how is it that an extremely heavy ship made of metal floats on water but a tiny piece of metal like a spanner easily sinks into it why is that some people who know how to swim can easily float but others like me can't to answer questions like these we need to understand the principle of flotation and this principle was discovered by a greek mathematician called archimedes and as a legend goes one day when archimedes well i'm using hulk as i don't have archimedes action figure anyways when he stepped into his bathtub he saw the water spilling out a very common sight but that day by seeing it something clicked in his head he got so excited that he jumped out of the tub and started running through the city shouting eureka eureka which meant i have found it i have found it what did he find whatever he found out is today famously called archimedes principle of flotation and it basically says that the buoyant force acting on any submerged object equals the weight of the displaced fluid so we'll first try and understand what this statement means and then we'll see if we can answer our original question so let's start with the buoyant force what does that mean well you might be actually familiar with this for example whenever you are inside a swimming pool or underwater you might know that you feel a little lighter right and this can be actually experimentally verified so over here i have archimedes who's hanging by a weighing scale and right now the weighing scale is showing 160 grams it's a toy right but we'll see what happens to that weight as i lower him inside water see what happens to it look at that weighing scale as i dip him under water look the reading becomes lower because archimedes is feeling lighter and lighter and this is not just true for water this would be true for any liquid so you submerge a body inside a liquid and that body will feel light but what does that mean or why is this happening well we know that his weight is not really changing right because his mass is the same so the gravitational force acting on him is the same so that's not changing so what could it mean well what could mean is that something must be pushing up on him to balance some of his weight making him feel lighter right so what's pushing on him well it has to be the water or the liquid and we'll talk about why water is pushing up on him a little bit later but turns out this is true not just for liquids this can also happen inside gases my favorite example for this is the helium balloon we know that when you let go of a balloon helium balloon it starts rising up which means again there must be a force acting upwards on it who's pushing it this time it must be the air so this means whenever we have objects submerged inside liquids or gases which are collectively called fluids by the way fluid means anything that can flow liquids or gases they have a natural tendency to push up on things and that force is what we call buoyant force and the word boy means to float i think it has a dutch origin but it's called so because this force is literally what makes them float this is what's pushing them towards the surface trying to make them float but we know not everything floats things can also sink right and that's why we are interested in in knowing what does this buoyant force depend on so that we can predict whether things will float or sink and that's what archimedes principle tells us it tells us what buoyant force depends on it tells us that this buoyant force should equal the weight of the displaced fluid okay what does that mean well again if we come back to our hulk or sorry archimedes we see that right now this much of his muscular body is under water right but before he stepped inside that space was occupied by water right so this means once the archimedes goes under water that much water should move out to make space for his body to come over there so it should move out where does it go well if there's space inside inside the container it'll just go up because water can easily flow right it'll just go up but if there's no space water will just fall out that's what we saw earlier this is what we call the displaced liquid the liquid that moves out or moves up to make space for the submerged body is what we call the displaced liquid and archimedes principle is saying the weight of this displaced liquid equals the buoyant force whatever is the weight of this liquid that equals the buoyant force meaning the more liquid you displace more weight of liquid you displace more is the buoyant force and the same thing is going to happen over here as well before the helium balloon came over here it was occupied by air which i'm showing by green so that we can see but once the helium balloon comes over there that air must have moved somewhere else to make space for the helium balloon now of course the hair and the liquid they will not maintain their shape they will of course they won't mention i'm just showing it this way but anyways the air must have moved right so again this is the displaced air and archimedes principle says whatever is the weight of this displaced air that will be the buoyant force acting on the on the balloon so now let's see if the earlier experiment makes sense you see as our muscular archimedes gets lowered under water more and more liquid gets displaced to make space for his submerged body and as more and more liquid gets displaced more weight of the liquid gets displaced and as a result the buoyant force starts increasing becomes bigger and so he feels lighter and lighter and so the weighing scale reads lower and lower makes sense right now before we explore why archimedes principle is true let's quickly go ahead and see if we can answer our original question so why does a metallic ship float let's concentrate only on the base of this ship so that becomes easier to analyze so if i only look at the base of that ship notice because there is no water inside that ship that means this much amount of water must have been displaced now that is a lot of water if you think about because this ship is pretty big and since it has this is a lot of water it has a lot of weight and therefore from archimedes principle the buoyant force acting on this ship must be very large large enough to to support the weight of that entire ship now let's say if we take the same amount of metal that same amount of metal and we flatten it now you might know this will sink but why because now you see it is only displacing this much amount of water only that much it's no longer displacing the water on top of it because the shape has changed can you see that and since the displaced water is little bit its weight is little bit so the buoyant force acting on that same piece of metal is little and so the whole thing will sink so you can now see the secret behind ships ships have a lot of empty space such that their metal occupies a large volume under water because of which they will displace a lot of water making sure the buoyant force is large enough to support its weight that's the secret on the other hand if you have flat things or things which do not have empty space they will not displace enough water or enough liquid in which case they can easily sink and that's why even if you take a tiny piece of metal which is pretty light it will sink because it's not able to displace enough liquid now let's try and answer why would i panic under water and sink well when you're trying to float in water when you breathe in that's when your lungs expand your body expands of course i've exaggerated over here but as a result the volume of your body underwater increases meaning you displace more water and so the buoyant force on you starts increasing and that can support your weight but when i am in water i would panic and i would start screaming as a result i will let all that air go and so my body shrinks and so i will displace less fluid and so the buoyant force decreases and good chances that i would sink which is why i always wear a life jacket when entering not so shallow water okay finally we might be wondering why is archimedes principle even true what's the logic behind this to answer that we need to first understand where the buoyant force even comes from well for that let's imagine we have our committees completely submerged inside water now because water has pressure it starts pushing on our committees from all the directions i've not shown all the arrow marks it actually has to push from all the directions but what's important is that the pressure increases with depth as you go deeper the pressure increases because water has to carry more weight on top of it and because of this the forces from the bottom becomes larger than the forces from the top and if you need more clarity on why the pressure increases with depth and why it puts forces in all the direction we've talked a lot about that in a previous video called pressure in liquids feel free to check that out anyways because the forces from the bottom is more the these forces don't cancel out if you add them you will get a net force acting upwards and that force itself is what we call the buoyant force so it comes from the pressure of the water but how do we calculate it well here's the inside imagine i took archimedes out and i filled that space with some other material let's say i fill it up with super heavy gold my question is do you think that the buoyant force will change or do you think it'll remain the same think about this for a while well let's think about this the buoyant force comes due to the pressure from the surrounding liquid right now putting some other material does that change the pressure no because the pressure in the liquid only depends upon how deep you go and that depth has not changed everything has remains the same and therefore the pressure remains the same so the forces at every point remains the same which means the buoyant force should remain the same that means regardless of what material i put in this space whether i put heavy gold or even if i put super light styrofoam the buoyant force will not change it does not depend upon what comes in this space does that make sense okay now you may be asking okay fine but how do i calculate that buoyant force well here comes the eureka moment since the buoyant force does not depend on what i put in this space what if i just put the same water now even now the buoyant force should remain the same but now i know that this piece of water is stationary it's not moving that means the forces on it should be balanced in other words the buoyant force should equal the weight of that liquid this piece of liquid only then this piece of liquid will stay stationary because think about it the whole water is actually stationary isn't it but what liquid is that hey when i put archimedes back in water it's that same liquid that gets displaced isn't it that means our buoyant force should equal the weight of the displaced liquid the archimedes principle eureka now it did take me some time to wrap this logic around my head so if you don't get this the first time don't worry ponder upon it for some time and i'm pretty sure eventually you'll get it so what did we learn in this video we saw that whenever objects are immersed in liquids or in gases which are collectively called fluids then they have a natural tendency to push up on those things and we call this force the buoyant force this occurs because in fluids due to gravity the pressure at the bottom is always more than the pressure at the top and as a result when you add up these forces there will always be a net upward force and how do we calculate this buoyant force well you figure out how much fluid gets displaced when you submerge these bodies and then according to the archimedes principle the weight of this displaced fluid will equal the buoyant force acting on them