 fine all of you please do this question quickly you have suppose a string at the end of the string there is a mass m the length of the string is l okay you are pulling this mass with some force and that because of that let's say the force is f it always remains horizontal fine so this Bob moves a distance it moves by an angle of theta as shown in the figure okay the length is l you need to find the change in gravitation potential energy how much it is between this location let's say this is location 1 and this is location 2 between these two location how much is the gravitation potential energy that has changed aware h1 and h2 are not given see you can assume this line to be 0 gravitation potential energy fine so once you assume that this line represents gravitation potential energy to be 0 then the potential energy of 0.2 will be what suppose this is the height edge potential energy of 2 will become equal to mg into h fine and what is h it is very similar to the previous one where h will come out to be l minus l cos theta okay so this is a right angle triangle from here to here this length is l cos theta okay so you too will come out to be mg l 1 minus cos theta fine so you do minus you and will come out to be this only because you won't you have assumed to be 0 okay now if you assume let's say this oriental line to be 0 will delta u change will delta u which is u2 minus u1 will it change or will it remain the same I'm asking you if you are changing the line for which gravitation potential energy is 0 with the change in potential energy vary or it remains the same it remains the same right it's like this you know that you take a length you take a scale all right so if this is 10 centimeter and this is 40 centimeter you have a reading it start with 10 centimeter and ends at 40 centimeter this length which is difference between 40 and 10 will remain 30 okay it doesn't matter you can take this as 0 if this is 0 if you take that to be 0 this could probably become 20 fine so 20 minus or minus 10 still it's 30 so length which is a difference between the two readings it remains the same fine so you can assume any gravitation potential line to be 0 the change in potential G remains the same fine so that's the best part about it you can you know choose gravitation potential G to be 0 at any location and you will be able to find same change in potential energy all right so I will now quickly talk about the implication of the potential energy the last concept we have learned that work done is equal to change in kinetic energy right this is the verb energy theorem now you can modify this theorem by saying that work done can be work done by conservative force plus work done by non conservative force okay plus work done by let's say other forces fine and you can say this is equal to change in kinetic energy k2-k1 getting it all of you so I am modifying the work edge theorem only so work done by conservative force we have just discussed work done by conservative force is negative of change in potential G plus work done by conservative force plus other forces work done will be equal to change in kinetic energy fine so if you modify this you will get okay what is wo wo is the work done by other forces like you're not sure whether it is conservative or non conservative so you just you know take it as other forces see this is non conservative because work done by conservative force becomes change in potential G so this is non conservative force so work done by non conservative force plus work done by other forces is equal to change in kinetic energy plus change in potential energy okay so if I club non conservative forces and other forces together so we can say that total work done by all the other forces be it non conservative or any other force will be equal to change in kinetic energy which is k2-k1 plus change in potential G which is u2-u1 fine so this entire thing gets modified into k2 plus u2 minus k1 plus u1 fine so this is another variation of work energy theorem here we are writing the you know we are writing in terms of potential energy also till now we never factored in the potential energy we always used to take the work done by all the forces fine now what we are doing we are converting work done by conservative force okay in the form of potential energy fine so if you take potentiality of the gravity then do not find out the work done by the gravity now are you getting it so if you are taking potentiality of any force then you should not find out the work done by that force and put it on the left hand side fine so these are the other forces other than for which you have considered the potential energy okay any doubts till now please text no doubts okay so we have modified our work energy theorem and now we have written like this guys this is the equation which you have to use in every question of this chapter fine so make sure you are familiar with this and you you are able to use it freely okay u2 is the final potential energy k2 is a final kinetic energy u1 is initial potential energy and k1 is initial kinetic energy fine this potential energy and kinetic energy sum that together that called as mechanical energy all right fine and if only conservative forces are applied if only conservative forces are applied on the system or mass or non conservative forces don't do any work fine then work done by other forces will become zero this is equal to u2 plus k2 minus u1 plus k1 fine so you will get u2 plus k2 is equal to u1 plus k1 what is u2 plus k2 this is final mechanical energy this is final mechanical energy sum of kinetic energy and potential energy and this is equal to initial mechanical energy fine so mechanical energy will be conserved if there are only conservative force acting on a system or let's say other forces are there but they are not doing any work then the mechanical energy will be conserved okay now we have talked about the the gravitation potential energy all right let's talk about quickly the spring potential energy also because even this work done by the spring does not depend on the path isn't it we have already found out that work done by the spring is what work done by the spring is half k x1 square minus half k x2 square right so it doesn't matter how x1 has come and from x1 to x2 how you have gone it only depends on x1 and x2 that is initial and final position okay and hence you can define the potential energy for the spring force also okay so according to the definition change in potential energy is equal to negative of the work done by the spring okay so negative of the work done by the spring will give you half k x2 square minus half k x1 square all right okay so this is the negative of the work done by the spring and this should be equal to change in potential energy so this is let's say u2 minus u1 okay now let's say if x1 is 0 what does it mean initially initially the spring in its natural length initially the spring is in its natural length fine so if x1 is 0 this term will become 0 so what you get u2 minus u1 you will get as half k x2 square fine now u1 is what u1 is potential energy of the spring when extension or compression in the spring is 0 fine so if you assume that in such scenario if potential energy when x is 0 if you assume that to be 0 okay again we are assuming here's something to be 0 okay so if you assume that spring has zero potential energy when it is in its natural length then the potential energy of the spring will become half k x square fine so I can write down a generic thing potential energy is half k x square for a spring okay and since it is a unique point where the spring is in natural length then we are assuming potential energy to be you know 0 and since it is present in all the spring all the spring will have a natural length right so we can all universally accept that okay let us call you know potential energy of a spring to be 0 when it is in its natural length fine so if we don't have to again and again find out or again and again have to assume when the potential energy of the spring will become 0 so everyone has accepted that they will say that when the spring in is in its natural length will all assume that potential energy of the spring is 0 fine now the x x can be compression and x could be extension x can be anything fine but it doesn't matter the potential energy will be equal to half k x square the spring potential energy will always be greater than 0 it can never be less than 0 fine this is something unique about the spring potential energy which was not the case with gravitation potential energy because gravitation potential energy can be negative getting it so spring potential energy is half k x square and hence the spring potential energy will always be greater than 0 okay all of you clear about this any doubt okay that's great now let me tell you one thing where most of the student falters see potential energy due to spring at times is tricky you need to look at initial compression or extension in the spring okay this is something which many students ignore fine so spring can be already compressed so spring can have initial potential energy itself getting it for example if I have a spring like this and on top of it if there is a mass mass M so spring is compressed so it already has a potential energy initially okay so there are a lot of such scenarios I have taken the most simple example to you know make you aware that potential energy need not be zero initially all the time fine so be cautious with respect to this see now let us further look at our modified version of work energy theorem work done by the other forces what is other forces other forces are the forces for which you have not considered the potential energy is equal to this okay now this potential energy it can be potentiality due to gravity and potentiality to spring both can be present okay so make sure you take care of both gravitation potential energy plus spring potential energy alright and usually you will have friction as the force which is other than the force for which you are considering the potential energy so this could be due to the friction could be fine so any doubts till now anything message me any doubts no doubts okay so we are all good for taking few questions