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Current time:0:00Total duration:9:27

Calculating pressure due to weight

Video transcript

say a gorilla is sleeping and the chimpanzee is standing on a very thin ice in the middle of some ocean now because the ice is pretty thin their weights can break the ice right it's possible because of their weights and so the question I'm gonna try to answer in this video is figure out whose weight is more likely to break this ice is it the chimpanzees or the gorillas now before we come to any conclusion let's first look at some data let's say the chimpanzee weighs about 30 kilogram and let's say the gorilla weighs a staggering 150 kilogram and imagine that because the chimpanzee is standing the area of contact with that ice is pretty small let's say that area is about 100 centimeter square that's basically the area of his feet and because this gorilla is sleeping on his side and gorilla is large that surf that area of contact is gonna be pretty big let's say that area is about a meter square and remember a meter is a hundred centimeter so this area is much bigger than this one okay so whose weight is more likely to break that ice now at first we might think hey gorillas definitely weighs so much more than the chimp so it's definitely his weight could break that ice right but remember whether you can break something or not not just depends upon your force but it also depends upon how concentrated that force is for example if you were to push on a paper with your thumb there's a good chance you won't break that you want pierce through that paper right on the other hand if you were to put that same force on that same paper but now you have to push it through a pin I'm pretty sure you can easily punch her that that punch of that paper right pierce through that paper why it's not because you put more force but because over here notice the force was divided over a large area but here the force was concentrated into a tiny area so what also matters is not not just the force but what also matters is the area of Conte and so in other words what matters is the pressure it's the pressure which tells us how concentrated the force is it's the pressure that tells us whether something is going to break or not more pressure more chances of breaking it and how do we calculate pressure we calculate pressure as force divided by area that's what it is how much force is getting divided by the area right and we've talked a lot about this in a previous video called thrust and pressure and so if you need more clarity on you know where this formula comes from great I do go back and watch that video anyways in our example which force are we talking about hey it's the force of force due to their weight isn't it it's that's the one that is pressing on that thin ice which could break that ice isn't it so this force in our example is going to be their weights and so in our example we will calculate that pressure as their weight divided by the area and how do we calculate their weight where is not the same thing as mass weight is a force due to gravity right and how do we calculate force now if you use Newton's second law force equals mass times acceleration and since you are dealing with gravity that acceleration will be G and so we'll calculate weight as mass times G and therefore in our example the pressure will be mg divided by the area and again we have spoken a lot about why weight equals mg in in previous videos called mass and weight and so again if you need more clarity over there feel free to go back and check that and so now that we know how to calculate pressure can you try and calculate who's putting more pressure on the eyes first go ahead give it a shot and just to make the calculation simple let's assume G to be 10 meter per second squared instead of 9.8 okay so pause the video and give this a shot first all right so let's first do pressure of pressure due to the gorilla on the ICG for gorilla it's going to be the mass of that gorilla that is 150 kilograms times G which we are assuming to be 10 10 meters per second square divided by the area of contact the area of contact over here is 1 meter squared okay what's that gonna be well let's write that down here that's going to be 1,500 kilogram meters per second square but kilogram meters per second square is the unit of force the unit of weight and that is also called Newtons right divided by one which is 1500 and we have meter square in the denominator and so that's the pressure due to the gorilla it's 1,500 Newton's per meter square which we can also call Pascal's or Pascal's so 1500 Pascal that's the pressure due to gorillas okay now let's do the pressure due to the chimpanzee and if you had not tried this before again now would be a great time to pause and try it a small thing over here is over here the area is in centimeter square so we need to be a little bit careful before we compare okay let's do it so the pressure due to the chimpanzee on the ice that's as called as PCC for chimpanzee it's going to be the mass of the chimpanzee which is a very tiny number it's just 30 kilogram compared to the gorilla times 10 meters per second square divided by the area and that area is hundred centimeter squared so let's divide this the zeros cancel out and I end up with 3 I get 3 kilogram meter per second square is again Newton because that's the unit of force divided by centimeter square and at first we might say hey look at this is such a small number compared to this this is thousand five hundred and this is just 3 right but we cannot compare directly because the units are not same this is in meter square so let's make the unit's same so let's convert this centimeter to meters how do we do that well we know one meter is 100 centimeters but since I want to convert centimeters to meters I want to know one centimeter equals how many meters right so in this equation he's going to divide by 100 so the right-hand side I'll have just one centimeter and so if the zeros cancel we get one centimeter is equal to one over 100 meter and so all we have to do now is just do the calculation and see which number turns out to be big so let's see we get three Newton's divided by a centimeter is one over 100 let me keep that as fraction itself let's go down a little bit okay so 1 over 100 meter squared that's what a centimeter is so let's carefully solve this simplify this 1 over 100 meter square becomes well I'll get a meter square over here in the numerator over here divided by 100 square is 1 and 4 zeros so 10,000 what is that equal to well whenever I have a fraction in the denominator let's be very careful I like to write this as the product of a reciprocal so I can write as 3 Newton's into reciprocal of this so 10,000 divided by meter square and that gives me look at that number 30,000 30,000 Newton's per meter square whoo that's a big number compared to the gorillas so that is Newton per meter square is Pascal so 30,000 Pascal's that is the pressure so let's put everything in one frame so we can see everything together okay so what we see is that the pressure due to the chimpanzee is super high compared to the head of gorilla I mean look at that why why is chimpanzee weighing so was so low putting so much pressure that's because he's standing and so all his weight is being concentrated into a tiny area and that's why it's putting an enormous pressure on the ice so you see because chimpanzee is putting a larger pressure this means is a bigger chance that the ice can break due to the chimp not due to the gorilla of course I'm assuming that the ice is pretty much uniform over here and here okay but anyways this tells us something right I mean if you ever find yourself stuck on some thin ice or something like that which is better to stand on it or to sleep on it to sleep on it right because when you sleep on it your pressure decreases