Hey guys. So let's check out this buoyancy problem. Here, we want to verify if a 100 gram crown is in fact made of pure gold. Almost all of these questions, the way you're going to validate that is by checking the density of the objects. Okay? So the density of gold is 19.32 grams per cubic centimeter or, 19,320 kilograms per cubic meter. Okay. Kilograms per cubic meter. And what we're going to do is we're going to calculate the density of this object and figure out if the density of the objects is 19,320. And if it is, this is gold. So if yes, if this is true, then it is gold. Okay? So if I ask you, is this gold? What you're doing is you're calculating density. So let's do that. So here, you lower it by a string into a deep bucket of water and then when the crown is completely submerged, so let's draw this. I will attempt to draw a crown. It's probably going to come out terrible. There you go. I told you. So it's completely submerged. It's got a little string here. You measure the tension to be 0.88. So there's a tension here, 0.88 newtons. There is a buoyant force always up and there's an mg always down. And we want to calculate ma. The next step is to just write that, that equals 0 by the way. The next step is just to write the forces. So all the forces going up equal all the forces going down. So fb + t = mg. Alright. And if you look at this real quick, you're going to notice that the density of the object is nowhere here, but you have to have a little faith as you start to change some variables around, as you start to expand some of these variables, the density of the object should show up And you don't stop until it does. So fb is the density of the liquid, so that's not good enough yet, times gravity, times the volume under, plus tension. We have that. We're going to plug in a little bit. Equals mass times gravity. Now we need the density of the object. So I'm going to rewrite the mass of the objects into the density of the object. Remember that density is mass divided by volume. Therefore, mass is density times volume. So it's the mass of the object. So it's the density of the objects. And it's always going to be the total volume. Okay? When you're rewriting mass, it's the total volume because you're looking at the total mass. And that times g. Okay? So we are looking for this. And if you take inventory here, we have the density of the liquid because it's water. Let's write that. We have gravity, 9.8. I'm going to round it to 10. Actually, let's make it 9.8 because we're trying to be very precise in our calculation. The volume under this object is entirely underwater. So volume under is the total volume, is the total volume, but I don't have that either. I don't have that either. So that's going to be a problem. Let's just leave it like that for now. Volume total + tension. Tension is 0.88. Let's go to the right side. Density of the object, that's what we're looking for. Density of the object. Cool. Leave it alone. Volume total, we don't have that. And gravity, 9.8. So we got a little bit of a problem which is this is my target but I actually don't have this either. So again, you're going to have to rewrite some stuff. Okay? So back to this equation here. If you solve for volume total, if you solve for volume total, you're going to get mass total divided by the density divided by the density of the object. So if you write this, the good news the good news is that you know the mass, it's a 100 grams, And though you don't know the density, at least that is your target. So this is a little tricky, but I'm going to rewrite it and you're going to see what's going to happen. You're going to have 980 (assuming 9.8) times the gravity. Instead of v total, I'm going to have mass, which is 0.100 kilograms, divided by the density of the object, pl...
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Buoyancy & Buoyant Force
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