 We've talked about work and energy for quite a while now, but it's time to answer the big question Why did we introduce these concepts? Because as we will see this will help us look at the world in a completely different way So let's take an example Imagine you take a bowling ball in your hand and let's say you throw it What's gonna happen? Well, that ball will speed up as it leaves your hand. Now if we ask the question, why did the ball speed up? What is the answer? Well, we can say well when you are throwing that ball you are pushing on it So you put a force on it and whenever you put a force on a on any object that object accelerates and therefore It speeds up and that's why the ball became faster and This is in accordance to Newton's second law. It says F equals ma Which means force will accelerate a body of course if there are more than one forces Then we have to calculate the net force, but we'll talk about that later Let's consider only one force as of now. So you're putting a force and that accelerates the body That's one way to think about it. Now. Let's think in terms of work done You see because you are pushing on it and you're displacing that body you're doing work on that ball, right? And when you're doing work, look at what happened to the ball initially it had no speed It had it was at rest so it had no kinetic energy But then after doing work notice it has gained kinetic energy So we can now say that by doing work. We have added kinetic energy to our bowling ball and So by doing work whenever a work is done on an object Kinetic energy gets added to that object. This is the new way of looking at the same situation Now you can also do work and remove kinetic energy if you want For example, imagine a ball is thrown at you and you try to catch it Now when you try to catch a ball like this again, your hand will move back a little bit Now think about what happened when you try to catch that ball your hand will start pushing it But this time it pushes it in the opposite direction and that's why it's slowing it down, right? But nothing about the work done Because you're pushing it in the opposite direction to the displacement work done is negative And now when you're doing negative work look at what happened to the kinetic energy the kinetic energy reduced So we can now say when you do negative work, you are removing the kinetic energy from the body so negative work removes kinetic energy from the body and This is crudely speaking what we call the work energy Theorem it basically says when you do work You either add or remove the kinetic energy from the body if you don't do work at all Then the kinetic energy will not change Of course, we'll derive the mathematical version a little bit later, but before we do that. Let's look at some more examples Let's say now you take that bowling ball and you drop it from some height now as it falls down It's going to speed up again, let's look at work in this case in this particular case gravity is pushing down on that ball and Make and the ball is moving in that same direction so gravity is doing positive work and Because gravity is doing positive work. It's adding kinetic energy to that ball and that's why the ball is feeding up Similarly if you were to take that same ball now and throw it up. Let's say you threw that ball up Now as that ball goes up, you might know it slows down Again, what's going on? Well, again gravity is pushing down on that ball. Remember gravity always puts a force downwards But this time the ball is going in the opposite direction So gravity is doing negative work and as a result gravity is removing kinetic energy And that's why the ball is slowing down This is pretty cool, right thinking in terms of work and energy Now things get even more interesting when there are more than one forces acting on the body So if there are more than one forces acting according to Newton's second law We need to now calculate the net force Meaning we have to add up all those forces Well, of course if the force in the same direction we add them if they're in the opposite direction We subtract them but anyways you calculate what the total force on that ball is and that will tell you what will be the Acceleration of our body, right? Now similarly if there are more than one forces acting on the body You calculate the total work done by all the forces and now that decides what happens to the kinetic energy So if that total work done by all the forces becomes positive Kinetic energy will be increased add kinetic energy gets added If that total work done ends up becoming negative that means kinetic energy will be removed And if the total work done is zero, which is totally possible Some forces can do positive works others might do negative work and we'll look at some example Then the total work done can be zero in that case kinetic energy will not change at all Again, let's look at a couple of examples of that Let's say there is a cupboard on a very rough floor very heavy cupboard and you want to move it So you start pushing on it. Let's say as you push on it. You slowly displace it from here to here Now after displacing after after you've pushed it the cupboard is still at rest So let's think about the kinetic energy Initially the kinetic energy was zero. It was at rest after pushing also the kinetic energy is zero So the kinetic energy didn't change at all So it was neither added not removed that means the total work done on this cupboard was zero Why clearly you pushed on it you did work then why is the work done zero? That's because there are more than one forces acting over here. So you are pushing on it and You are doing positive work But because the floor is rough Friction is pushing on that cupboard in the opposite direction doing negative work So you are doing positive work friction is doing negative work So it just so happens that the two work done's cancel out total work done ends up becoming Zero and that's why the kinetic energy didn't change at all Another way I like to think about this is when you're doing positive work I like to think that you are adding kinetic energy to the cupboard But at the same time friction is removing that kinetic energy from the cupboard and that's why the kinetic energy didn't change at all Okay, let's do one more say I take this very cute puppy which is initially at rest. It's at rest right now I push on it and I raise it up slowly and Finally again, it's at rest So even here the kinetic energy did not change that means the total work done on this puppy is zero But why clearly I am pushing on it and I'm making it move So why is the total work done zero? Can you pause the video and think about this one? Well again, I am pushing on it and I am doing positive work and I am trying to add kinetic energy to this puppy But there's one more force acting on this puppy which one? gravity gravity is pushing down on that puppy and As a result it's doing negative work because it's in the opposite direction of the displacement And so gravity is removing kinetic energy from the puppy at the same time So I'm trying to add kinetic energy gravity is removing the kinetic energy and that's why there is no change in the kinetic energy at all So my positive work is cancelled out by gravity's negative work making the total work done zero So now that we have some idea of the work energy theorem Let's go ahead and derive the mathematical equation for it. This will be useful for problem solving All right, so I need to connect work and kinetic energy, right? So again, let's start with just one force if there's one force acting on the body Then the work done by that force the work done would be the force Multiplied by the displacement. Let's call the displacement as s Okay, what do I do next? Well, I want to somehow bring velocities into the picture because I want kinetic energy, right? And I can do that by substituting f equals ma because that's how acceleration comes and then from acceleration I can bring velocities. So if I substitute f equals ma, so I'll get m times a Times s But I don't want acceleration and I don't want displacement. I want velocities so can you think of a connection between acceleration displacement and velocities initial velocity and final velocity Yeah, go back to Equations of motion think about this great idea to pause the video and see if you can remember an equation Well There's an equation v square equals u squared plus 2 a s This is perfect because this will help us connect a s and write it in terms of v and u So I want to get rid of a s, isn't it? So let me isolate this on one side and put everything else on the other So if I rearrange this we'll get v squared minus u squared divided by 2 That equals a times s, right So now I can substitute that over here So that'll give me M times a s is v squared minus u squared divided by 2 oops Let's use the same color U squared divided by 2 and now if I open up that bracket see what I end up with left-hand side is work and that equals MV square by 2 What is MV square by 2? That's the kinetic energy Final kinetic energy so we can call it as the final kinetic energy Minus you get MU square by 2 what is MU square by 2 that will be the kinetic energy Initially before I start pushing it and this is The work energy theorem mathematically It's saying the same thing that we discussed already if you do positive work Notice the final kinetic energy will be more than initial That means you're adding kinetic energy if you do negative work. You are removing kinetic energy This equation is also telling that if you do 100 joules of work as an example Then your kinetic energy will increase by 100 joules. So you're you add 100 joules of kinetic energy Similarly, if you do 100 joules of negative work, then you will remove 100 joules of kinetic energy So you can kind of now see what work really represents when you do work on a body What happens to that body? It's kinetic energy changes So whatever work you do that much kinetic energy gets added or removed and again If there are more than one forces acting on the body what happens now You just have to calculate the work done by all the forces So we can say this will be the total work done or we can say this is a network done So the total work done on on a body will decide how much kinetic energy gets added or removed and We will see in future videos that certain kinds of problems can be solved much faster by using this equation Rather than f equals m a Okay, so to summarize what did we learn in this video? We learned the work energy theorem Which is basically saying that when you do positive work on a body You add that much kinetic energy to the body and if you do negative work on that body You remove that much kinetic energy from the body Of course if there are more than one forces acting on the body Then you have to calculate the total work done and that decides how much kinetic energy gets added or removed