Condition for floating (video) | Gravity | Khan Academy

Video transcript

– [ Instructor ] How do you decide whether something is going to float or sink in water or any liquid for that matter ? immediately I should think, well, that ‘s identical 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 model, ships which are very heavy, made of metallic element can float on water. Yet something like a wrench or a smash, which could be made of the same metallic element, which is very light compared to the embark can easily sink. So it ‘s not their weight unit, 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 does n’t depend on system of weights, but it depends on concentration. 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 permit ‘s say we did n’t know. How would I figure it out ? Well, I have to first think about the forces acting on it, veracious ? 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 aureate. The jurisprudence of coerce that we might be familiar with is its own weight. Because of gravity, it has its own burden that ‘s pushing it down. And is there any other violence acting on it ? Yes. There ‘s a buoyant force out. Water is pushing up on it. We ‘ve seen before that when you put any aim in a fluent or gas, in fluids they have a natural tendency to push up on those things. And we call that as the “ buoyant power ” and a man called Archimedes tells us that the buoyant military unit acting on that object equals the weight unit of the fluid that it displaces. So basically before this gold chain came complete hera, that space was occupied by this water, right. nowadays, when that gold chain comes over there, that water has to move away, making quad for that amber chain, is n’t it ? The water that moves away is what we call the preempt water. It ‘ll actually go up and the stature of the water will increase, but I ‘m equitable, you know, removing it over here so that we can see that displeased water. Okay ? And Archimedes tells us that the buoyant wedge equals the weight of this preempt water. So we can think of it as the weight of this chain of water. so whatever is this consider, that much would be the buoyant force. And if you need more clearness on, you know, why this is true and everything. We ‘ve talked a lot about Archimedes ‘s principle and irrepressibility in former videos. so big 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 think if this was heavier, if the chain of water chain was heavier than this, then this power would be heavier, would be larger. And as a consequence, our amber chain would float. On the other hand, if the chain itself was heavier than the chain of water system, then I would a gold chain would sink. So you see it ‘s all immediately. immediately 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 did n’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 concentration of aureate and water system. What ‘s concentration ? Density is a act which tells us how much something weighs per unit book. here, let ‘s take an exercise 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 concentration. It would say that concentration 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 amber, so imagine a bantam box of one centimeter cube wholly made of gold. That would weigh 19 grams. That ‘s what it says, 19 grams per centimeter cube. now it does n’t have to be a box. It can be any human body you want. vitamin a long as you take one centimeter cube collocate of that amber, it will always weigh 19 grams. That ‘s what this act is telling us. So let me equitable get rid of that. so immediately I know every centimeter cube of this gold range weighs 19 grams. Okay. What about body of water ? good, we can look up the density of water. It turns out to be one gram per centimeter cube. Whew. This means every centimeter block of this water weighs one gram. Every centimeter cube of this gold weighs 19 grams. sol can you tell then which one is heavier ? I ‘m reasonably certain you can. It ‘s the gold. Because gold is heavier it ‘s weight will be larger. And as a result, our amber chain is going to sink. All right, let ‘s take another exercise. Imagine I took a big box of wood and this is on a empty box. This is completely filled with wood let ‘s think. That ‘s a solid box of wood, very heavy. immediately again, I want to figure out whether this is going to float or sink. What to do ? We ‘ll do the same matter. Well, let ‘s work out the forces. We know it ‘s being pushed down by its own weight unit. And this time, this is much heavier than the gold chain because I ‘m taking a big box of wood, think 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. immediately 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 ? sol again, I can look up the density of wood and the concentration of forest 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 block 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 reasonably certain you can, you can think about this. So it ‘s clearly it ‘s this water system weighs more now this time, mighty ? The box of water will be more, because of that, that means our buoyant force this slant will be larger than the weight of the box. And as a resultant role, our box will float. And so right in front of our eyes, we ‘re seeing that weight does n’t decide whether something will float or sink. We are having an highly heavy aim, which is floating and an extremely light object, which is sinking. Why is that happening ? Because we ‘re seeing that something which is highly heavy, can displace even heavier total of water, which is why it is floating and something which is light is displacing evening lighter amount of water because of which, it is sinking. You see the mysterious to floating is that your objects should be able to displace evening heavier sum 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 urine. In other words, the density of the object should be smaller than the concentration of the water. then it will float. Okay ? then 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 good for water. It can be for any liquid or gas. And by the means, how do we calculate density ? Well, the density is normally calculated as mass divided by its book. See, mass divided by volume uses the concentration of that object, a hanker as it ‘s smaller than that of the fluent, it will float. And of course, if you need more clearness on this, where this comes from, we ‘ve talked a lot about that concentration in previous videos. then great to go spinal column and watch videos on concentration. Anyways, now we can answer our original question. So why is it that if I put a wrench, it will sink ? A wrench are made by and large of steel and steel has a density of eight grams per centimeter cube, roughly. Which is manner more than that of water, and that ‘s why if you put it in body of water, it ‘s going to sink, larger density than water. On the early hand, what about a ship ? A embark, which is made of the same material. Why does n’t that sink ? even it should be heavier than water per centimeter block, right ? No, it ‘s not because a ship is not wholly made of metallic element, not wholly made of steel. Unlike the wrench, a ship has a distribute of empty space in it because of that, the metallic occupies a much larger bulk. equitable think about it. I take that metallic and I put a fortune of empty space in between. I increase its bulk. The density starts decreasing, properly ? And that ‘s the clandestine for ships. They have a huge volume. And therefore if you take the bulk of this integral ship and you divide by its volume, you will find that its overall density will distillery be smaller than that of water. That ‘s the secret. Okay. so ships have a concentration smaller than that of water, and that ‘s why if you put them on water, they will float. so long report short. What did we learn ? We saw that if an object needs to float in water or any fluid for that count, it needs to be able to displace an sum of fluid, 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 ordain to float the object needs to have a smaller concentration compared to the fluent. On the other hand, if the object has a larger concentration than the fluid, like gold in water, it will not be able to displace the come of water adequate into its weight and it will sink. Hey, will happen if the object has the same concentration as that of the fluid ? I ‘m reasonably certain you can figure that one out yourself.

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