b equals M g. The next step is always going to be almost always going to be to expand this FB what do you mean by that? We're gonna rewrite FB based on its equation, which is this. So instead of writing FBI, I'm gonna rewrite it as Rogov quote. So let's do that density. Remember of the liquid gravity and volume under equals to M. G Right away, G cancels. And this is gonna happen quite a bit. Not always, but quite a bit. And we wanna know the density of the objects. Now, if you stop for a second, you look here, you will see that density Rho object isn't anywhere in this equation, right? It's not here. You have density, the liquid, But that's not what we want. So it actually is here. But you have to look a little bit more carefully. It is going to be inside hiding inside of one of these things here, right? Are there any of these things that you can rewrite that you can rewrite to make this variable show up? And there is. And I warned you about this, that we were gonna be using this equation all the time. So very often you're gonna rewrite things to make variables show up. Okay, so, um, the ray we're gonna do this is density of the object is mass total, divided by volume total. Therefore, mass total is density of the object times volume total. All right, so what we're gonna do is we're gonna replace mass with density volume, and now we're gonna have our variable there. Okay, So the density of the liquid times volume under equals density of the object, which is what we're looking for. That's good, uh, times volume total. Cool. Now realize also that we know we know the volume under. Okay, we know that we are 70% underwater, so I can rewrite volume under as 70% of or 700.7 times volume total. Okay, it's rewriting this here. So if you do that, you can cancel these two outs and then we are basically done. The density of the object is 20.7. The density of the liquid we are in water were in water. So this is just 1000. So the density of the object is 700 kilograms divided by her per cubic meter. Okay. It makes sense. It should make sense that the object is floating above water because it is less dense than water. Therefore, it rises to the top. I wanna talk about one last thing here. Um, notice here that I had said that the volume under the water is the same as the total volume. But that was before That was before he released in the object moved this way here. Now the volume under is less than the volume total because some of it is above cool. That's it for this one. Let's keep going.

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