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## Class 9 Physics (India)

### Course: Class 9 Physics (India) > Unit 3

Lesson 4: Thrust & pressure# Calculating pressure due to weight

Let us calculate pressure due to the weight of a gorilla and monkey. Created by Mahesh Shenoy.

## Want to join the conversation?

- 1m=100cm so how is 1m square greater than 100cm square?(2 votes)
- No it is meter squared and cm squared a cm is a hundredth of a meter right but since it is squared it is 10000th of a meter squared( 100 squared= 10000).(1 vote)

- A hammer exerts a force of 1.5N on each of the two nails A and B. The area of cross section of tip of nail A is 2mm(square) while that of nail B is 6mm(square). Calculate pressure on each nail in pascal.(1 vote)
- Nail A - P = 1.5/2* 0.000001 = 750000 Pa

Nail B - P = 1.5/6 * 0.000001 = 250000 Pa

I hope you get it.(1 vote)

## Video transcript

- 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.