 So, now let's talk about tension, right, so as I said before, this is not the tension which you guys have during the exam or before the exam, this is a tension force, so what is tension force? Let's study. So, look at this figure, what do you see there is a container and if you notice the container is being lifted by lots of cables, steel cable they are and you can see the arrow, right, arrow direction, so notice that direction of arrow. That is where the tension is going to act, ok. Now steel cable experiencing tension and so is the container attached, so you know along that cable there is a force which is acting and that is called tension force. Look at this example, so here what is happening, there is a tug of war going on, ok. And so hence the team is pulling the rope here, if you notice this is the rope being pulled and hence the rope is, you know, so when you are pulling the rope back, the rope is pulling you forward, isn't it? And that is where the tension is acting, right, so when you are pulling the rope towards you, the rope is pulling you towards the other side and the force then is acting along this line, so this is the tension force. So rope is experiencing a tension force right now. Now look at this suspension bridge, so you can see there are lots of cables which are trying to hold the bridge at its place. Again these suspension cables are experiencing a force which is called tension. Now again you would have seen a crane very often, so hence the chain which you can see over there is experiencing tension, right. So what is this tension force? So tension is a contact force which acts along one dimensional connecting objects if you see, you know, you can, when I say one dimensional that doesn't mean that there will not be any second dimension, what I mean here is the length will be much much higher than its, let's say, breadth or width, okay. So then typically these kind of objects will be called as one dimension because one dimensional because it is very dominating in one dimension but the other is significantly lower as compared to the first dimension. So hence here you can see the length of this rope is much much higher than let's say the width d or the diameter d. So these kind of objects will be called one dimension, so you can see the steel cable here or the rope here or the steel cable again here or the chain here, all are examples of one dimensional object because the length is significantly higher than the thickness. So when such thing, whenever these kind of objects are attached to any other object then and they are in, you know, when they are tight that is also important, right. So just because there is a thread attached to an object there will not be any tension, it has to be tight first of all and it should be a single dimension object. Whenever that happens, whenever there is such kind of contact established then we say that the string is under tension. So let's say if you suspend something from sitting, so this string is experiencing tension, right, from what? From this object underneath and from the contact above, isn't it, where it is connected. So the entire string or the cable is under tension, okay. So if you just observe the string, let's say this is the piece of string which is there. So there will be one force acting upwards or pulling it upwards and there will be one force pulling it downwards. This is what, let's say this is the string and someone is pulling it down and someone is pulling it upwards that is then, then we say the string is under tension. Similarly, let's say there is a chain, there is a chain, chain, something like that, there is a chain and this chain you are pulling towards this using some force F and some other friend of yours is pulling it in this direction, another force F. So we say that the chain is under tension or there is some force tension which is being applied on the chain, okay. So now, at which point does the tension act then? Now it acts everywhere actually, so what does it mean? So if you cut any cross sections, if you cut it here or here or here or here, you will experience the same amount of, or some tension there, right. Same amount or not depends on the mass of the string and the, or the string rather. So but then assuming that it's very light string then you will see that everywhere same amount of tension is acting if the string is massless, okay. So that we will study why it is in Newton's laws later, but for the time being please understand if the string is massless then there will be tension at any point the tension will be same. So at any point tension is going to be same like that, right. So any point if you cut this string here or here or here, you are going to get the same tension provided the spring or string is massless, but if it has some mass then you are not going to get the same tension everywhere, but there will be some tension force at every point in the string. I hope this is clear, okay. So in which direction does the tension act? It always acts along the length of the connecting object whether it is rope, chain, cable whatever, right. So in this case you can the arrows show you the direction of tension. So I have shown two directions, two ways why two ways because let's say this is the cable and it is hanging from ceiling and it is being pulled by a mass downwards let's say whose mass is m, okay. So if you only consider the string over here let's say we are drawn only the string only the string. So what is happening? There is a contact here. The contact of the ceiling is going to pull it upwards there is some force applied by ceiling onto the string and there is some force applied by this mass by the mass so hence the string is being pulled downwards, right. So there are two forces which are acting hence the double arrow. So double arrow means the tension one side the string is being pulled like this and the other side the string is being pulled by like that and hence it is under tension, okay. Now let's talk about spring force. Now what is spring force? Again very common force in our day to day life. Where have you seen a spring guys in your day to day life? Let me enumerate them for you. So these are the cases, common cases which you have seen. So these are suspension spring if you can see this is underneath your vehicle. This is a spring here in your bicycle there is a spring here in your bike motorbike and there is also spring in the train wagon if you can see this is these are the springs are used. And you know the uses of all of these springs why are these springs used? They are used as shock absorbers, isn't it? So that the comfortable ride is ascertained, okay. Now these are the springs. Now these are vehicles for suspension. Now you would have also seen springs here, isn't it? If you dismantle your jotter pen you will see a spring over there as well. So many a times in our childhood we used to take it out and play with it, isn't it? Now similarly if you would have seen a stapler again, so in the stapler again this spring is there which make sure that the pins are at its are their right places before you go for stapling, isn't it? So stapler also has a spring you can check that out. These are some different types of springs which you see have come across this is called tension spring this is called compression. Why is this tension? It will be pulled, you know, so for example in lifts and all you will see these kind of tension springs. Compression springs are what you are used in shock absorbers. These are spiral spring which you would have seen in your toys to, you know, make the vehicle toy car move on its own. These are some kind of torsion springs. If you have seen a clip which we use for, you know, putting it on our clothes when they are, you know, spread on the wires for drying you would have seen those clips. So these kind of torsion spring are used in those clips. These are examples, some other types of examples are called leaf spring which is there in your trucks and bigger vehicle heavy vehicles. This is something called wave spring. So this is another type of spring which is typically used in machinery for example in your mixer grinder kind of a thing where let us say you want to seal off the wet portions of the machine from let us say electrical connections. There is where you will see this kind of spring are used. So these are all industrially used. These are different types of springs. You know, springs were studied by, you know, or basically the, you know, these are nothing but elastic, elasticity. So basically this concept was studied in detail by a person named Hook and he was contemporary of Sir Isaac Newton in Britain, okay. Now what did this guy observe and what did he suggested? So let us say there are these three cases that there is a spring and these are three different status of the spring. So in the first case, the spring is unstretched, okay. So let me first elaborate more on this. So this is a system of massless helical spring. Now this is an ideal case but we start our discussion on, you know, with ideal case where we are assuming that the spring is having no mass whatsoever or very light mass, very, very small mass, right. It's a helical spring attached to a wall on one side and a block of mass M on the other. Now this is case one. So spring is unstretched. So there is no deformation in the spring. It's in its natural length. So X naught here is the natural length of the, natural length of the spring. The spring is applying zero force on the mass right now. Because unstretched spring will create no trouble for you. So it's applying no force here. So there is no force whatsoever on the adjacent mass M. Now let us say that you pull these springs because of the help of some external force towards the right and leave, leave that mass after stretching the spring. So right now the spring is under stretched condition. So X1 here is the stretched length of the spring. That is how much extra it has gone. It has, it has been stretched by X1 minus X naught. So right now this is a stretched length. So the new length is X1. So the extra length which was added to the spring by pulling was X1 minus X naught. I hope you understood this. The spring is applying a non-zero force towards the left. Now what is the tendency now? So you can see this arrow. Now this arrow means there is some force now non-zero force by which the spring is pulling the mass M towards itself towards left. So basically it wants to come back to its original shape. And that is what is called elasticity, elasticity. So the spring is trying to retain its original shape. So if you remember we talked about inertia. So spring also has inertia. It does not want to get deformed. So if you try to deform it, it will try to come back to its original shape. That is, that is called, that property is called elasticity my friend. So because of that elasticity, the mass is going to come back, go back. And the spring is going to get to the original shape. If on the contrary, if you push this spring inwards, now you are compressing the spring. So again what will happen? The spring will try to come back to its original shape. So again there is a spring force which is acting now in the reverse direction. So initially, when you are moving the string towards right or pulling, stretching the string, then the force applied by the string is towards the left, isn't it? It starts pulling. If you move the spring to this direction, then it will start applying a force in the opposite direction. So you can see there is a change in two directions, there are two different opposite directions. So what does it mean? If you push the spring, it will push you back. If you pull the spring, it will pull you back like that. So hence the spring applies a force in the direction opposite to the direction in which it is come, you know, moved, is that understood? So that is what it is, that is what is the nature of a spring. Now friends, you would have noticed I have given you an expression or relationship which is f is equal to minus k times x. Now this k is called spring constant which is related to the elastic behavior of the spring. It depends on the geometry and the material of the spring. So every spring will have a different k value. So I will be showing this in a demo after some while. So higher the k, higher the stiffness constant is also called stiffness constant. So higher the stiffness constant of the spring, it will require more amount of force to move by the same amount of distance. So we will be discussing this again in much detail when we are taking a friction separately and sorry, the spring force separately. So that again you will see that. So what is f? f is equal to minus kx. So what is f in this case? f is spring force my dear friend. So the force applied by spring onto the object. What is k? k is called spring constant. It is a characteristic constant for one particular spring, depends on its geometry as well as the material which we have used. And what is x? x is defined like this, the extra stretch or compression in the spring not the new length of the spring mind you. This is the extra length which you introduced by pulling or extra length which you reduced by compressing the spring. I hope that is clear. So this is difference in the new length and the original length is called x. Now y is there minus sign. So if you see the minus sign indicates that the direction of spring force on the object is opposite to the direction of the displacement of the object, is it not? So when x is this way, this is x direction, then spring force is going to be in this direction, hence opposite. Similarly when x is in this direction, so spring force is going to be in this direction, hence opposite. So hence minus sign is to indicate that the spring force is opposite to the displacement of the object which is attached to it. That is what is called Hooke's law my friend. So we are going to, you know I am going to describe this Hooke's law with a simulation. The link of the simulation will also be given. So you use the simulation and see how for different k values, you know you have different, let us say behavior of the spring and that you can simulate by changing the k and x values and see for yourself. So with this, we come to an end of the different type of contact forces which we are going to study. All these forces will be taken separately for detailed analysis and study, but so far for understanding of the Newton's laws of motion, this bit of knowledge is good enough. So now we will be moving towards the next step and that is we will first define the units of force and post that, we will talk about some historical background of laws of motion and then we will talk about laws of motion. So I hope you understood this session as well. So this is the simulation for Hooke's law guys which I was talking about. So in this case, the simulation says that the initial spring force is 50 Newton. So there was an external force which stretched or compressed the spring with 50 Newton force and then it released, it released the object over there which is shown like this. And the spring constant has been taken as 1 and let us see how does this spring behave. So when I press the animate button, you can see the spring is now oscillating or the mass is oscillating, the spring is compressing, getting compressed and then getting stretched like that. Initial amount of force which was provided was 50 Newton and because of that this is the behavior of the spring. Now what we can do is we increase the value of let us say k and just observe what is happening to our the object which is there. You can see now the swing is little stiff. So hence it is not that smooth it was earlier. So hence if I keep increasing the value, you can see it impacts the motion of the spring heavily. So hence higher the stiffness and then you can see the same amount of force will not be able to move the spring for a larger distance. So this is stiffness constant or spring constant. As I reduce it, then what happens now you can see the swing has increased. So hence if the spring constant is low, the spring is with the same amount of spring force initially which was applied, now it is having more span or what we call technically as amplitude of this swinging object has increased. So this is what I was trying to show you. So hence if I reduce the force, let us say initial force I have reduced and again because of that also you can see if I reduce the force also you can see the now the spring has come to stand still because now there is no external force which will initiate the motion. So the moment I increase it and you can see very small amount of movement. So hence larger the external force initially will provide it is going to go or it is going to swing more. So this is what the simulation suggests. Let me stop it. You provide the link to this simulation what you can do is you can test it for yourself.