Condition for floating

- [Instructor] How do you decide whether something is going to float or sink in water or any liquid for that matter? Now I should think, well, that's very simple. If something is very light, it's going to float. And if something is very heavy, it will sink. But that is wrong because we know for example, ships which are very heavy, made of metal can float on water. Yet something like a spanner or a nail, which could be made of the same metal, which is very light compared to the ship can easily sink. So it's not their weight, which that decide whether something will float or sink, then what does? Turns out, it's their density. And so in this video, that's logically figure out why it doesn't depend on weight, but it depends on density. So let's imagine I take a chain of gold and put it in water. And I want to know where that it's going to float or sink. How do I do that? Well, since it's gold in water, you might already know what's going to happen, but let's say we didn't know. How would I figure it out? Well, I have to first think about the forces acting on it, right? I mean, if I knew that it's being pushed up, then it's going to try and float. If it's being pushed down, it's going to sink. So let's think about the forces which are acting on our chain of gold. The law of force that we might be familiar with is its own weight. Because of gravity, it has its own weight that's pushing it down. And is there any other force acting on it? Yes. There's a buoyant force. Water is pushing up on it. We've seen before that when you put any object in a liquid or gas, in fluids they have a natural tendency to push up on those things. And we call that as the "buoyant force" and a man called Archimedes tells us that the buoyant force acting on that object equals the weight of the fluid that it displaces. So basically before this gold chain came over here, that space was occupied by this water, right. Now, when that gold chain comes over there, that water has to move away, making space for that gold chain, isn't it? The water that moves away is what we call the displaced water. It'll actually go up and the height of the water will increase, but I'm just, you know, removing it over here so that we can see that displeased water. Okay? And Archimedes tells us that the buoyant force equals the weight of this displaced water. So we can think of it as the weight of this chain of water. So whatever is this weighed, that much would be the buoyant force. And if you need more clarity on, you know, why this is true and everything. We've talked a lot about Archimedes's principle and buoyancy in previous videos. So great idea to go back and check them out. Anyways. Now we can see it all boils down to figuring out which of these two is heavier, because imagine if this was heavier, if the chain of water chain was heavier than this, then this force would be heavier, would be larger. And as a result, our gold chain would float. On the other hand, if the chain itself was heavier than the chain of water, then I would a gold chain would sink. So you see it's all now. Now it's all about figuring out which one is heavier. If this is heavier, it will float. If this is heavier, it will sink. So which one do you think is heavier? A chain of water or a chain of gold? Now again, you might know the answer to this, but let's say we didn't. Let's say I had no clue. How would I figure this out? Well, one way to do that is by looking up the density of gold and water. What's density? Density is a number which tells us how much something weighs per unit volume. Here, let's take an example and make a lot of sense. So if I were to look up the density of gold, it would give me something like this. The symbol stands for density. It would say that density of gold is 19 grams per centimeter cube. Now what does it mean? This could mean that if I were to take one centimeter cube of gold, so imagine a tiny box of one centimeter cube completely made of gold. That would weigh 19 grams. That's what it says, 19 grams per centimeter cube. Now it doesn't have to be a box. It can be any shape you want. As long as you take one centimeter cube chunk of that gold, it will always weigh 19 grams. That's what this number is telling us. So let me just get rid of that. So now I know every centimeter cube of this gold chain weighs 19 grams. Okay. What about water? Well, we can look up the density of water. It turns out to be one gram per centimeter cube. Whew. This means every centimeter cube of this water weighs one gram. Every centimeter cube of this gold weighs 19 grams. So can you tell then which one is heavier? I'm pretty sure you can. It's the gold. Because gold is heavier it's weight will be larger. And as a result, our gold chain is going to sink. All right, let's take another example. Imagine I took a big box of wood and this is on a hollow box. This is completely filled with wood let's imagine. That's a solid box of wood, very heavy. Now again, I want to figure out whether this is going to float or sink. What to do? We'll do the same thing. Well, let's work out the forces. We know it's being pushed down by its own weight. And this time, this is much heavier than the gold chain because I'm taking a big box of wood, imagine that. And according to our Archimedes's principle, it's going to displace an equal amount of volume of water. That same shape you can say, a box of water and it is going to be pushed up by a buoyant force, which is the same as the weight of this water. Now again, to figure it out, you know, whether this is going to float or sink, I need to know which of these two weights is more. I already know that water for every centimeter cube it weighs one gram. Now I want to know what about the word? How much does it weigh per centimeter cube? So again, I can look up the density of wood and the density of wood turns out to be 0.7 grams, per a centimeter cube. Whew. So every centimeter cube of this box weighs 0.7 grams, every centimeter cube of this box, which has the same size and shape as this, but every centimeter above that weighs one gram. So which one weighs more? Can you video and think about this? I'm pretty sure you can, you can think about this. So it's clearly it's this water weighs more now this time, right? The box of water will be more, because of that, that means our buoyant force this weight will be larger than the weight of the box. And as a result, our box will float. And so right in front of our eyes, we're seeing that weight doesn't decide whether something will float or sink. We are having an extremely heavy object, which is floating and an extremely light object, which is sinking. Why is that happening? Because we're seeing that something which is extremely heavy, can displace even heavier amount of water, which is why it is floating and something which is light is displacing even lighter amount of water because of which, it is sinking. You see the secret to floating is that your objects should be able to displace even heavier amount of water. And when will that happen? That can only happen provided per centimeter cube your object is lighter than water. Otherwise it will sink. So the secret to floating is per centimeter cube objects should be lighter than water. In other words, the density of the object should be smaller than the density of the water. Then it will float. Okay? So with water, if you wanted to figure it out, if something's going to float or not calculate its density and check whether it's lighter than water. So general, the floating condition is that density of the object should be smaller than the density of the fluid. It's not just for water. It can be for any liquid or gas. And by the way, how do we calculate density? Well, the density is usually calculated as mass divided by its volume. See, mass divided by volume uses the density of that object, as long as it's smaller than that of the fluid, it will float. And of course, if you need more clarity on this, where this comes from, we've talked a lot about that density in previous videos. So great to go back and watch videos on density. Anyways, now we can answer our original question. So why is it that if I put a spanner, it will sink? A spanner are made mostly of steel and steel has a density of eight grams per centimeter cube, roughly. Which is way more than that of water, and that's why if you put it in water, it's going to sink, larger density than water. On the other hand, what about a ship? A ship, which is made of the same material. Why doesn't that sink? Even it should be heavier than water per centimeter cube, right? No, it's not because a ship is not completely made of metal, not completely made of steel. Unlike the spanner, a ship has a lot of empty space in it because of that, the metal occupies a much larger volume. Just think about it. I take that metal and I put a lot of empty space in between. I increase its volume. The density starts decreasing, right? And that's the secret for ships. They have a huge volume. And so if you take the mass of this entire ship and you divide by its volume, you will find that its overall density will still be smaller than that of water. That's the secret. Okay. So ships have a density smaller than that of water, and that's why if you put them on water, they will float. So long story short. What did we learn? We saw that if an object needs to float in water or any liquid for that matter, it needs to be able to displace an amount of liquid, which is heavier than the object itself. And that it can only happen provided per centimeter cube, the object is lighter than the liquid. It's for that reason, in order to float the object needs to have a smaller density compared to the fluid. On the other hand, if the object has a larger density than the fluid, like gold in water, it will not be able to displace the amount of water equal into its weight and it will sink. Hey, will happen if the object has the same density as that of the fluid? I'm pretty sure you can figure that one out yourself.