 Okay, so let us start mechanical properties of solids I will see what is going on in your school in my school actually they're doing a kinetic property of gases Whatever kinetic kinetic theory of yeah Only can be theory. Yeah, right now they're doing that Yeah, even for us, they're doing the same thing all the laws and the and all of that Okay, that that is what I I am doing in nps as well, but then chapter was remaining So if we don't do it, it'll keep on Getting delayed Let us complete this up Okay So after this we will probably start kinetic theory, right? Yeah Okay, so this particular chapter focuses on mechanical properties of solid So we have already done Two chapters related to properties of matter. Can you tell me what are those? We're doing later to liquid. I mean fluid, right? So we have done mechanical properties of fluid. Yeah chapter any other chapter related to properties we have done We've done surface tension and all of that, but yeah, we did um thermal properties of matter Properties of matter we have done mechanical properties of liquid and thermal properties of all the matters whether it is gas liquid or solid, okay now thermal properties are very similar when it comes to a liquid or gas or any solid but when it comes to mechanical properties Mechanical properties are different between solid and liquid or gas, okay And also the kind of prop mechanical properties that you are interested in solid You are not interested in similar kind of properties of a liquid for example In liquid I am more interested in pressure And the velocity of the flow Okay, that is a kind of mechanical property I am focusing on But when it comes to solid solid doesn't flow And solid will not move, uh, you know immediately because of the pressure difference. It will not start flowing So those properties are useless to study for the solid now We are Focusing on strength of solid when it comes to mechanical properties solid Why we are focusing on strength of solid because solid is the material that we are using to build the machines to build the Bikes cars planes uh buildings Everything is matter of solids, right and when it comes to building any such structure We need to focus on the strength of that material fine So same kind of The property will not study for gas or liquid because I don't care about strength of liquid It doesn't mean anything actually All right So that is the reason why two different chapters in this chapter. We are focusing on strength of solid. Okay Yeah, and if you take civil engineering Then you're going to study the same chapter for the next two three years there. There are a lot of Small small details that are there for example, you know that If I have to make a metro station Then I need to first of all study How is the soil there if the soil is loose and it is not able to hold the structure it It's not strong. I'll not be able to build pillars on top of that soil Okay, and similarly I'll not be able to build a multi-story building But if soil holds good, then I can think of building a big structure on top of it Otherwise the soil only will not support then everything will fall apart So that is a reason why you know, uh suppose few years back on some Let's say on some surface there was lake Now lake is disappeared, but uh that lake is encroached And now people are building structures on that Space where lake was there, but it is not a good idea because the soil there may not support You know very strongly All right, so and then we need to also understand how the solids will behave when It expands Will it crack? Or how much it will crack how much load it can take? And different kinds of loads are also there. Okay, for example, if I take a brick and if I Try to apply a lot of four. I mean if I put a lot of force from above the brick Suppose this is a brick and if I push from this side and that side it'll take a lot of load but if If I same brick if I fix this point and if I push from this side Then this brick will break Yeah, yeah, there are Lot of finer details when it comes to mechanical properties of solids and also you might be seeing in earlier days People used to have Beams on the terrace also So they will have beam inside the room which is placed on the roof So this beam will definitely bend like this. So how much it will bend What will happen if it bends whether it will crack or not if it cracks Then will it completely fail? So all those kind of properties are of great importance Whenever we build any structure Okay, so that is why this chapter is there just to introduce to you that such things exist And things are not in great detail. That is why a very small chapter is there in front of you Okay now Coming back to the strength of solid As we have mentioned that The strength of solid will be different with respect to How you are trying to apply the force or whatever makes it break So we need to categorize Different kind of forces that can be applied Okay, how it is applied and things like that Fine. Now before we start this chapter, let us take one example. Suppose there is a pencil heel You know, right, what is pencil heel? Yeah, yeah This is the pencil heel and this is elephant's leg Okay, so Both of them are standing this lady is standing on a wooden plank On just pencil heel And the elephant is also standing on a similar wooden plank Okay on one leg the elephant's mass is around 6000 kg Okay, the mass of this lady could be just 60 kg Where do you think the more chances that the solid will have a dent on it permanent dent With the heels right heels because it's concentrated at one. Yeah pressure is more pressure So it is not about force that breaks the solid Okay force doesn't cause a material to break It is a Force per unit area that Breaks a solid All right So force per unit area is more important than Force itself You may be applying huge amount of force, but if that force is spread across a greater area force per unit area will be lesser Yeah, yeah Then that will not break Material what I'm trying to say is that there is a fixed value of force per unit area for every solid to break So it is like force per unit area if it is 100 then this solid will break So if I take just one unit of area and if I have 100 unit of force then force per unit area is 100 Okay, but if I take 1000 Newton of force and 1000 unit of area also then force per unit area is one only Yeah, yeah Even if force is more the material will not break The material breaks because of force per unit area that you must understand Yes Now if that is understood we need to also understand the way we are applying force also The way this force per unit area is applied that also plays a very very important Role in terms of whether a solid will break or not For example, when when an earthquake comes Okay, it just shakes the building a little bit And the building collapses Okay, and uh Similarly, if you apply a similar kind of force per unit area from top and bottom to the building the building nothing happens to the building right and when you take a piece of let's say Paper try to stretch it from both sides The paper will not break Okay, the moment you use a scissor It it immediately breaks with a small amount of force or you can just tear it apart from the top It it you know it loses its integrity it goes off Okay, so that that's why the way you apply force per unit area Also matters Okay, so now let us understand in how many ways can you apply this force per unit area? Okay So suppose you have a piece of solid Let's say I draw a cube over here in how many ways Can you deform the cube forget about breaking it breaking is the outcome when you deform it too much it will break So in what ways can you deform it? By Pushing it I mean or keeping one one end of it like the base stationery and simply pushing the pushing one side of it Okay, so you could either increase its length you can stretch it both sides Yeah Okay, when I'm saying increasing its length it could be width or height as well All are same Yeah, that is one way you can stretch it from both the sides another way is you can Push it from here keeping the base fixed So there's an entire solid will get distorted Okay, like this it will get distorted It'll move the side will move like this getting it. Yeah, I got it And another way is that you compress it from all sides the volume will decrease For example, you take a sponge and compress it from all sides. It'll get compressed Okay, so there are these are the three ways three typical ways in which you can deform a solid Now, of course, it may not be that only one mode of deformation might be applied on a solid There can be let's say two or three kinds of deformation happening together Okay, but then when we are studying we should study one by one in order to understand what is going on on that kind of deformation And once we know how multiple deformation Cause and effect it is then we can combine and analyze it together when they are All right, so I'm going to introduce few concepts before we start Discussing the various kinds of deformation One is stress Other is strain Tell me what is stress and what is what is stress tell me It's the Oh, it's the uh, it's basically the restoring force acting for unit area What do you mean? For example, if you have a rubber band, I mean Something like that and then you stretch it Then it will it will be a it'll try to pose that deformation and there'll be a force acting In the direction opposite to what you stressed and that acting for you know And that that force is basically the discerning force is basically the stress felt by the Rubber band when you stress when you stretch it and that acting for Unit area of the rubber band is The stress what you are applying what it is. Isn't that is the stress what you apply for unit area? Yeah, I mean, I think, uh, yeah, it should be a correct Isn't that also equal to the restoring force when, uh But then why it is defined as restoring force? Is is there a situation when both can be different? Uh, you always think yeah, yeah, it can be that is usually when it, uh, I mean Yeah, when it can't When you're from the force you apply on it is too much too high for that to be enough restoring force Okay, see, uh, thus You can take a common this thing sense things that stress is with respect to how much stress you take for example, if a simple, uh Thing is there one person may think that is very stressful The other person will think that it is not so stressful So it totally depends on how you react to a particular situation Okay, similarly, you know, you can apply let's say 1 lakh Newton to uh, just a rubber band Okay, but rubber band itself is not capable to resist more than 100 Newton Okay, then it will not React to 1 lakh Newton itself. Okay, you understand what I'm trying to say. Okay, yeah It will it can't take 1 lakh Newton. You are giving 1 leg Newton, but it is not taking it It can only resist up to 100 Newton Okay, so if you apply it till 100 Newton then whatever you are applying will be equal to the stress After that it will remain 100 only or it will break Okay, okay. Yeah, okay, so that is the difference and That makes More sense when you compare the strength of two solids Suppose you take steel and rubber if it is about force applied You can apply infinite force to the rubber infinite force to the steel So both have the same strength. Is it no the strength has to do with how much resistance you are creating against What force it? Right, so steel will resist more So yeah, I still can take more resistance more stress. All right So stress is the amount of restoring force An object will have So the resistance against the force applied, right? Yeah resistance force permanent area Okay Yeah, yeah, and most of the time it is whatever you're applying permanent area So both are same only most of the time Force permanent area now. Tell me one thing Uh, you have a piece of solid Like this if you apply force F Okay, and this is area a So stress is how much? F by F by it is free to move on a frictionless table Oh, then there's no stress. Oh, yeah Why no stress? Is there a net force on it or not? Yeah, yeah, yeah There is net force so force point area is not No stress that is the difference. Okay. If we calculate force permanent area as what force you are applying Pernate area, then you will be confused. Okay. It is about resistance All right, how to calculate the resistance Resistance by whom resistance by the block only? Yeah, so what you do is that you cut this block Imagine this block is cut Okay, if you cut this block Then whatever is a force over here At this point is the resistance and this is your force Okay Adding is all right, but if I apply Equal and opposite force. Let's say if I apply F only over here, then what will be the acceleration No, zero will be zero net force is zero Then if addition is zero this F should be equal to that F only Wherever you cut Yeah, yeah, are you getting it? So if it is the object is at rest Whatever you're applying will be equal to the resistance force only anywhere you cut along the block Yeah, I got the net force should be zero It is at rest fine Yeah, and uh this force you can apply or you can just tie this end Uh on a wall. Oh, sorry, you can uh Let's say clamp this end on the wall so that it doesn't move then wall will apply the force Different mechanism now. What is trained? It's the Change in length for unit length That is mathematical What is conceptually? What is train? It's okay. I don't have to put it The amount is uh solid is deformed Oh Is it the amount uh the solid is deformed No, it is basically It is you know the strain has to do it Basically, how much deformation has happened And that's what I'm trying to say Yeah, so it's the amount of deformation, right? You are giving stress to the solid All right Because of stress, what will happen the solid will get deformed. Yeah The stress is cause And strain is the effect Oh It is like when you say I'm applying force Acceleration is the effect of the force Similarly when you apply stress strain is the effect of the stress No Okay, it is the effect of the stress and we are trying to quantify The deformation of the solid Now of course that solid will get deformed in a different different manner So I cannot give a single formula for strain It may be that length is getting deformed It may be that volume is getting deformed or it may be that the the shape of the object is getting deformed Fine. So different kind of deformation has different kind of definition Okay. Yeah