h times a that's the volume displaced, so that means that the buoyant force is equal to density of the fluid times acceleration due to gravity times the amount of volume that was displaced. Now here we went down a distance h, so look what we got here. How much is the increase? Well the change in pressure is given by the density of the fluid times acceleration due to gravity times how far you went down. Now we know that as you descend into a fluid the pressure increases. So the area I can take out because it's the same for top and the bottom, so that means that it's the change in pressure times the area. Now the buoyant force is the net force exerted on the object by the fluid, so that means that it's equal to pressure at the bottom times the area minus pressure at the top times the area. So the downward force is pressure at the top times the area. Same way pressure at the top is pushing down. So the pressure at the bottom, the force that's acting on the object is pushing up because that's what direction, I mean if it's going to push on the object well what's, it's going to push up right? So the upward force is pressure at the bottom times the area, because force is pressure times area. Now pressure is force per unit area, and it points in any direction. The fluid has a pressure in it, so there's a pressure at the bottom and a pressure at the top. Alright, so why is Archimedes Principle true? Well we can look at a situation in which we've got an object immersed in a fluid like this, alright now what are the forces acting on this object we're going to draw a free body diagram because we're good Physicists so we've got weight and then we've got 2 forces that are acting from the fluid. So you just need to be careful about that distinction. We'll see that there're equations that you can derive that are perfectly valid when the object is fully submerged but that are not true for floating objects. And that means that its weight has to be canceled by an upward force, what's that upward force? That's the buoyant force, so these are the 2 separate situations and they're entirely separate. So in the floating situation we always have the buoyant force is equal to the weight of the object because the object is floating. What that means is that the volume displaced is actually less than the whole volume, because some of it, is floating on the top, we said it was floating. If the object is floating on the other hand, then what that means, is that it's not all the way immersed. All I need to know is what's the volume of the object and I'm done. Alright, now so that makes it really, really simple. So that's the volume of the object that's immersed in the fluid times the acceleration due to gravity.Īlright now we have 2 major situations in which we can use Archimedes Principle, if the object is completely submerged, so the entire object is immersed in the fluid then the volume displaced equals the volume of the object. Well what is that? Well it's the density of the fluid times the volume of the volume of the fluid that's benen displaced. So buoyant force equals weight of the displaced fluid. And so what Archimedes said was that, that buoyant force is the weight of how much fluid the object is displacing. Alright so we've got a force from the pressure on the bottom and a force from the pressure on the top we add them together, we want the net force and that's the buoyant force. Now what does a buoyant force mean? The buoyant force, is the net force that is exerted on an object that's immersed in a fluid. So what Archimedes said was that the buoyant force on something is equal to the weight of the displace fluid. Archimedes Principle has been around for a really, really long time and it was very important to rulers of like Greece and Egypt years and years and years ago, and we'll talk about why in just a minute. Alright let's talk about Archimedes Principle.
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