Calculating pressure due to weight

- Say a gorilla is sleeping, and a 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 questions we wanna try and answer in this video, is figure out whose weight is more likely to break this ice? Is it the chimpanzee's or the gorilla's? Now, before we come to any conclusion, let's first look at some data. Let's say the chimpanzee weighs about 30 kilograms, 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 centimeters squared. That's basically the area of his feet. And because this gorilla is sleeping on his side, the gorilla is large, that area of contact is gonna be pretty big. Let's say that area is about a meter squared, and remember, a meter is 100 centimeters, so this area is much bigger than this one. Okay, so who's weight is more likely to break that ice? Now, at first, we might think, "Hey, gorilla 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 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 won't pierce through that paper, right? On the other hand, if you were to put that same force on that same paper, but now, you went to push it through a pin, I'm pretty sure you can easily puncture that, puncture 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 just the force, but what also matters is the area of contact. 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, get ready to go back and watch that video. Anyways, in our example, which force are we talking about? Hey, it's the force due to their weight, isn't it? 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? Weight is not that same thing as mass. Weight is a force due to gravity, right? And how do we calculate force? Well, if you use Newton's second law, force equals mass times acceleration, and since you're 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 m g, divided by the area. And again, we have spoken a lot about why weight equals m g and 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 ice first? Good, 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 ice. G for gorilla. It's going to be the mass of the gorilla, and it's 150 kilograms, times g, which, we are assuming, to be ten meters per second, squared, divided by the area of content. The area of contact over here is 1 meter square. Okay, what's that gonna be? Well, let's write it down here. That's going to be 1500 kilogram meters per second squared, but kilograms meter per second is the unit of force, unit of weight, and that is also called Newtons, right? Divided by 1, which is 1500, and we have meter squared in the denominator. And so, that's the pressure due to the gorilla. It's 1500 Newtons per meter square, which we can also call Pascals, or Pascals. So, 1500 Pascal. That's the pressure due to gorilla. Okay, now let's do the pressure due to the chimpanzee. And if you have 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 careful before we compare. Okay, let's do it. So, the pressure due to the chimpanzee on the ice, let's call this "PC", C for chimpanzee, it's going to be the mass of the chimpanzee, which is a very tiny number it's just 30 kilograms compared to a gorilla, times 10 meters per second square, divided by the area and the area is 100 centimeters squared. So, let's divide this. 0's 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. Now the question might say, "Hey, look at this, this is just a small number compared to this." This is 1500, this is just 3, right? But, we cannot compare directly because the units are not same. This is in meter squared. So, let's make the units same. So, that's convert this centimeters to meters. How do we do that? Well, we know 1 meter is 100 centimeters. But since I want to convert centimeters to meters, I want to know 1 centimeter equals how many meters, right? So, in this equation, I'm just gonna divide it by 100. So that right hand side I'll have just 1 centimeter. And so if the 0's cancel, we get 1 centimeter's equal to 1 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 3 Newtons, divide by, a centimeter is 1 over a 100, let me keep that as fraction itself. Let's go down a little bit. Okay, so 1/100 meter squared, that's what a centimeter is. So, let's carefully solve this, simplify this. 1/100 meter squared becomes, allowing you to meet our square over here. In a numerator over here, divided by 100 square is 1 and four 0's. So, 10,000. What is that equal to? Well when ever I have a fraction in the denominator, let's be very careful, I like to right this as the product of reciprocal, so I can write as 3 Newtons into reciprocal of this, so 10,000 divided by meter squared, and that gives me, look at that number, 30,000, 30,000 Newtons per meter square. Oh that's a big number, compared to the gorilla's. So that is Newtons per meter squared, it's Pascal's, so 30,000 Pascals. 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 that of gorilla. I mean look at that. Why, why is chimpanzee weighing 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 how he's putting an enormous pressure on the ice. So, you see, because chimpanzee is putting a larger pressure, this means there's 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? Well, to sleep on it, right? Because when you sleep on it, your pressure decreases.