 hmm let's take a question now guys going forward I am assuming that you guys will use this particular relation although you can solve the same question by just using total work done is equal to change in contingency you don't need this particular relation but then since we have derived it okay and when it comes to spring using this relation is easier than using work done is equal to k2 minus k1 so try to use this particular relation get familiar to this because you know at times this will give you a quick answer all right so all of you draw this figure there is a mass m like this spring with spring constant k is there okay so mass m is released from the rest from a height h as shown in the figure it slides and compresses the spring of stiffness k you have to find the maximum compression in the spring okay find out the maximum compression in the spring quickly root of 2 mgh by k see whenever you use work energy theorem you are using it between the two points point number one and point number two you can pick any of the two points fine so I'll take the two points where the point number one is this and point number two is where the spring get compressed maximum right so spring will get compressed till the velocity of mass m goes to zero fine so at the maximum compression the velocity of mass m will become zero fine so let's try to use this particular relation only so what done is what zero gravity is doing the work but that work you are considering it as a potential energy fine and you're saying that this line this line could be the logical point the line for which you are assuming gravitation potential to be zero fine so you one is what initial potential g will be equal to mgh fine k1 is zero it was at rest okay then you do is what finally the block comes to the level horizontal level where I mean that is a level where you assume the gravitation potential to be zero so this is zero this is gravitation potential energy but then there is a spring potential energy at point two initially there was no spring potential energy now there is a spring also so spring will gain a potential energy half kx square and we know that k2 is zero so u2 has two potential g spring and gravity so if you substitute it you get zero is equal to u2 which will come out to be half kx square gravitation potential is zero so this plus k2 is zero minus u1 which is mgh plus k1 which is zero fine so from here you'll get the value of maximum compression in the spring which will come out to be two mgh by k okay let's take up next question you guys have any doubt on this particular question any one of you have any doubts sir why is the work zero see who can do the work normal force doesn't do any work in this case because normal force is always perpendicular to the displacement it acts perpendicular to surface fine gravity can do the work but that work you are already factoring in in a form of potential energy so you can't factor factor in the work done by the gravity twice fine so there is no other force so only gravity is there and when it compresses a spring all the spring also applies a force but then even the spring force you are considering it as a potential energy fine so no other force is left that is why work done will be equal to zero because this is the work done not by all the forces but by the other forces for which you have not considered the potential energy see now let me caution you okay so there's a small caution here now what will happen is that you will develop your own version of conservation of energy okay so you will be like a friction would have been there then we will have considered right yes you will consider the work done by friction the friction is there okay so the caution is this you should write it down because this is something which destroys the chances to solve the question do not create your version of work energy theorem that you should never ever do if you start doing this you'll be always confused okay because I have seen students you know making version of work energy theorem themselves like they'll be like okay loss in potential energy will be equal to gain in cutting energy or loss in cutting edge you will be able to gain in potential energy or some random stuff okay so do not put your brain in you know for creating a formula always fall back to this particular relation before every question first write down this and just one by one find out the values u2 k2 u1 k1 and work done by other forces all of you clear about it do not create your version of work energy theorem you may get some questions right okay you may get it right I'm not saying you'll not get it right but you'll confuse yourself and you'll never be confident okay so let us move to next question in case you have any doubts feel free to message you can message your whatsapp you can message on the chat whatever you may feel comfortable and I will not take your name another best part about the online class is that you can you know secretly ask a doubt you can be anonymous so if you are feeling you know conscious when you ask a doubt I mean you can freely text me your doubts I was very conscious of asking doubts in a class so I always used to keep quiet and later on when everybody used to go I used to ask anyways so a block of mass m okay there is a block of mass m that strikes a light pan fitted with a vertical spring so there's a small pan like this it is a light pan okay it strikes a light pan fitted with a vertical spring after falling through a distance of H so it falls a distance of H then strikes this pan okay if the stiffness of the spring is K find the maximum compression in the spring get the value of maximum compression in the spring maximum compression in the springs okay what is the maximum compression no Niranjan that's not correct the one who has sent me the WhatsApp message it was not correct you can just take a pick of whatever answer you get and send me across should I do it those who are sending me answers over WhatsApp please understand I cannot chat with you I can only look at what you are sending okay so don't ask me questions on WhatsApp that I mean don't try to chat with me or you can post your doubts that is fine that I can address here guys see this is the probably the initial phases of you learning the application of work energy theorem right so start the question by writing the you know formula itself so always write this down and then start solving it right and when you write potential energy of the gravity you need to understand what point you are taking zero potential energy all right no till now nobody has sent me the correct answer no good many of you are sending me message one of you send me an imaginary answer as in root over some negative quantity that will be not correct definitely hmm who is this Sukheer that's correct let's see how to solve this particular question maybe Bharat you are doing some silly error probably the conceptually it may be correct but then does it matter so do it slowly and get it right the first time okay till now only Sukheer has sent me the correct answer fine let me now solve this particular question I want everybody to participate see you can clearly see that I have got at least 12 answers from people who have what sent me and only one was correct so don't hesitate to answer you can be wrong right now you can see that only one person was right and everybody else was wrong don't hesitate okay let's try to solve this now let's assume that when it hits the spring the spring get compressed by a distance of x so this is the maximum compression let's say x is a maximum compression fine so I'll take my second point there only this is my point number one and point number two is the point where the spring get compressed maximum all right so what I'll do I'll draw a horizontal line and I'll say that the line that passes through the maximum compression point of the spring represents gravitation potential g to be 0 fine so what does it mean u2 automatically becomes 0 and u1 will be what u1 will be equal to mg h plus x I'm talking about gravitational potential energy fine many of you might not have taken x while finding the gravitation potential g okay the u2g and u1g now there is a spring potential g finally u2s is also there which is half kx square okay so what is left now k1 is 0 right initially the object was at rest and finally also it is 0 now the one assumption we are making throughout can you guess what is the assumption we are making here when we are applying this over here the assumption we are making is that no energy is lost due to collision fine if energy get lost due to collision you cannot take point number one and point number two when the spring get compressed because in between there's a collision okay so there is no other force that is doing work other than gravity and spring for which you have already considered the potential energy right so you get 0 is equal to u2 which is a spring potential g that is half kx square plus k2 which is 0 minus u1 now there is no spring potential g initially but there was gravitational potential g that is mg edge plus x fine plus kinetic edge is 0 so you get a quadratic equation just solve this and you'll get the answer okay the answer should be this x will be equal to this is what you should get fine so I hope it is clear in case you have any doubt please message immediately any doubts so let us move to next question right let us take up the next question it refers to a figure so let me draw the figure first all of you please draw it with me small m this is a last question then we'll take up another concept so this is a scenario okay so two blocks of mass small m and capital M they are placed like this this is the ground okay they're connected by a light spring of stiffness k they kept on a smooth horizontal surface as shown what should be the initial compression of the spring what you're doing is you're compressing this small m okay what should be the initial compression of the spring so that system will be about to break off from the surface so when you compress it right so suppose you compress it up to this level okay and then you release it so when you release it okay what happens is block will try to move up because a spring force okay and when it moves up spring may get extended also fine so you need to find out how much should be this compression in the spring initial compression x0 so that capital M can break off from the surface so capital M you need to find x0 what is x0 for which capital M breaks off from the surface attempted breaking of the surface means that capital M leaves the surface capital M jumps off should I do it what is the condition for capital M to leave the surface what is the condition all of you normal force to be zero okay now if if it is placed just like that normal force will never be equal to zero because there is a gravitational force acting on it which is mg and since it is not accelerating there has to be a normal force which is equal to mg fine but what if there is a spring force upwards which is let's say kx1 and then if you balance out the forces read kx1 plus n minus mg then this is equal to zero you'll get condition when normal force becomes zero so normal force becomes zero when extension in the spring becomes equal to capital mg by k this should happen then only it will leave the surface let me call it as x2 initially it was x1 fine now try to do this with chapter from book one is going on in school know that is not correct you need not know the spring length okay because that doesn't matter spring constant is given so deviation from the length of the spring is what determines okay so we are at par with whatever is going on in school I received another answer see there will be initial compression already in the spring you need to find out further how much you need to compress it okay now let me do this I'll do this now okay so let us say that when it is kept at rest the spring has some compression right let us say x0 was an initial compression which is mg by k okay this much compression will be already there because small m is a m is sitting at the top of the spring okay now let us say that you have further compressed it by a distance of x1 okay and then released it so what will happen now is that from a compression of x0 plus x1 it should go to extension of x2 then only capital m will be able to jump off okay so this is our initial point this is our initial point and this is our final point so between these two point I'm going to apply work energy theorem fine let me take up another color pen I'm using only yellow and white how is this nice okay so fine so I'm going to first write down work energy theorem work done is u2 plus k2 minus u1 plus k1 now you'll see that only gravity and spring forces are there and both of them you are considering potential energy so this left hand side becomes 0 okay so w is 0 u2 is what the final this thing final potential energy so u2 will have gravitation potential energy let's say u2g and it will have a spring potential u2s fine so we need to first assume what is a zero gravitation potential so we can assume that the level where it is initially compressed that is the gravitation potential g to be 0 fine so I can say that initial gravitation potential is 0 fine so final gravitation potential g will be what mg into x0 plus x1 plus x2 because x1 is compression so from this much down it should go that much up it should get extended the spring so total height from this zero potential g line will be x0 plus x1 plus x2 okay I hope it is clear in case not please message final spring potential g will be half k times x2 square because x2 is the extension in the spring now all right and then I need to quickly find out initial gravitation potential g which is 0 because that's where you have assumed the gravitation potential g to be 0 and initial spring potential g is half k times what half k into what square x0 plus x1 square guys okay u2g see I have assumed this line to be zero gravitation potential g this is a line initially the block was in and right now block is compressed okay so this is initial position now finally what should happen finally this spring should get extended by x2 right now it is compressed compressed by how much x0 plus x1 so it should move up by x0 plus x1 and then further go up by x2 so if you if it moves up by x0 plus x1 it will go to the natural length and then it should go to x2 further up okay so that's how you get gravitation potential g as half x0 plus x1 plus x2 sorry mg into x0 plus x1 plus x2 that is gravitation potential g and spring potential g is nothing but half k into whatever extension or compression square is it clear now so this is u1s okay and w is 0 so just substitute this is u2 sum of gravitation potential g finally plus spring potential g and this is u1 sum of gravitation and spring potential g and anyways since we are finding the minimum compression initial kending edge will be 0 and final also I am taking it to be 0 is it clear all of you it was not a very straightforward question but I thought of taking it up is it clear kindly message yes or no if you have any doubts doubts what break Niranjan are you not enjoying it we'll see Ashutosh we'll see