 Now let us talk about the kind of deformation that we will see or kind of stress that we are going to see. So you can probably draw, let's take one by one, the first one is a longitudinal stress. Now longitudinal stress is about the deformation of a length of the object, okay. Now if I am focusing on deformation of the length only, then why will I draw the entire cube? I will assume a wire of the material, isn't it? So suppose this is a wire, I am taking a wire like this, it may be made up of some matter, maybe copper or steel and I am applying force, let's say this is F, this is F, all right? Length is F. So net force is 0, okay, I am ignoring the mass of the wire. So if net force is 0, the stress is called longitudinal stress, in this case when it is along the length, we are calling it longitudinal stress. Then it is denoted by sigma, okay, so sigma is given as what, force per unit area, okay? And if the area of cross section is A or the radius is R, then it will be F divided by pi R square, R is the radius of the wire, right? So this is my stress, this is the cause of the deformation, all right? Cause cannot be force because if I use a thicker wire, same length, thicker wire if I take, if I apply same amount of force, okay? So same cause should give me the same effect, that is why I am calling it a cause, all right? So if I am calling force as a cause, that's not proper because the thinner wire will give more deformation for same force, so force is not the cause. But if I divide force with the cross section area, then I will realize that force per unit area is lesser for this case, that is why the effect will be lesser. That is why I am defining cause as force per unit area, which is F divided by pi R square, all right? Now let's talk about deformation, all right? Now God hasn't come and told us that deformation value should be this much and this is the formula for deformation, we have to create a formula for deformation, but of course deformation is happening. So we will observe what is happening during deformation and then try to quantify or put a value against a deformation, okay? So suppose you apply this much stress and the change in length happens, change in length is let's say delta L, so now length is L plus delta L, okay? And you have applied F force, same length got stretched. So is deformation delta L? Yeah. Yeah. Roshi, is deformation should be quantified as delta L? Yeah, yeah. But it also depends on the original, original what? Length, right? Correct. So if I am having same stress or same cause, I should get the same effect because it should not depend on anything else. But what Dhruv is saying that if I take delta L as my deformation, then if I take double the length of the wire, if I take double the length of wire and if I have same amount of cause, which is force per unit area, then the deformation will be 2 times delta L, okay? 2L plus 2 times, why 2 times delta L? Because you can divide it into LL length. Yeah, that increase by delta L. Delta L will increase from upper side, delta L from lower side. Yeah. Okay. Okay. Not proper. So deformation, if I measure change in length per unit length, then it will be proper. Oh, okay. Anise. Okay. And this deformation, the quantified value is also called strain. Okay. This is referred as epsilon. Okay. Okay. Anise. Okay. Anise. Anise. And there was this scientist whose name was Hooke. Yeah. Yes, gave us Hooke's law. Yeah. He told us that for small deformation, what is deformation? It is not delta L and it is not L. It is delta L by L, okay? For small deformations, sigma is directly proportional to epsilon. Or the stress is proportional to strain. That is why Hooke's have told us. All right. And you can find out the proportionality constant by doing some experiments. So sigma will be equal to some constant k times, let's say, if a times epsilon Fine. This constant k is what? Proportionality. Modulus. There is a name to it. This is called modulus of elasticity. Oh, okay. And in case of the longitudinal stress, it is also referred as Young's modulus. Oh, this is for longitudinal. Now Hooke's law is valid for all kinds of stress. But if it is longitudinal, then this constant is called Young's modulus and k is referred as y. What do you think the Young's modulus should depend on? Or modulus of elasticity should depend on? The material. It depends only on material, nothing else. The modulus of elasticity depends only on the material or the property of material. So basically, modulus of elasticity is one of the mechanical properties of solids. Okay. So for steel, modulus of elasticity will be different. For copper, it will be different. Okay. But if you take a steel, it doesn't matter what shape and size of steel you take. Modulus of elasticity will remain same. Okay. Drew was saying something? No. All right. So since stress is proportional to strain for a very small deformation, let us try to see in case of longitudinal stress, at least how a typical solid will behave. Okay. So I'm going to basically plot a graph between stress and strain. All right. So if stress is proportional to strain, what kind of graph I should get? Straight line. A straight line passing through a region? Yeah. Yeah. Let's see what is the actual observation. The heading is stress-strain curve. Trace has joined a lot of hobby classes, is it? Keeps on going for violin concert and something. Yeah, he does violin. Only violin or something else. I'm not sure actually. I just know that he plays the violin. Artist. Stress-strain curve. So for a small strain, it is directly proportional. So you get a straight line. Okay. So this is stress. I'm going to say this is sigma. And this is strain. Let's say epsilon. Okay. It goes straight like this. But after some time, it no longer remains linear. It changes little bit. It goes like this. Then it goes like that. And like this. And after that, it breaks. And you can see that at the end, stress decreases. But strain is increasing. Yeah. Have you ever stretched membrane or any polythene from your hand? When you stretch it, you'll feel the resistance is there. But when it is about to break, the resistance is suddenly gone. Yeah. Okay. So this is what is a typical behavior of any solid as well. Okay. And this, I'm not saying exactly this kind of graph you'll get for each and every solid. But most of the solid will show a typical graph like this. Okay. So it makes sense to name the notable point. At that point, the x point, the solid breaks, right? Yes. It is called fracture point. Okay. Breaks. So no point drawing beyond this. So basically, the solid can't get deformed more than this value of epsilon. Yeah. Are you getting it? Yeah. More than this kind of epsilon is not in the graph itself. It is not possible. If you break apart. Okay. Okay. Now, see what will happen. The sigma will be proportional to epsilon till it is a straight line. Yeah. Yeah. So this point where it ceases to be a straight line is called proportional limit. Right down. Now, you know what happens if you release, I mean, you have applied this much stress. The object came here. It got deformed by this value. And if you release it, it will go back. Yeah. So zero stress, zero strain. So nothing will happen. Okay. But after you go from the proportional limit, even if sigma is not proportional to epsilon till this point also if you release, it will go back. It will go back to this point and no deformation or no permanent deformation happens. Okay. This is, this point is called yield point. But after this, if you increase the stress or strain increases, then it will not be able to retain its original shape and size. It will get permanently deformed. Yeah. So suppose you go to this point C and if you release it, it may come to here. If you release it, sigma will become zero. You're not applying any sigma, but even if sigma is not there, even if you're not applying any stress, epsilon is not zero. What it does, it means it means that it has permanent strain. Even if sigma is zero, strain is present. Are you getting it? Yeah. And this dotted line doesn't mean that it has followed this path. Nobody knows what is the path because when you release from here, suddenly it reaches here. And at this point, it is not the path. Nobody knows what is the path. Okay. And there will be a point which will correspond to maximum resistance. By the way, this yield point is also called elastic limit. Elastic limit is much better term because it correlates. This point which represents the maximum stress. What does this call? Do you remember what does this point they call? This represents something called strength. Yeah, I don't remember. This is tensile strength of the material. This represents tensile strength. This is the maximum stress it can handle. Maximum stress it can take. Yeah. There's a difference. Okay. This is the tensile strength. And this point E is a fracture point. Fine. So this is a typical stress strain curve. And until and unless specified in this chapter, we are going to assume that we are dealing a situation between O and A straight line. Okay. Okay. Okay. So this is a typical graph of a solid, but doesn't mean that all the matter on the earth behaves like this only. Okay. Okay. There is an elastic tissue on the blood vessel in the heart. It is A-O-R-T-A-O. How does it? Aota. Aota. Aota. So you see, right? Whenever heart pumps the blood, Aota will expand and contract. So it is getting deformed and then regaining its original shape. It is continuously handling. So it is one of the things which doesn't get permanently deformed. Right? So the kind of graph for the Aota is like this. This is the kind of graph between stress and strain. Okay. Of course, Aota will not, you will not be able to strain Aota beyond a certain point. It doesn't matter what kind of, whatever kind of stress you apply. Okay. So this will keep on happening. It will get deformed. Then again, come back. Okay. For a million times in a day, this will happen. It will always come back. Yeah. Of course. The heart will not get deformed. Yeah. If it gets deformed, it's gone. All right. So this is the, this is the stress strain curve. And let's talk a little bit mathematical now. So basically, in case of longitudinal stress is basically whatever force you apply, assuming that object is at rest, force per unit area is Young's modulus times change in length divided by the original length. Isn't it? Yes. So this will give you Young's modulus to be equal to force per unit area divided by delta L by L. So you can say that is FL by A delta L. Can you tell me what is the unit of Young's modulus? It would just be Newton per meter square. It is Newton per meter square only. Yeah. Okay. So, and you can say Pascal as well. Yeah. But usually we say Pascal for gases or liquid. We say Newton per meter square. That is better. Right. And because the strain is dimensionless. Yeah. And the kind of value for Young's modulus that we're dealing with is very high. So now if Young's modulus is less, it represents stronger material or otherwise. To represent weaker. The Young's modulus is high. What does it mean? The Young's modulus is less. Then I'm saying if Young's modulus is high, what does it mean? Young's modulus is very high. Then, oh that means that it's stronger, right? Why? Well, you know, because that means that it can take more restoring, this more, the magnitude of restoring force is greater. Right. For a very small deformation or a very small value of delta L by L, even if delta L by L is less, but if Young's modulus is high, the resistance against the deformation is very high because Young's modulus into a small quantity becomes a large quantity. Yeah. The Young's modulus is high, the material is stronger. Yeah. Okay. Now tell me, rubber band is more elastic or the steel is more elastic? Rubber band. Steel. It's more elastic. Rubber band will be more elastic and how you define the elasticity. You know, before we, I mean, I perfectly understand that from where you're coming from. Okay. But then first, if we are talking about technicalities of it, we need to first define what is the elasticity or what does it represent? Okay. So Dhruv, can you tell us what does it mean elasticity means what? The amount of body was deformed, I guess, when a particular amount of force is applied. So if a body get deformed very high, you're saying it is more elastic? Yeah. A brittle object can break. It is like infinite deformation. It breaks. Yeah. Brittle object more elastic. So that is not a definition of elasticity. Yeah. There can be two ways in which you can define elasticity. One way will be the amount of deformation that can happen so that it comes back to its original shape. So whichever object takes greater deformation to reach the initial state, okay, without permanent deformation will be more elastic. Okay. That's one way of defining. Another way of defining is whichever object can take more amount of force without permanently getting deformed. Are you getting two different ways of defining? The greater the deformation can take before reaching the initial state means that it's more elastic, right? No. Elasticity has to do with the other one where it has to do with the large, what is the largest amount of force which you can apply in an object so that it will come back and retain its original shape. Okay. Yeah. Good. Of course it will be steel. Yeah. Yeah. Okay. But on our head elasticity means that what is the largest deformation that can happen so that it will come back to its original shape. But that is not the way it is defined elasticity in physics. Okay. So it is basically, it has to do with how you define it. It is nothing to do with common sense or anything like that. So for the first time probably you are encountering a definition like this. So typically the value of Young's modulus is of the order of 10 raised to power 5 Newton per meter square. Okay. It's very high and of the order of 10 raised to power 5. Not sorry, not 10 raised to power 5. It is 10 raised to power 9. Sorry about that. Very high. Yeah.