 going forward let us not write down equations only free by diagram we will talk about. All you have to do is draw the free by diagram. This vehicle is accelerating with acceleration capital A. Now let us keep the vehicle fixed. This is fixed. You have to find acceleration of m1 and m2. Coefficient of friction is over here is mu. That is the pulley right? Yeah that is the pulley. Just draw the free by diagram. Done. With a free body diagram you should draw only one body at a time. Not multiple bodies together. Done. Okay for m1 this is tension T. There will be a normal reaction and one there will be another force m1 g anything else? Friction. Friction. If you assume that it is sliding accelerating then the friction will be mu times n. You are assuming that it is sliding. It may not even move. These two will remain like this. They do not move. This case is when acceleration is not equal to 0. What about the other mass m2? It will have m2 g. m2 g but what? Tension. Then what else? The surface is rough. Yes. How much? Tension should be mu times n. What is n? m2 should be here right? If it is there m2 will be like that. What is the magnitude of m2? But if m2 is there there will be net force on m2 horizontally. It should create an acceleration horizontally. But there is no acceleration horizontally. So m2 is 0. N2 is 0. Friction is also 0. N2 is 0. It is like this. A chalk. If it touches this away it will leave it. There will not be any friction. But if you take a chalk like this and move your hand then the chalk will not slide. Why? Because now you have chalk. There is a normalization on the chalk from the hand which is creating acceleration of the chalk. And then there is a friction and that is the chalk is not going down. It will fall down. There is no friction actually. So there is no friction over here. So what are the equations here? If you look at m2 T minus m2 g is equal to 0. 0? No. It is not 0. If this acceleration is 8. What will be its acceleration? 8. 8 downwards right. That is the constant relation. Both their accelerations will be same. Both of their accelerations are same. That comes because we are assuming the string length is fixed. The acceleration has to be same. Isolation has to be same. Physics has nothing to do with it. It is a mathematics. If this goes 1 centimeter this way then it has to go down by 1 centimeter. At the same time. So displacement, velocity, expression everything is same. So m2 g minus T is equal to 0. Wait. Are you able to understand? Alright. Any doubts? You know these two masses are same because string length is same. So for m2 the equation is what? m2 g minus T is equal to m2 a. For m1 what is the relation? For m1 what is the equation? T minus mu n1. It is equal to m2 a. m1 a. So m1 a is 0. Okay? Yeah. And one more direction in which you can write the force equation for m1. That is m1 minus m1 g will be equal to 0. These are equations. Okay? That m2 a is equal to m1 a. Fine? Any doubts? No doubts. No doubts, right? Okay, let's go to the next one. Wait. So, but then after this, like that's it? Yeah, that's it. Sir, we don't have to equate. We don't need to equate the a. Yeah, that's it. m2 a is equal to m1 a. So mt is equal to... a a are equated, no? a and a both are same. Yeah, sir. No, but it's the same, they're following the same speed. No, you are talking something else. You say speed, then talk about acceleration. You say acceleration is same, then you say m1 a is equal to m2 a. What are you saying? Sir, the constant, like the acceleration of the road is constant. That's what I've written now. m1's acceleration is a and m2 is also a. I am not writing m1 a1 and m2 a2. Whereas using same a, it means they both have same acceleration. Understood? This is theta, okay? You have this mass m, like this, okay? This is having friction mu. The wedge has mass capital M. Both can move. You have to draw a free-body diagram. Just draw the free-body diagram. If pulley is fixed, you should not remove the pulley. Where pulley is fixed on the wedge? Don't remove. When you draw a free-body diagram of mass capital M, pulley is a part of capital M, okay? You can cut these strings when you draw a free-body diagram, but don't remove the pulley. It's a part of capital M, a part of capital M. Like on the wedge, which you don't know. Should I solve? Which one is the easier one to draw? But small m, is the direction of acceleration known for small m? No. So we'll have to calculate that. You don't know the direction of small m at movement. It moves along the wedge, also moves like that. And direction is fixed? Horizontal? Understood what I'm trying. Can you repeat what I said? Okay. I think this... So what acceleration does the wedge remove? I just have to find out. Okay, this is, let's say small m, okay? Small m, what are the forces acting on it? Mg. Mg. Straight forward. Then normal reaction. I just forget about friction. There is no friction unless it's a little complicated. Friction is not there. Where is this normal reaction? What else? Tensions. Tensions. That's it. Anything else? No. That's it? Okay. Only this much? The direction of acceleration is where? But you can split the acceleration into two parts. One with the wedge. The wedge is going along the wedge. Let's say small a and with the wedge it is capital a. Sir, I didn't get how you can say to the wedge is that small m. Wait, have you understood small m? Small a is the wedge. How much it is accelerating? Add acceleration of the wedge on it. We'll give you total acceleration. So this small m accelerates with respect to wedge and also with the wedge. So with respect to wedge it slides down the wedge. Yes or no? Yes. If you are standing on the wedge you will feel as if it is going down the wedge. It goes down the wedge also with the wedge. Yes or no? Yes. Because wedge is sliding. Which way wedge can slide? There is no other way wedge can go. Yes. Fine, so that is what we have done. It's relative acceleration and then acceleration of the wedge is added on it. Fine, this is actually J advanced level question. I expect you to solve this. Don't worry if you are not able to. I am not expecting any of the questions that I have taken today to solve the first go by you. Because today's class I am introducing to you that how to apply this thing. I am making you learn. There is not like a test where you start judging yourself that you are not getting anything. If you are not getting a lot of things it means that you have a lot of things to learn. Fine? You should feel good that you are learning many things than getting frustrated that you are not. If you are not understanding what I am saying then you should feel bad about it. I mean are you able to understand what I have just said? Everything is a wedge's thing. What are the forces on the wedge? There will be capital M G downwards. What else? Normal. There will be normal. There will be tension. This way and tension like this. What else? There will be normalization from here also. Equal and opposite force, right? This is N1. This is also N1. Total acceleration. And acceleration of the wedge is like this. Why don't the wedge move like this? Because of this normal reaction. There will be comfort of this normal reaction like this. It will push the wedge. How is that N1 like that? They are not meaning. What? Because N1 on small m is like this. So small m will apply N1 in opposite direction. What are the opposite reactions? Sir, I didn't get how there will be tension in that direction. There will be tension like this and this. So why is there tension in the horizontal direction? Because it doesn't along the string. Which one you are saying? This one? Yeah. So there is a string. The string will pull this point. But... Doesn't that create like a push force on the... On this point? Yeah. No, this force is on that. This force is on this. Oh. Wait, wait. So on this... This is on this point. To find out what is the force. This point is getting pulled and what is the force. That point is getting pulled. That is tension only. Yeah. But in string wasn't it a pull force? It is a pull, no? See, is pulling it or not? This point is getting pulled or not? Yes. And that point is getting pulled? Wall, whatever there is pulling and here the mass. Wait, wait. I think you are a little bit confused with the tension. This is the string. Throughout this is the string. From here to here I have drawn the string. Getting it? Alright. Now that wall with the force of T. Okay, this is the force. Pulls the wall. Fine. Pulls it? Yes. Okay. The wall will equal in opposite reaction to the string with T. Equal in opposite reaction. Okay. Now you cut anywhere. Suppose you cut is getting pulled this way by T. And this point is getting pulled by that point like this T. Anywhere you cut. Anywhere you cut there will be equal in opposite reaction forces. This point is getting pulled like this. That point is getting pulled like that. So tension is everywhere you can draw like this. Both the direction. This direction represents the lower part of it. How it is pulling and that is how the upper part is pulling the lower part. Yes. Sir, I didn't get why as the two end points. Like in the middle it's fine that the opposite. Okay. Let's do one thing. Let's forget about all these difficult ones. No, no. I think there are some basic doubts. We will not get into all these questions right now. Tension is tension, right? Tension is the problem. Tension is going to give tension. Okay. So suppose string and a mass is attached to it. Like this. Okay. I am saying tension forces T throughout the string. So on tension is T. Up with tension T. Okay. Block will pull the string down with tension T. Equal and opposite force. The string will pull the roof down with tension T. This will get pulled by the roof by a tension of T. And if you cut in between by a tension of T. That point is getting pulled by the upper point by a tension of T. Now suppose you have this scenario. All of you focus here. Suppose you have this. Suppose you have one block like this and then another block. This is M1 and this is M2. Can you draw a freeway diagram for both the masses quickly? Only for tension and gravity. Okay. Let's see. For M2, let's draw first. M2. M2G. Yeah. Then what? T on top. Tm. Let's say this is T2. T2. M1G down. M1G down. And T2 down. And T2 down. And also T1. T1 up first. This tension and that tension will be different. T1 up first. Two different strings. Okay. With all force this string is pulling the roof down. T1 system. That will simplify. This is fixed. The wedge is fixed. Actually wedge is not fixed but I am making you fixed. Making this fixed for you to focus on other things. There is full via force of F. This is M1. M2. Okay. This thing is going this side with excitation A. Actually we don't need to write any equations. Just write down the free bird area. Is pulley part of the wedge? Yes. Part of the wedge. Both the pulleys are part of the wedge. This side you have pulley part of the wedge. You wanted to pull it? So this time. Okay. Focus here. Yes sir. All of you done? Yes sir. Okay. So which one is the easiest one to draw? This one. This one. This one. Right. So if we draw it quickly. Force. Let's say N1. This is? Mg. Leftist tension. This is tension. That's it? No. N2 N1. N2 N1. Any doubt here? No. N2 N2. There is tension P. Mg. Mg. N2. N2. N2. U1 N2. That's it? Yeah. Yeah. What about the wedge? Fixed wedge. Fixed wedge. Fixed. Yeah sir. Only gravity. Only gravity. And not gravity. No more tension. No more tension. Tension also right? This is T. Yes sir. Tension also right? This is T. There will be this. There will be this. And there will be horizontal force also. It is fixed. Horizontal force. Something is fixed. It can't apply. Horizontal force is right? No. It has to balance that thing. Exactly. So there is a horizontal force also. I thought the two keys will balance it. No. It is implied. This is implied. But what we do is... Okay. It has a final T back to it. And then there is also... This is the normal of between these two. There is a normal between this and that. Okay. So horizontal force will be opposite of whatever is a net horizontal force that way. It is fixed. No. If there is no horizontal force to balance out the net horizontal force that way, you start moving. Yes sir. But that horizontal force will be like that. Okay. It is not friction. Not friction. Okay. It is like this. If I push the wall, the wall is not moving. So there is a force opposing my force. Which is not friction. Okay. My purpose for today was just to draw the favor diagram. When we do this chapter. I am just giving you a hint. Those who are giving hint. I am not going to solve it. The hint is net force horizontal direction should be zero. That's all. Okay. If that hint is sufficient, you can solve it. I mean that should be sufficient. It's just not going to be fun. Vertical also zero. It is not moving vertically as well. Right. Okay. So we are talking. Stop talking. Enough. So today we have taken a lot of difficult ones actually. Okay. We directly went into some of the very difficult questions which are as in J advanced. Okay. But if you do those difficult ones and now if you look at those easy ones, it feels a lot more at ease. So now, you know, if you look at these kind of questions that police there, two masses are connected. What is the frustration? You will feel very comfortable. Now if you look at this kind of question that there is this mass, what is the frustration of this mass, if the wedge is fixed, you will be easily doing it. Okay. So that's the good thing about doing the difficult ones. If you do the difficult ones, easy ones you feel very comfortable with. Okay. So I will be circulating a set of situations in which you have to draw the. We won't be chemically done. Yeah. Yeah. I mean see if your aim is J advanced, you should not wait for me. Last year, whatever J advanced batch is right now going to pass out. When they were in 11th, when, you know, I just tell you my experience with them. So class 11th, same thing started. I have taught them vectors and I have circulated the same sheet which I have circulated. Couple of them haven't slept next day morning. They had slept for couple of hours. Same next day morning, they have sent at least 50 images of the whatever they have done. And they said that I have we have done. Give us more. Within next one or two days, they have finished it. Okay. Then when I was teaching free by diagram, okay, they have finished the achievement. That's how they started. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay, and now I will tell you. Okay. And, you know how well they start with? So if you are doing the vectors workspace, don't feel great that you have done something which is, which nobody has done it. There are a lax of people who have been doing much harder work than what you can imagine. Okay. absolutely no time for anything else you should not even wait for the teacher to teach you you should not wait for me to to to teach you few questions on let's say I haven't taken up any question where spring was there right so a normal student what you'll do okay fine since spring related question was not done let me skip the spring questions that is fine for J mains and whatever and everything else you're preparing for but if your aim is J advance you should not wait for me just go all out waiting my point so that's how it is and that's it so I'll be sending you a set of diagrams set of things where you'll be trying free body diagram okay and now I think this is the last class before we resume again