Transcript for:
Mastering Work, Energy, and Power Concepts

foreign ERS welcome aboard welcome aboard welcome aboard so today's session is basically a all-rounder session for all the students who want to Ace in work our energy chapter so this is here your physics Master visa and vedantu who has been teaching for a very long time and what I aim to do in this particular session because many students want to revise understand in depth and also apply the formulas and the concepts of work for energy so this session is for all the students and let me tell you the importance of this chapter guys at least one question 100 is going to come in neat not just that in many chapters like collisions or electromagnetic induction or even electrostatics or even rotation and shm and so many other places you will see the application of work or energy so it will come like a combined concept so that means easily you can crack four to five questions if you know this concept and obviously you should know the other Concepts as well so take this like a very important High weighted chapter and pull it put in your 100 effort okay welcome Anish hello hello sumita hello Deva nice to see you guys I hope you guys are doing great and I hope you guys had your dinner and I hope you have hit the Subscribe button and I hope you smash the like button if you have not done that please do that right now because it means a lot to me and shows your support attendance and dedication if you want such more videos you need to do that so let's begin with the class now in work our energy what are the main things that are very important first thing is work and how to calculate it and how to you know understand which sign it is in and how to you know uh to make the calculations when forces are variable and through graphs and all that then next thing is power how to calculate power and how to relate power force Etc the next thing is you know understanding the different forms of energy like kinetic potential energy and the last one is applying all these Concepts together in a principle called work energy theorem or just mechanical energy conservation theorem okay so let's understand all these Concepts one by one I hope you got the flow of the chapter so these are the main four key areas which you are going to focus in this particular session yes so Jewel definitely if you start from now you can still correct Nate and please don't spam just like others are saying also Hello nice to see you guys good evening good evening good evening yeshu nice to see you guys so what is work in simple words imagine that we have some object okay so this is some body or some object on that object let's say for example there is a force which is acting okay let's say there is a force which is acting which is probably one of the many forces it could be just one force does not matter the body might move in that direction might move in some other direction possible you might be pushing something here but if it is already moving there then it will slowly turn in the direction of your push so push and your actual motion can be in two different directions possible so lot of people generally have that confusion okay why you know displacement in some other weird Direction and Y force in some direction doesn't matter so this is your displacement of the body this is the force acting on the body let's say the angle between them is Theta so what am I talking about over here what is work work is basically the transfer of energy from one body to the other by an agent called Force so work simply put is nothing but what the transfer of energy the transfer of energy via an agent via an agent what is that agent guys the agent is called Force that produces that produces some displacement that produces some displacement think about it think about it if I lift this remote I am applying some Force without that agent it won't work and I'm transferring some energy I just had my dinner just like you guys hopefully and I am lifting this up that means you know I'm using my energy and I'm transferring it here and I need Force for it I cannot just look at it and I'll be like okay listen lift up man come on I do like om groom room and then it starts lifting up no it won't it needs Force so that is that agent without which work is not possible the way I Define work in physics the way I Define work in physics is basically F cos Theta into s but in Vector notation you just call it as F Vector dot displacement vector this is the main formula for work guys work is f s cos Theta or F dot s what is this dot this dot is your scalar product I hope you remember this I hope you remember this from Vector lesson but even if you don't it's okay this dot is basically telling there are two vectors on both sides one vector here and one vector here so when I put a dot here it means take the magnitude of this Vector take the magnitude of this vector and multiply it with the cosine of the angle between these two vectors that's it so this is also called as dot product this is also called as a DOT product it is also called it is also called as a scalar product it is also called as a scalar product the reason why it is called as a scalar product is very obvious work is actually a scalar quantity work is actually a scalar quantity it is not going to have any direction do you anytime say I am doing 100 joules of work in the north Direction meaningless life so we never talk about Sir you know I ate 80 joules I ate 80 joules of energies are today while going in the upward Direction all right I just care about the number don't tell me which direction I don't care yes so whenever it is a cross it is a vector very good Rakesh dot dot is a scalar dot is a scalar cross is Vector cross is a vector OK cross will have sign in it dot will have cos dot cos cos dot cross when do you when do you do like this guys when do you do like this thank you Anish when do you do this when do you do this oh my Lord please protect me I have committed a sin I have committed a sin this is a cross right this is a cross right cross sin sine Theta understood guys vector understood Freya got it now you will never forget it no now you'll never forget it very good awesomeness guys now talking about talking about the unit talking about the unit of work what is the unit of work so if I do one newton if Apple One Newton of force and one meter of displacement then the amount of work done is basically one joule one joule correct similarly if I convert it into if I convert it into dine so then it will be one die in one Dion of force and I displace it by one centimeter then the amount of work done will be one ERG and also remember one joule is basically 10 to the power 7 ergs this is the conversion factor joules towards Earth is CGS unit and Joule is obviously SI unit something which you should be very well aware of now guess what this is not the only way you can write this is not the only way you can write work but there is another way like sir what is that another way observe carefully I can write cos Theta with force or cos Theta with s it doesn't matter I can combine both these both of these together or these two together it will be interpreted in the different way it will be interpreted in the different way but the final outcome is the same what do I mean by that observe just imagine if I tell you come on boys girls this object okay is being pulled it's having a force it is also having some displacement how about I split the force into two components there is one force which is pretty much useless I am not going to bother about it so much which is the F sine Theta component but the other component is f cos Theta F cos Theta component and that is basically that is basically in the direction of the displacement so how about looking at it like this it is a force in the direction of the displacement force in the direction of the displacement multiplied by the displacement perfect makes sense so how about writing work is basically Force force in the direction direction of that displacement in the direction of the displacement multiplied by multiplied by the displacement itself multiplied by the displacement itself right it is also the right way of saying it also I know another way of looking at the same thing I am just interpreting it in a different way instead of combining cos Theta with f how about s cos Theta and leaving this Force alone and leaving this Force alone observe how what happens now I will just show the force as it is I'll just show the force as it is but this time I will split the displacement into two components displacement into two components one component will be her this will be S cos Theta the other component is pretty much useless which is sine Theta component now how are you going to write work guys how are you going to write work guys it is force into displacement in the direction of the force so it is basically the value of that force it is the value of the force multiplied by multiplied by the displacement in the direction in the direction of the particular Force both the definitions exactly reflect the same equation there is no difference it's just a way of understanding or way of solving the question for finding force is that clear no calendar this is not Collision this is only for uh work power energy I will be taking up 12 standard topics also very soon since bold exam is far away no there is still time don't worry I'll be doing it OK great I hope this is clear everybody understanding this point awesome uh Sunday there will be a problem solving uh sorry venkateswan there will be a problem solving session this with the circular motion because if you just take work for energy it will be two less I'll be doing circular motion and work for energy together then you will have lot of fun lot of good problems come together now guess what work also has a sign guys it is a one shot good lecture big lecture it is going to be very very useful for Concepts formulas understanding application problem solving pyq session separate with a circular motion okay so concentrate now the signs of work okay the signs of work just focus on whatever I am saying guys you don't even have to think you don't even have to worry about Sir what are you going to do next week don't worry I know everything what you need I know what to do what not to do okay even if it just blindly attend us you will be like ah it is happening it is happening I don't have to break my head oh I have to do that or I have to do this oh when is Sir going to don't break your head on that just follow me that's it you will see you will be at a different league in different level signs of work work has three signs positive negative and zero positive sign when I say positive sign that means either the force and your displacement and your displacement are in the same direction or just it means that your force and displacement and your displacement basically make an acute angle acute angle that is the meaning of positive work what it also means is that you are giving energy imagine I'm pushing somebody and that person is also moving in the same direction just imagine I'm pushing pandu just visualize pandu and I'm pushing pandu in the same direction I am doing positive work it's a plus thing plus marks positive marks I'm doing good thing so positive understood guys okay yes yes venkatesh I'll be taking it up soon not now okay next there is a lot of time don't worry about it just focus on whatever I'm doing right now next thing is negative work when I say negative work that means the force the force is either opposite to the displacement or it is making an angle more than 90 degrees that means as simple as it is making obtuse angle obtuse angle imagine somebody is going this way but you're stopping him he's coming like this you are like stop stop okay I'm going out of the screen but I hope you get the idea the person is coming like this and like stop stop so force is that where displacement is here so that is basically sucking away the energy from the system that is a bad thing because I'm asking him to stop so it's negative work understood okay last thing is zero work obviously so zero work how is zero work possible you will be like sir it's obvious one is you know force is only not there oh yes definitely I don't apply only any Force a body is mine on its own okay maybe you know something was just sliding I have not done only anything it's like okay is this moving with a constant speed okay no work you have not done any work you cannot take credit for that because you have not done anything no Force no work okay second thing you applied force your teacher gives you punishment imagine teacher gives you punishment and teacher is like listen push the ball only if you push the wall then I will excuse you and you can sit on the bench you start pushing the wall whole day or pushing the wall the wall doesn't move uh what useless thing displacement is zero work is zero but you will be like sorry I am tired sir so where did that energy go es went into your muscular you have not done work on the did you transfer energy to the wall no right your energy is lost to the surroundings you started sweating you increase metabolism your muscular energy it's lost within you not gone to the wall so work done on the wall is zero because displacement is zero is that clear everyone and the last thing how many of you can tell me this how many of you can tell me this there is one more way work can be zero look at the formula probably you'll get an idea same timings usually at nine o'clock or five o'clock or seven o'clock I'll be updating you the timings on the telegram Channel or on the community okay yes you can see cos 90 is zero constant is zero ah okay so basically what I mean to say is that the force is perpendicular is perpendicular to the displacement perpendicular to the displacement how is that possible oh imagine I move something round and round I move something round and round what will happen guys the displacement is along the circle displacement is along the circle force is towards the center centripetal force don't you see displacement force is always perpendicular you have not done any work like the moon going around the earth is gravity going to do work no gravity is only changing the direction it is not giving energy to the moon or you take a ball connected to a string and rotate it okay rotate it and leave it the string is only changing the direction of the ball it's only turning it it's not adding or taking energy so no work done so whenever forces are perpendicular zero work is done is that clear Bacha everyone with me on this I hope this is understood great so now that you know what is work and how to calculate work let's do some basic questions on that okay let's understand some very very easy and simple questions and then we'll go to some more good better questions just imagine guys there is this surface okay we are just going to solve some examples now this is an example okay observe this imagine imagine that there is a block over here and this block has some Mass let's say I call it m okay or maybe I can give it some value maybe 5 kg maybe 5 kg all right and what happens is there is a force acting on it like this and the force makes an angle let's say 60 degrees here okay the force is let us say 20 Newton 20 Newton and in this process what happens is this block ends up moving let's say 10 meters 10 meters is the displacement of the block that is what it is the question is the question is find the find work by all forces acting on it what is the work done but all the forces acting on it let's try to do it okay simple question let's start with simple and you will see all kinds of question and there will be a separate pyq session also now show all the forces first of all without doubt how can you proceed the first force that I'm going to show the first force that I'm going to show is the weight the weight is going to act like this and that is 5G there is also a normal force which is going to act like this correct normal force is acting up the weight is going to act down okay this force is acting at an angle 60 degree I can split it into two components one component is here one component is here other component is here which component will you really bother F cos 60 or F sine 60 let's say if you guys can really think about this yes work done by Center Beetle force is zero shall be yes because it is perpendicular to the displacement every time every time perpendicular to the displacement hence it is 0. sine 60 says dakshini madhumida also saying sign Sandhya also saying sign sushma saying cause an is saying sign Aishwarya saying cause for those who are saying sign interesting guys see which is the displacement this what did I tell you if you remember correctly force in the direction of displacement into displacement this is the concept now you have to apply it that's what I told you right I'm going to teach you applying Concepts if you remember formula f s cos Theta you will say cos but no this is not the angle with the displacement it is the angle with something else it's with the perpendicular so actually speaking it should be taken as 30 degree so cos 30 is sine 60 or best way the component is nothing but 20 sine 60. this is the component that you should bother this is a completely useless component it is just perpendicular to the displacement you should not bother about that component is that clear everyone everyone yes Tamil I'll be coming there soon don't worry now over here what we will do next is the work done by the external force will be nothing but force in the direction of displacement which is 20 sine 60 multiplied by the displacement which is 10. what is sine 60 guys what is sine 60 guys come on think and tell me it is nothing but root 3 by 2 root 3 by 2 correct so now 20 into 10 20 into 10 200 200 by 200 so it will become 100 root 3 100 root 3 you can also approximately say root 3 is root 3 is [Music] 1.732 so this will be approximately [Music] 173.2 joules so that is the work done by the external Force similarly if I ask you what is the work done by gravity what will your answer be gravitational force is 5G displacement is 10 the angle between them look at it carefully displacement and force are at 90 degree Force here displacement they are 90 degree so cos 9 D cos 90 is 0 so the answer is zero if ask you what is a work done by normal force what is the work done by normal force normal is up displacement is 10 but again the angle is going to be 90 degrees guys normal up displacement there 90 degrees So Gone it will be zero now if I ask you what is the total work done what is the total work done like it happens in your project like one person contributes a lot these two people are not contributing only does it happen teacher has given you an assignment do this project complete this homework together solve this task together one person very sincere does everything other two people are chilling chill Madi relax enjoy LOL so this plus this plus this only this guy is doing work nobody is doing work nobody is doing work so the final answer will be 173.2 joules everybody with me exactly that's fun that's the answer cool guys understood how to solve this problem very nice let's take up another question okay let's take up another question now here you will also learn about dot product a little bit so let me give a brief idea about dot product in case you have forgotten so here is all about dot product here is all about dot product in case you have forgotten it so imagine if I take unit Vector I cap with unit Vector I cap what is the answer for that guys what is the answer for that guys I dot I both are same vectors in the same direction so 1 into 1 into cos 0 cos 0 is 1 1 into 1 into 1 is 1. so that is the same as J dot j which is also the same as K dot k is that making sense everyone with me very good if I do I dot j i dot j then what will be the answer I dot j or maybe J dot k or maybe K dot I the answer for that will be 0 the answer for that will be 0 very good now with this you get an also another idea that you know what if I have a dot b is it the same as B dot a I think so because uh a dot b is a b cos Theta B dot is b a COS Theta a B and B are the same thing so yes they are equal so that is also equal to a b cos Theta very nice so then you might be wondering sir what if I have something I cap plus something J cap plus something K cap okay goes with DOT product with something I cap okay something I cap something I cap something J cap something K cap what do you do in such cases that something could be anything like two three four one minus one ten anything so maybe ax a y a z similarly BX sorry b x b y b z what happens guys in such cases I goes with I because I dot j or I dot k is 0 J goes with J because J with I or J with K is 0 K will get multiplied with K because K with i or k with J is again 0. so guys only multiply people of similar kind only multiply people of similar kind it's like Audi guy audio logger will go with audio lover if somebody likes BMW he'll be like oh you also like BMW okay come on let's hang out together oh you like baahubali movie even I like baahubali movie come let's hang out together so people of similar kind hang out together in dot product so what you will see is the answer is a x b x plus a y b y plus a z b z that is what the final answer is is that clear excellent guys awesomeness actually okay now imagine I give you a question over here imagine I give you a question over here something like this if pandu applies pandu applies how much force I give it in icap J cap K cap type notation f is equal to maybe I don't know 10 I cap minus 20 J cap plus 4K cap Newton and displaces and displaces what does it displays a box a box from from example 2 comma 0 comma minus 1 2 2 comma 4 comma 1 okay so this many meters so this many meters he has moved it so what is the work done so what is the work which is done by pandu interesting question this is very common again if you notice so let's see how to do this see guys in such a question you are given the force you don't know the displacement so you need to find the displacement how are you going to find the displacement you know initial you know final it was here it was there displacement it was here it was here now the displacement is just the change or the final minus initial position go by the logic displacement is always the change change in position change in the position value that means it is the final position minus initial position if you compare these two you will quickly notice this is your final position and this was basically your initial position agree with me very nice so let's write it down final position is basically 2i cap plus 4 J cap plus K cap just the coordinates become the components coordinates become the components minus here you will see two I cap there is no J cap oh there is only K cap directly it is K cap guys okay so minus you can just say k cap that's it now just subtract the two two I minus 2i gone Zoop vanish so four J cap is remaining like I can see K minus minus becomes plus so 2K cap uh this is nothing but meter so that is your displacement but I don't want that I want the value of the work work is force dot product with displacement so I need this so 10 I cap minus 20 J cap plus 4K cap dot product with 4J plus 2K 4 J plus 2 K so guys like I told you I goes with I oh bachara nobody is there for him he likes bahubali nobody is there who likes baahubali I will go with I only nobody is there so go on this will go with j k will go with K so what is the answer guys check this out minus 20 into 4 minus 20 into 4 guys it is minus 80 right minus minus 80 guys minus 20 into 4 is minus 80 okay 4 into 2 4 into 2 16 right so plus 16 over here let's see how many of you have put up the answer very good guys very good some of you have put up the answer over here oh sorry what did I just do why did I put 16 all right sorry uh four into two it's eight am I right yeah so this will just become minus 72 joules minus 72 joules everybody with me on this minus 72 joules very good Hari Sudan who is pandu pandu is our classmate here Hari Sudan's question who is going to answer somebody has to answer Hari Sudan's question he's confused sir all these are understood sir but I didn't understand this only first word only I didn't understand who is pandu everything else I understood interesting okay great yes what is your doubt everybody clear till this point so whenever displacement is not given find that out and then find the work so this is another beautiful important type of question now the next concept and that is work by variable Force work by variable work by variable Force okay work done by variable Force now you'll be like what is this work done by variable Force R okay let me explain this to you imagine there is a body Warrior now at this moment there is some Force now as it moves little bit ahead let's say the force becomes small then as the body moves more ahead you know then the force probably reverses and then as soon as the body even slows down further maybe the body slows down further and then again suddenly the force becomes very large you can say the force is changing magnitude Direction anything is possible guys so this is basically called as a variable Force so if you look at it graphically if you look at it graphically it will make more sense so imagine this is your displacement and this is your Force graph okay this is origin you will see probably the force will suddenly increase then it decreases it changes the direction and again goes positive so anything can gonna happen very good very nice answer very creative answer Anish pandu is the assistant lecturer in vedanta physics department very true yes you know okay okay okay so when I see it from here um especially when the screen is far I miss out some words sorry guys I sometimes mispronounce your names happens with me all the time okay so now what you do is basically you find small small work the small work done the small work done the small work done will be Force Force multiplied by the small displacement multiplied by the small displacement so d w is the force into the small displacement but but the total work done the total work is basically the sum of small work like for example when you have to complete a project one day only will not complete no the assignment project whatever task one day you will do okay five failures next day maybe you took some print out of some picture and put it next day maybe you put some cover third another day maybe you did something else oh you have to decorate something another day you found one more article and you put it in the project or next day you got some model you put it so every day you should do small small tasks so the total thing is the sum of all the work that you have put same way over here guys when you do that in mathematics it is called integration what is it called integration I have spoken about it many times in the previous lectures also so you can just watch that basic maths class so it is f integral DX okay integral of f d x so that is basically the way you should look at work done by variable forces this is very important this is variable Force now whenever there is integration what should come in your head see when I talk about derivatives what comes in your head in graphs yes Prem Kumar nothing happens overnight if magnitude is asked can we just take the modulus yes yes yes uh but you take the modulus later on not first do not take the modulus first and then multiply it because then you are forgetting the COS Theta value okay yeah sure then yeah so when you think about derivatives you think about slope so when you think about integration what do you think about area correct so you have to find the area but you need to be little careful when you are measuring this area this area will be positive area because this is above the horizontal axis whereas this area has to be considered as negative area guys this is basically negative area again as it goes up it becomes positive area so the area also has signed depending on whether it is on the top or at the bottom so when you find out the total work done take the sum of all of them including the signs be careful OK so you can also say that this is actually the area under area under the force versus displacement graph the area under Force versus displacement graph crazy so we got to know about all of this let's proceed further to One More Concept before going ahead the next concept is the classification of forces into two categories the two categories are let's see so forces can be categorized into two main categories so what are the two categories observe this the first category is just called as conservative forces conservative forces and the second category obviously will be called as non-conservative forces non-conservative forces now what do I mean by conservative and non-conservative forces let us try to understand them as well okay just imagine if I have to push something from here to there if I have to push something from here to there will the path which I take matter or only where I start and where I end matter what do you think can you suggest a course of IIT which is full of mysteries very nice question let me tell you every branch is mysterious it's just you need the I for it okay as simple as you know Civil Engineering also has many Mysteries right till computer science okay so there is nothing like only this branch has Mysteries everything if you look deeply has so many unanswered questions path matters only initial and final position matter I will tell you what it depends some forces only the path matters how you go matters some forces how yoga does not matter where you start where you end matters where you start where your end matters what is need exam preparation guys what do you think does the path taken to crack neat matters or do you think oh I was here in 10th standard I got this much percentage and Final Destination okay I got a government Medical College seat or I got this college or that college does that matter what you think okay it's a open-ended question there is no answer for it from my side I want you guys to think about it and probably put and debate about that in the comment section it will be interesting to hear your views about it okay so I'm not saying it is this or that I just want to hear your views that's it so I just put a thought in your head all right anyways so in conservative forces what happens is the path does not matter only initial and final position matters so these kind of forces sorry these kind of forces are basically path independent path independent work so only initial and final position matters position matters that's all whereas in non-conservative the path matters for the work done path matters for the work which is done definitely not just this if you start and come back to the same point if you start and come back to the same point then the total work done is zero in case of conservative the total work for a closed path for a closed path is zero so if you start and come back to the same point you will see that the net work done is big fat zero here here work done in a closed path were done in a closed path is not zero if you come back to the same point you will see it is not zero I'll give an example imagine you push something push something push something push something push push push push and bring it back like every time I was pushing it I was pushing it Force displacement Force displacement Force displacement Force displacement every time I was doing positive positive positive positive work so how can the work be zero yeah it is not zero but there are some forces where you move it sometimes the force will do positive or sometimes it will do negative work and by the time it comes back total work done will be zero so there are forces like that so that will be conservative okay now what are the examples then you will be like ah yes our Resource Conservative oh why I didn't think about it best example is the gravitational force gravitational force or even electromagnetic force electromagnetic force or you can even say spring Force spring force or even elastic force all these forces are conservative in nature gravity when you take a block up will do let us say negative work when you bring it down it will do positive work and you take it up negative positive total version 0 negative plus positive zero but friction is not like that friction is not like that you move it here friction acts opposite negative work you move it back friction as opposite again negative work total work done negative plus negative negative only so work done in closed path is not a zero exactly so not just friction guys there are many people which are evil which are evil like friction who are the evil forces friction viscous Force if you have studied fluid mechanics or have some idea about viscosity like honey tar is viscous oil or water is not viscous you get is free flowing or drag Force air resistance force very bad evil force it will suck away the energy it is non-conservative force all these forces including even normal force or even tension force all these forces are non-conservative in nature everyone with me Rakesh buoyancy is a conservative Force buoyancy if you have to put buoyancy buoyancy will be a conservative Force okay keep this in mind everyone yes I've been in Tamil Nadu many times okay so does friction always do negative work no Prem Kumar it can do positive work also okay it can definitely do if everybody is clear till these two points were done by variable force and conservative non-conservative Force let's go do some questions on this okay here is a question on this so let's see if you guys can figure this out if of force in one dimension motion in one dimension motion is given by F is equal to 2 x Cube Newton to move to move an object from from x equals to 0 to x equals to 2 meters fine or you know find the work done by it find the work done byte okay start doing it guys and pose the answers as soon as you complete the question and find the answer okay I'll be explaining it slowly because some people might want to listen into the solution properly that's okay okay uh how work in a closed path non-zero Sandhya okay I'll just come to it hold on just give me a second let me just complete this okay one example of positive friction definitely Prem Kumar just hold on let me just complete this question first observe now okay I've heard all your doubts I'll just do it hold on so first of all work done work done okay just imagine is nothing but integration of f DX why am I using this because force is variable so the moment it is variable I have to think about antenna will be alert oh integration okay I have to do integration integration of 2 x Cube DX but remember there will be limits it will be definite integration you remember definite integration with limits so whenever you see from here to there from this to that from now to na then then you will see integration with limits the first point will be lower limit then last point will be the upper limit 2 is a constant so put it outside so integration of two x Cube DX limits are 0 and 2 meters now this will become 2 x cubes integration X cubes integration is X raised to 4 by 4 3 plus 1 by 3 plus 1 is 4 guys okay and the upper limit is to lower limit is 0. now the next thing that you're going to do is to First substitute 2 so it will become 2 raised to 4 by 4 then substitute 0 so 0 raised to 4 by 4 and then subtract the two guys 2 raised to 4 is 16 right it's nothing but 16. so this will just become 16 by 4 minus 0 16 by 4 4 4 2 is not nothing but 8 joules so that is basically your work done is that clear very nice shama very nice now we are very good yes no no joules very good yes yes yes yes dakshini yes chandana very good uh awesome awesome shall we very good Anish okay now going back to I think two people had asked some questions yes yes I'll be doing the entire chapter in this session itself okay so the second point of non-conservative force and how can friction do positive work okay work done in closed path is not zero just imagine let's say I take this example imagine I take this body and I move it like this okay I move it like this this is the path along which I move it okay fine it's a closed path what do you mean by close path you start and end at the same point it need not be circular it could be anything but you should come back to the same point that is the meaning of closed path okay now in this path how will friction act how will friction at friction will land opposite right like this like this like this like this like this like this okay every time it is acting opposite to the displacement here it will do negative work negative work negative or negative negative negative negative negative whole time it was negative saddest fellow whole time it was negative what is the total work done by friction positive negative or zero negative is it zero no that's it so work does not close path is not zero for forces like friction everyone fine clearer understood but for Gravity like forces but for Gravity like forces it will not be so if you take this Mass on the top and you go like this and you go like this and you come back over here you will see as you go up go sideways go down and come back over here you will notice that in this path gravity is acting down gravity is acting down so it will do negative work it is going like this it is perpendicular so it will do zero work it is going down gravitational force is also down so it will do positive work it is going like this because it is perpendicular it will again do zero work negative 0 positive zero minus plus zero so the total work done will be zero is that clear is that clear everyone with me on this very nice the same thing you can also say about tension imagine there is a dog I have a dog I take it to morning work okay morning I take the dog to walk so imagine this is my dog okay so this is my dog okay so I'm taking it to the walk for a walk sorry this is tension okay this is tension I take the dog like this this is my path now this is my path I take the dog like this and it completes one complete lap or one complete round in my building in my Society whatever so guys tension is like this tension is like this tension is like this tension is like this tension is like this tension is like this tension is like this is tensional doing positive work everywhere positive positive positive positive positive positive positive positive positive positive be positive come on guys total work done not zero no so it is a non-conservative force is that clear is that clear everyone with me on this understood oh give me a thumbs up guys okay last thing how can friction do positive work many people ask okay just imagine just imagine I'm holding a block and I'm holding a block like this okay I'm holding something and I move it or this way or that way okay I just move it so imagine whatever platform it is on it is under motion if it is under motion won't this also move this will also move right like this when I move my hand the block also moves which is kept on the talk talk who is going to do it friction right where will friction at this way or that way think carefully and answer think carefully and answer less think carefully and answer the friction will act this way because who else will provide the displacement because the other forces are weight and normal there is no other force apart from weight and normal right so who is giving that acceleration who is giving that motion there is only one force and that is friction so in Block on block problems you will see the upper block if the lower block is pulled you'll see the upper block experiences a friction in the same direction of the acceleration great great so hence the answer for that hence the answer for that is that the work run in the case of friction were done by the friction will be positive so a lot of people think friction can only do negative or that is wrong that is wrong okay we are not discussing pulleys and tension right now because that was the separate chapter that is Newton's law so I'm going to focus more on wordpar energy okay uh what is it m uh let me tell you Bacha even if I get one path now even if I get one path where work done is not zero it is considered as non-conservative it cannot be like hey come on man all these parts I did zero work only three parts I did negative work okay come on man make it make me 70 positive 30 percent you make me non-conservative either this or that even if you get one path where non-zero work is done the tension is is considered as a non-conservative force is that okay bicycle riding and running is positive friction well uh that will come under separate category rotational motion okay in rotational motion you will see friction will not do work in case of rolling motion of bicycle wheels so friction actually does not do work in Rolling motion Okay cool so let's move on now guys you are asking all random questions now what is pseudo force that is a completely separate topic so guys make sure that you are asking something which is relevant to the topic if you ask me something sir what is sudo Force guys I'm not here for that if you are going to ask me relevant questions Final Answer else that will be completely ignored okay so stick to the topic I don't like you guys debating from the topic okay now moving on to the next one moving on to the next question let's see if you guys can solve this imagine I take some body from here to here and then from here to here okay and then here to here imagine or yeah I'll take one more point maybe here then here to here and then here to here and then here to here let's call this point a b c and d and let's say it's given to me that when I go from A to B the work done the work done is let's say 20 joules 20 joules when I go from C to B when I go from C to B the work done is let's say 10 joules when I go from C to d c to D let's say the word done is let's say 40 joules the question is when I go from when I go from D or rather a to d when I go from a to d and I go from a to d then how much amount of work is done assuming it is a conservative Force assume that it is a conservative Force doing work so how much work will be done to go from a to d that's the question okay let's see if you guys can solve this okay think about it carefully okay so guys observe carefully since it is a conservative Force I know the total work done should be zero another total were done should be zero so going from A to B how much energy am I taking I go from here to here I take 20 joules I take 20. if I have to go from B to C oh that is not given but what I have been given is if I go from C to B if I go from C to B I will take 10 joules of energy that means if I go from B to C how much energy will I need guys if I go from B to C obviously minus 10 if I go here it is 10 if I go there opposite it's minus 10 exactly negative of that c to D is already given C to D is already given how much is this 40. the only thing remaining is this work it from here to here here to here here to here and here to here so I think I know what to do now so total work done is zero so work done from A to B is 20 then plus plus negative 10 plus 40 plus work done from D to a is 0. great 20 minus 10 is nothing but 10 10 plus 40 is nothing but 50 so 50 plus work done from D to a is zero correct guys everybody with me excellent a so work done from D to a is negative 50 joules but the question says a to d not D to a we have to find what is the actual work done from what what is the actual work done from a to d so work done from a to d will be negative of this so it will be plus 50 joules that is the final answer plus 50 I know Sunday I know I know it is from a to d so I found it from D to a I know in the end I have to put a minus sign so that is there at the back of the Mind is that clear everyone with me on this ok so this is how you can solve questions on conservative non-conservative Force variable Force I have done some questions okay let's do the next part okay slowly we are moving ahead in this chapter and I'm pretty sure you are slowly building that confidence you're slowly remembering those things which you have probably forgotten or probably you might have seen seeing these things for the first time which is still good if you are able to grasp even 50 to 60 percent of it and I hope guys you are smashing the like button if you have not done that yet not fair okay so let's go to the next part and that is basically the types of energies the first one being the kinetic energy will talk about kinetic energy okay so kinetic energy guys what is kinetic energy it is the energy of motion so energy which is basically due to motional it is also called as emotional energy not emotional it is emotional it is not because of emotions happiness sadness and all that this is a scalar quantity this is a scalar quantity it is also measured in joules or herbs if it is CGS okay and also interesting thing is it depends on your speed also just imagine you're traveling in a train or a bus there is a luggage there is a suitcase or something kept beside you imagine something like this there is some Bag kept beside you you're looking at the back you are in the train or the bus what is the energy of this bag guys what is the energy of the bag no frame we do not use a sign for kinetic energy we do not have plus and minus signs yes rubesh obviously I'll be sending the PDF that's standard conservative is independent of the path yes exactly I think I mentioned that Prem in the previous slides is there a new is there any kinetic energy of this bag I am sitting and observing it nothing it's moving along with me wherever I go wherever I go I go here I go here I go here I go there what is the kinetic energy of the bag for me nothing but for you guys but for you guys is this bag moving is this bag moving for you does the bag have some kinetic energy come on guys answer quickly or else I'll keep moving I'll faint come on answer quickly does the bag have kinetic energy for you yes right perfect but for me no for me it is not rest I'll be like ah the bag has no kinetic energy so what does it mean what does this mean ah thank God my hand is paining okay so guys it means it depends depends on the Observer depends on who is observing it depends on the Observer or frame of reference observers perspective matters your point of view matters so it is a Observer dependent entity okay so what is the formula for kinetic energy one my task the formula for kinetic energy is half m v square and you can see speed square is there so no sign Connecticut is always positive if somebody somebody else kinetic Converses negative 100 joules slapping on the face throw him away it's not possible guys so kinetic energy can at Max it can be zero but it can't be lower than zero so kinetic energy is always more than or equal to zero keep this in mind also one more interesting thing if you just multiply and divide by m you can multiply and divide by m so it will become M Square by m into V Square which I know is also half m v whole Square by m Mass into velocity must into velocity guys what is it it's momentum so it will also become P Square by 2m so that is also kinetic energy something which you should remember so half MV square or momentum Square by 2 m 1 and the same thing one and the same thing exactly yes relatively yes Anisha it depends on the relative frame or relative Observer definitely crazy awesome let's move ahead to the next part this was kinetic energy the next energy that I should be talking about after kinetic energy which is the energy of the motion is nothing but potential energy so let's talk about potential potential energy when I use the word potential what does it actually mean it means ability it means ability ability to do what you might ask potential energy means what ability to perform to perform work and it is stoned in that body it is stored in that system or that body example I take this remote or I take some dumb object I take some dumb object like this water bottle it'll be like sir does this have energy sir then I'll be like okay you want to know whether it has energy you know what you should do leave it just leave it free I don't want to do it it will break I will get nice beatings at home okay so if I leave it I know it falls I know it will fall it has ability to perform work it has ability to manifest and show its energy it will fall it will get kinetic energy where did it get kinetic energy from it got it from the potential energy because of gravity there was no gravity around me it would be like ah it is floating in space just like it happens with astronauts in the International Space Station so right now there is gravity so it falls oops I I just held it now okay great so same way if I ask you guys do you have potential energy for cracking neat reply to that is a fire emoji or maybe put some ice if you have potential energy put fire if you don't have potential energy for need put ice yes no you have no you have no potential energy how do you know you have potential energy guys how do you know you have potential energy become free think freely become independent the more you are constrained you cannot show your potential energy this dumb water bottle also has potential energy but it will not show it until I leave it ah fell down same way you can also show your potential energy unless and until only when rather you free yourself and when you start thinking freely out of the box creatively until you hold yourself you will not be able to show your potential energy agree or disagree very good now this energy this energy is also a scalar quantity it is also a scalar quantity it is also measured in joules but there is a catch here it is not you know you don't talk about Observer here here you talk with respect to something always this bottle has gravitational potential energy okay how much one person will let 10 joules so there will be like 20 joules other will be like 40 joules then you will be like what is it 10 20 40. then comes the answer see gravitational potential energy spring potential energy elastic potential energy electrical potential energy all these forms of energies are always measured with respect to something like who is that something sir something depends on you it's always chosen it's a it's a line or it's a system or is it it's a configuration it's a particular state which is chosen to be zero and with respect to that you measure the energy with respect to that always and thank you for putting up and lighting up the chat box guys yes we needed this winter fire very good thank you for warming up so always choose some situation some position some line some situation some configuration as zero maybe when the bottle is here I call it zero or right now you have zero energy OK I tell him listen you have zero energy now when I take the bottle here oh from this to here oh you have 10 joules of energy so it's always measured with respect to something you always measure it with respect to something understand that so always measured measured it's always measured with respect to something called as zero reference zero reference very important keyword over here that you are learning it's always measured with respect to zero reference for example when you take a spring when you take a spring thank you yeshu so much thank you Ruby so much thank you Ani so much and thank you everyone when you keep it naturally relaxed chill then it has no potential energy probably when you strain it when you compress it then it has potential energy so a spring and in the relaxed state spring that is relaxed that is relaxed it has no potential energy or if you take charges positive positive charges negative positive charges they will attract or repel each other attract or repel each other correct depending on positive negative negative negative positive positive you ask this charge go there this starts go there like it happens no in school also two people are talking interacting teacher will be like listen you go there that corner you go there that corner what is he doing I don't even know what is he looking at why is he laughing there I don't I can't see him only nataka is also saying what is he doing what is my friend doing I can't see him so no interaction no potential energy no interaction no potential energy so guys that is considered as a zero energy state so charges charges separated very very far away from each other also you can take for gravitation block kept on a ground block kept on you know uh some level on some ground level on some ground level you can say these are all examples that is the meaning of reference so everything is measured with respect to that everything is calculated according to that that is a meaning of zero referring I'm referring to that and then measuring it I hope this is clear yes Prem Kumar that's how friends are made when the teacher shifts the thing no so then what happens you make new friends that person who has quiet also starts becoming making noise after a few months or few weeks everybody is making noise teacher is under attention you know so that's what happens okay great so let's move ahead and talk about the next part now there are few kinds of potential energy that you should know about usually when you talk about potential energies what are the names that you have heard just put it in the chat box what kind of names have you heard guys about potential energy I think you would have heard about gravitational potential energy gravitational potential energy hundred percent you have heard what else have you heard have you heard elastic potential energy elastic potential energy stored in the rubber band a stretched bow very good spring very nice many people are saying spring very good spring potential energy very nice have you also seen something else apart from this yes electrostatic electrostatic electrostatic potential energy electrostatic potential energy very nice perfect so all these are examples of potential energy now the moment you look at their names now you should think like CID you should think like CID I have seen this person somewhere like it happens no police is finding out missing persons report have you seen this person then suddenly one person comes are you I have seen this person somewhere where have you seen this or sometimes also it happens with you oh I have seen this person somewhere I have I don't know is it ringing a bell is it ringing a bell as a drinking bubble can you do gravitation after this lesson okay I'll think about it butcher I'll consider it just put it up in the comments or else it will slip from my mind have you seen these names together somewhere before this very good Salve is our CID perfect raw agent salvi murugan very good Perfecto so let me go back a little bit let me go back a little bit over here Gravity electromagnetic spring elastic buoyancy so guys all these names are what conservative non-conservative have you ever heard viscous potential energy frictional potential energy tension potential energy normal potential energy drag potential energy have you ever heard such names guys have you heard anybody saying that nobody's would have said that right if somebody tomorrow comes and tells you or you say normal potential energy one tight slap guys take a one tight slap tension potential and retention potential and one tight slap viscous potential is a one type slab drag potential energy one tight slab frictional potential as you one tight slab these okay all these are valid so guys what you should realize is that conservative forces have potential energy or potential energy associated with conservative forces it is also created with with conservative forces flexor why is our only conservative what did friction do wrong what did friction do wrong friction is evil friction is evil it takes away you move the object here friction will like come on tax come on give me this give me that you bring it back frictionally like again take it take it take it but consider it is not like that you move it here and you bring it back total were done zero whatever it gives it takes whatever it takes it gives so whatever it gives it takes whatever it takes it gives that means it stores and restores stores and restores so it does not keep anything for itself when you come back so that is why it has ability to perform work it has some potential energy associated with it it can store energy it can store energy look at this world it can be stored that is why it is associated understood exactly Sandhya very good yes frame yes nitya very nice then come is the next topic which is obvious what is the relation between mathematical between conservative Force conservative force and potential energy in general is there some kind of relationship the answer to that is yes I'll be like sir what is the relationship here it is the work done by the conservative Force a is always the negative change in the potential energy this statement this statement has hardly been understood by many students and you might have read this or heard this statement and you would have seen the next thing which will come probably before also but many people don't understand what it means let me make you understand this by providing an example just imagine just imagine if you have okay just imagine if you have some body okay and you move it up you move it up okay you just move it up this is the displacement this is the first case the second case the same body you just move it down this is your displacement okay now think and tell me guys in each case as you take it up right the gravity is going to act downwards right the gravity is going to act downwards mg is going to act downwards so tell me what is the work done by gravity what is a work done by gravity is it going to be positive or negative just answer that just answer that is it going to be positive or negative displacement of force down opposite over the negative okay work done is negative perfect very good did the potential energy increase or decrease just answer that then did the body's potential energy increase or did it decrease oh I take it up potential energy is increasing increasing oh so the change in the potential energy is positive right change in the positive potential energy is positive right everybody got it perfect now go the reverse way with a reverse way as you go down gravitational force acts down gravitational force acts down if I ask you what is a work done by gravity what is the worry done by gravity gravitational force down displacement down angle is zero because they are parallel oh okay it is going to be positive work if I ask you change in the potential energy it's coming from top to bottom to bottom it has lost potential energy it has lost potential energy so change in the potential energy negative what does this tell you if were done by gravity is positive the change in the gravitational potential energy is negative and if water done by y savarasa basically if this is positive this is negative this is negative this is positive it's always opposite in sign now do you understand why this minus sign has come now do you understand why this minus sign has come everybody with me mind blown now you are like oh now I know why I should attend Shreya service class great awesome now what is work done formula guys work done is Small work small change so why do you write these are small change in potential energy small J small work more work more change small work Small Change obviously what you do what you get if you do small work we'll get small change if you apply more work more change that's all so work length is forced into displacement right the conservative Force into the displacement is a negative U or bring this DX below bring this DX below so guys this will be minus d u by DX minus z u by DX very important formula you know what this means Force the conservative Force is the negative gradient negative gradient of potential energy very important line that I am writing here it will save your day even not just here but even in electrostatics magnetism so many places even in gravity awesome okay now I'll be like sir what the hell is this gradient sir have you heard this but what is this gradient gradient means change with respect to distance change with respect to distance if it is DV by DT d u by DT it is the rate of change rate with the time if it is change with respect to distance it is called gradient so these are mathematical terms which you should know the next time anybody says pandu gradient what will you think rate of change of pandu with a distance how we spawn to changing when he moves from here to there if I just say rate of change of pandu then like how respond to changing with time understood so rate of change is purely time but change with distance is called gradient got it awesome awesome guys now there is a very interesting thing associated with this so that is basically Force versus oh sorry not force versus ah what is this U versus X graphs that you get U versus X graph potential energy versus potent uh displacement graphs imagine imagine this is basically X this is basically energy okay and I tell you listen the potential energy is changing like this goes like this and goes like this every point there is different value of potential energy what do I mean by that extend the spring so much this is the potential energy so much more potential energy so much more energy I take this Mass here this much energy take it here this much energy so with position the energy is changing agree okay so maybe there is somebody the energy increases decreases increases decreases something is happening some random graph is there of potential in a reversal distance okay now according to our formula my dear students f is equal to minus a d u by DX minus d u by DX now if you look at it carefully if I draw a tangent over here any place if I draw a tangent if I draw a tangent the slope the slope of the tangent will be D U by DX so strictly speaking this is negative slope of U versus X graph everybody agrees with this U versus X graph slope is exactly what this is excellent a now imagine if I ask you add this particular location at this particular location is the slope positive or negative is the slope positive or negative put it up in the chat box for offered guys everybody should answer here is the slope positive or negative if you have attended my basic math class slow positive negative what is slope derivative everything you know and if I miss those classes please watch it sir which book is the best for question solving MTG is their kid our tathwa material is there best book is tatva else if you don't have no problem use MTG or use DC Point h c bar model these are good books okay so positive very good so what will be negative of a positive minus here in this part in this part what you will see in this part what you will see is the slope is positive but the force will be negative okay okay everyone but in this part in this part or in this part slope is negative slope is negative negative a negative is positive so here slope is negative the force will be positive clear understood so that is why that negative sign is very very very important keep this in mind cool guys can we go on to the next concept so we have learned what is potential energy what is uh what are the different forms of energy how is it related to conservative Force using this formula and how the graphs also have to be interpreted now the two main things which you should know is the formula for gravitational potential energy what is the formula for that so my dear students if you have some body of mass m and you move it up move it up by a height of H you move it up by a height of H then you are increasing the potential energy so the change in the gravitational potential energy is m g h u is generally the symbol for potential energy just like you have k for kinetic energy so I am increasing it by MGH but the same thing the same thing if I bring it down right like this then the change will be negative m g h always the change in the energy is what matters for most of the cases okay great so that is for gravitational potential energy similarly there is a Formula which you should know for spring potential energy or elastic potential energy so imagine that you have a spring which is right now relaxed it is at its natural length so it does not have potential energy this is right now natural length it has no extension or compression whatsoever now the same spring what you do you either elongate it or or basically you compress it like this so you have stretched it by X or you have compressed it or you have compressed it by X in either of the cases you have added a spring potential energy to the system of the value half k x square this is the formula so you should know this formula also and obviously this is very easy you have seen this is probably nine standard itself spring potential energy half k x square everyone what is X n what is K spring constant remember f is equal to k x I hope you remember this so when you pull and you pull the magnitude of the force is k x is the minus sign important yes or no that's when tell me which channel am I teaching English Channel I am not wasting time no I am teaching for meat only butcher with my glasses people last year they used to watch my lectures on J channel and then they cleared meat so if I'm exclusively doing neat syllabus for need students dedicatedly okay for you guys obviously are going to like create wonders in need exam definitely okay yeah so no need of minus sign why because it's magnitude minus you can understand yeah whether it is this body or that body it depends which body you are talking about accordingly you could minus sign so don't bother about minus K so or minus my array waste it is okay so don't bother about that minus sign great I think we should solve some questions now all right so we have talked about this graphs and we have talked about potential and as well as kinetic energy so let's do some questions guys let's do some questions okay now look at this if the Force acting produces produces a potential energy of U is equal to minus 5 x Cube plus 4X plus 5 joules example then find then find the force at X is equal to 2 meter so that is the question the energy changes with X find the force acting on it at 2 meters crazy question what is the theory behind this question from energy how to find the force but to potential and force oh potential energy and force are related how are they related force is the negative gradient of potential energy force is the negative gradient gradient means rate of change with respect to distance okay so now what is my next step f is equal to minus d by DX U is given how much is it minus 5x Cube plus 4X plus 5 crazy so minus minus becomes plus 5 comes outside it is just derivative of x Cube just using simple rules of derivative addition subtraction minus plus becomes minus 4 goes outside derivative of just X guys 5 is a constant anyways but still I'll write it derivative of 5 with respect to X ok so this will become 5 x cubes derivative is going to be 3 x square minus 4 DX by DX is 1 constant's derivative is 0 so this will become 15 x square minus 4 that is your force and the question is at 2 meters the question says at 2 meters so therefore Force at 2 meters will be put 2 over here 15 into 2 square minus 4 2 square is 4 4 into 15 is 60 so 60 minus 4 very good so guys what will be the answer over here it will be nothing but 56 Newton so this will be the value of the force 56 Newton not minus 56 minus 56 will be there in the option to confuse you because many people are going to forget the minus sign all the people who forget the minus sign will get Negative marks if you remember oh there was a minus sign you take into account all of the calculations don't do mistakes you will get the answer as plus 56 Newton okay everyone I'll try Bacha is saying this week I'm planning to complete uh work for energy and then probably also go to circular motion circular motion also very important and then I will take a combined session of pyq's problem solving on both these chapters okay great let's do another question all right look at this imagine if the ah let us say I take a question on one of these things I have taken all these things right okay uh let's take a question on this spring okay if the spring is extended if the spring is extended by let's say for example 2 meters okay the spring is extended by two meters of force let's say ah 40 Newton needs to be applied 40 Newton needs to be applied example now the question says how much more work how much more work needs to be done needs to be done to further to further extend it by two meters further extend it by 2 meters that's the question that's the question let's see how many of you can do this okay let's analyze the question first initially the spring will be obviously at its natural length there is no extension at all there is some spring constant but I do not know that then what happens is the spring gets extended by 2 meters so the spring gets extended by basically how many meters two meters then what happens the spring is further extended by 2 meters further extended by 2 meters that means what is the total extension guys what is the total extension 4 meters right the total extension will be 4 meters right very good in the first case how much force was applied how much force was applied onto it it was basically 40 Newton second time I don't know but okay I'll just keep it as it is so for the first extension for the first extension using the force value is K times of X so faulty is equal to K multiplied by extension so the value of K will be 20 Newton per meter that's the initial X extension which is giving me the spring constant why do I need spring constant because I think from this I can find how much energy this has then I will try to find how much energy this guy has this has this much energy this has this much energy oh why did the energy difference come I think I have done work because I did work that's why the energy changed so that's the reverse thinking that I thought so guys if I ask you what is the initial energy like it is half K initial extension Square K value is 20. what is the extension extension is 2 so 2 square so correct guys so 2 square is four four by two two into twenty right this is 20 is nothing but faulty uh joules of course this is 40 joules everyone with me very good siren awesome awesome now last part what is the final energy over here what is the final energy over here half k x final Square K value 20 okay put 20 x value four oh there four square sixteen so this will become 20 and 2 cancels becomes 10 and this is 16 so this will become 160 joules this is your final energy so the last part will be what is the work done the work done will go in changing changing the potential energy that means final minus initial that means 160 minus 40 which is nothing but 120 joules so the work done is 120 joules not minus plus I will do work because I am increasing its energy I have to perform positive work only then it will increase its energy not negative work is that okay always change is final minus initial not initial minus final change final minus initial okay everyone clear oh understood of where you would pray Maha very good very good awesome dakshini very good crazy proud of all of you okay let's do another question let's do another question imagine if the momentum if the momentum of a body is the momentum of a body increases increases by let's say you know 100 percent then kinetic energy increases by how much percent that's the question let's try to figure this out okay I think it is directly formula based maybe I just need to be careful about the calculations of percentages and all of that momentum and kinetic energy how are they related kinetic energy is the momentum Square by 2m that is the formula okay fine now according to the question the kinetic energy sorry the momentum increases by the momentum increases by hundred percent so the final momentum will be initial momentum plus that increase which has happened plus that increase which has happened how much is hundred percent of P if I tell hundred percent of stressor means complete if I say 50 percent of stresser means half the body 25 percent hardly anything 75 percent hundred percent fifty percent seventy five percent hundred percent ninety percent eighty percent guys obviously it means P only so final momentum has become 2p okay final momentum final momentum has become 2p so my dear students what will be the final kinetic energy it will be 2 times of P whole Square by 2 m okay 2 square is 4 and what I'm left with now what I am left with now is P Square by 2m now observe carefully this P Square by 2 m is exactly the old kinetic energy so it is 4 times the old kinetic energy so this is your final kinetic energy guys this is as good as saying it is K plus 3K so what does this mean this is the increase this is the increase right so the final kinetic energy is original plus 3K so how much is that increase it is basically three times or 300 percent that is the answer exactly three times or in percentage terms 300 percent of that excellent day that's all you have to think that's how these questions come usually in neat exam moving on to the next part and this is the last few things okay that we are going to see and that is power now let's go to Power ful how fast you can do work so power is all about how fast work is done work is done it is also rate of doing work rate of supply or basically doing or basically losing energy or work energy or basically work that is what power is so strictly speaking the formula for power is d w by DT now work done why DW rate of doing well rate means always with respect to time now d w by DT I can also write it as Force dot displacement with respect to time because work is forced into displacement this is small work so small displacement this dot because that is how it is force I can separate these terms and write it beautifully as d s by DT now what is radius by DT what is d s by DT it is nothing but velocity rate of change of position displacement its velocity so power is also Force dot product with velocity as simple as that either use this formula or use this formula it's one and the same thing if you talk about power it is also a scalar quantity because you can see dot product dot product means scalar product answer is scalar answer is scalar jaromatic classes here regularly thank you so much okay then also another thing is the unit one joule of work if I do it in one second it is called one watts of power and there is another unit which is called horsepower one horsepower is roughly speaking 746 Watts 746 Watts something which you should know very simple okay everyone with me all right also remember one more thing power can also have signs like this power can be positive definitely in the case of force which is parallel to the velocity so force is basically parallel to the velocity or making an acute angle then you will see Power is basically positive there is another case where the power can be also negative that means you are sucking away the energy so either the force is opposite to the velocity or the force makes an angle which is obtuse with the velocity just like work guys and there is another case where the power can be a big fat 0 0 then you will see the force will be perpendicular to the velocity or there is no Force only one and the same thing yes there are many memes on what and I was seeing one funny conversation between two British people um one guys sir one guy's name is not or surname is not last name is not another guy's name is uh what he's like hi my name is what they're like okay what is your name he's like yeah my name is what then he's like no what is your name sir my name is what then this guy's like uh who are you I'm not no I'm not asking who are you not who are you he's like no my name is not what are you saying okay I'm I am what so a very funny conversation between two British people that I was just seeing today crazy HP full form Hindustan petroleum no horsepower horse horse power okay so one average horse has a power of 746 joules per second power okay great great so let's probably see a question on this if a block if a block mass m false from rest false from rest what will the power B after Time After Time T that's the question how will the power be after time D let's try to solve this question guys so first visualize there is a mass m at time 0 it starts falling from rest so no velocity at all after some time after some time it comes down over here the same mass it has gathered some speed so there is some velocity this is at some time okay so the question is what is the power by the gravity what will the gravitational power in fact I should put what will the gravitational power be after time T gravitational power means I need gravitational force so let's show the force force is in this Direction crazy so the force will be basically weight which is mg weight which is mg okay so the power due to gravity will be Force gravitational force gravitational force multiplied by the velocity of the particle gravitational force is mg the problem is with this guy velocity how much is this velocity guys how do you find it out I think we should use kinematics because it is accelerating due to gravity so I know final velocity will be initial velocity plus acceleration multiplied by the time final velocity is V initial velocity is zero rest acceleration due to gravity G time T So V is basically GT V is basically GT so just put it over here just put GT over here so what are you going to get the power due to gravity After Time T is m g into G is G square into T that is the answer no I didn't want height because height was not given only in terms of T I can find it out okay so suddenly that won't be the answer amazing great great uh I'll definitely come up with some timetable and some timelines for all of you guys in the days to come it's a very important topic for you guys I know let's come to the last few things and that is basically first is work kinetic energy theorem and then we'll talk about mechanical energy conservation imagine I have a system imagine I have a system there are many bodies inside of it inside of it there could be you know internal forces as well between them so these are basically internal forces forces which act within the system and maybe from outside also they are experiencing something like external forces what happens is in such cases because of these forces these bodies might change direction speed Etc so the kinetic energy might change and it is basically proven that when all these forces perform well the total work changes the total kinetic energy of the system as simple as that so basically put the total work done by all the all the internal all the internal and external and external forces external forces changes changes the total kinetic energy of the system as simple as that nothing else so I can just say that work done by internal forces Plus work done by external forces is basically change in the kinetic energy change is Delta that's all so I can also combine these two as the were done by literally everything all the forces is final minus initial kinetic energy this is the main statement of work kinetic energy theorem all the forces when they do work they change the kinetic energy that's all yes now very interesting thing that you should know about work kinetic energy theorem is this if if imagine all the work done by all the forces if it is positive then what will happen guys to the kinetic energy what will happen to the kinetic energy that will also be positive change in the kinetic energy will be positive if LHS is positive rhs will also be positive this means that the kinetic energy is increasing what does it mean kinetic energy is increasing imagine some body which is being pushed like this and it is moving also like this so obviously the speed will increase this is the meaning of work done is positive same way I can say if the total work done is negative change in the kinetic energy is negative so the kinetic energy is basically decreasing decreasing example will be the body is moving here body is moving here but the force is over here so in such a case the speed is definitely going to go down that is the meaning of it is that clear everyone awesome now this was work kinetic energy theorem for all of you there is another theorem or another law which helps you solve the problem you can use either this or that I will tell you how to use both of them in the next slide but for now just observe this first of all what is mechanical energy mechanical energy mechanical energy is just simply put nothing but potential energy plus kinetic energy the sum of potential energy and kinetic energy is called as mechanical energy simple now there is a law which talks about the law of conservation how energy cannot be destroyed or created basically law of conservation of mechanical energy law of conservation of mechanical energy what does this law tell me conserve means it maintains conserve means it maintains law of conservation of marks if you maintain your pace of studies your marks neither go up nor goes down if you do something extra then it goes up if you do something bad then your marks go down so this law says that my total mechanical energy is a constant when will my mechanical energy be constant simple if evil guys who are the evil guys non-conservative Force example friction viscous drag all these tension normal these people do not do anything they might stay quietly they might be there but they should not do any kind of work they should not give not take then I will say the total energy will be conserved like you know a friction is not there or friction is not doing any evil job air resistance is not there so when I drop something all the potential energy gets converted into kinetic energy so these examples uh where you pull a bow and release the arrow the potential energy gets converted into kinetic energy so there is no loss then you will see that mechanical energy is conserved so you will see kinetic plus potential is constant and this is only true if the work done by non-conservative force is zero evil people who are the evil people friction normal tension viscous drag these people should not interfere else whatever work they do will change else else what will happen whatever work the non-conservative force will do the non-conservative force will do that will go in changing the mechanical energy basically Delta I so that will change that will change the mechanical energy of the system as simple as that let's take an example to understand this or even this theorem okay this theorem as well as this law I will make you understand using a simple question observe this simple question guys just observe imagine there is a surface there is a wall over here okay right now and just imagine that there is a spring like thing over here and there is this block it's a smooth surface this mass is coming with some speed let's say V after some time what happens this mass will hit the spring the spring will get compressed the muscle Slow Down slow down slow down slow down and stop and then it will be thrown back Slow Down slow down slow down stop and thrown back when it stops that time the spring is compressed by maximum amount so I'll show that I'll show that over here observe the spring is compressed by maximum amount the block has compressed it maximum so when Max compression happens what will be the speed it will have come to rest for a moment it has come to rest for a moment the question is how much is this maximum compression how much did it get compressed by is that clear okay so let's try to solve this question the first method that I am going to use method one is work kinetic energy theorem let me use this theorem and find out the value of x okay how do we do that okay let's draw the free body diagram let's start by it in this system what are the different forces put it up in the chat box obviously weight will be there normal will be there and spring force will be there these are the forces and the boxes motion the motion of the Box the motion of the box is over here um so if I use this theorem the total work done the total work done by all the forces is change in the kinetic energy so it will be work done by normal Plus work done by gravity plus were done by Spring Plus work done by Spring is final minus initial OK think how much work will normal do it will not do anything it will not do anything so put zero gravity is again perpendicular so nothing zero spring force is here why is it here because when I go there spring will push me this side force and displacement opposite so minus always work done spring energy Etc is always half k x square standard formula final energy rest for a moment so that means no kinetic energy minus initial half MV Square so put half m v Square minus minus half half cancels so it will become k x square is equal to m v Square that's it but I want X exactly so x square is m v Square by K so therefore X is equal to V under root M by K so this is my final answer this is my final answer everyone with me so I've ignored friction friction and all is ignored so I have assumed that all the surfaces over here are basically smooth so ignore the friction ignore the friction everyone cool okay now this was one way of doing the question believe me there is another way that method 2 is via conservation of energy conservation of energy principle so let's see how to do this whenever you have to apply this theorem no I suggest personally please make a story in your head look at the entire situation simulate it in your head think what is happening and make a story of which energy got converted into which which energy oh my mom gave me this much money I spent it here I gave it to my friend my friend gave some money in the end of the day I had this much money so make a mental calculation like that this block it was moving so what will it have kinetic energy okay it went when stopped why did you stop spring oh the spring stored the energy did anybody else suck or give the energy no gravity no it did not go up or down nothing else so can I not say that the kinetic energy of that block went into the potential energy of the spring this is the story that I made in my head see if this makes sense to you is that making sense to all of you everyone so guys what is the kinetic energy of the block is it not half MV Square what is the spring potential energy is it not half k x square half of gone so m v square is equal to k x square so x square is equal to V square m by K so therefore X is equal to V root M by K is it not the correct answer same thing but which one is giving you the answer easily which one is giving you the answer easily happy Pongal to all the kids thank you so much for remembering belated rather which one is giving the answer easily which one is more easy to understand and apply this right so usually you are going to use this not this and you're like so why did you teach it I'll tell you when I will use this because there will be some situations where this will not be so easy to make a story not everybody is a good story writer sometimes mechanical energy potential energy is there then kinetic energy is there then friction is there then suddenly some this work is done then that is done you are like confused that this is doing work or this is taking work whether this is energy is increasing decreasing you're confused in such cases avoid this go through this because this is simple because in those complicated cases where story making becomes difficult because you just have to write oh this Force this Force this Force this works this work this one positive negative positive negative this much this much this much I solve it and get the answer so this is very systematic but lengthy but it will give you the answer this one is short but if you are able to make the stories got it everyone awesome so guys that's all that I wanted to teach you today we have covered right from work to finding you know work done for variable forces and integration and area then we also went to conservative non-conservative forces we also talked about kinetic energy potential energy and there are some which is mechanical energy then we also spoke about how potential energy is related to conservative force and the relationship and their graphs and we also talked about power and how it is the rate of doing work towards the end I have shown you two methods and you should be knowing both the methods work energy theorem and energy conservation and their conditions when it is applied that all these things will be available to you in the PDF where in the telegram where in the link is there in the description box go ahead find it out you will get it and if you want more help you know where to find the crash courses or even the long term batches it's all there in the chat box just find it out and you will be able to enroll happily okay so you know what to do after the lecture is over put it up Mark your attendance even if you're watching it recorded Sarah voices lecture uh I had a lot of fun just put up a small smile you are yeah if you don't have anything to say makes my day okay and I will do that one one comment that you put right it will give me so much of energy for the next class so make sure you hit the Subscribe button so that you don't miss my next class which is going to be on Thursday if I'm not wrong and also make sure you smash the like button if you enjoyed the session of course and stay regular keep working hard use the notes and build up the confidence let's crack neat together okay that's it from my side have a good night as well as the captain share signing off