 Welcome to all of you to IIT Bombay and thanks to Professor Fatah for his very, very inspiring speech. And see we have been teaching this course myself and my colleague Professor Inamdar for over four years now and it has been very enjoyable and as Professor Fatah mentioned that what is basic necessity is that to interact with students more that is one of the things that we keep doing on a regular basis. As far as engineering mechanics is concerned we see that the you know rules are very simple as such it is a very simple course and when the students actually come to J E they already have some experience you know they already have their learning skill on mechanics. So that is having said that it is not true probably all colleges and universities. So our students tend to perform better and as a first year student they are always sincere that we have to keep in mind. So as I said what we will do over the you know period of time is that in this five days basically we are going to spend very little time on the lecture. So it will be let us say half an hour to 45 minutes lecture and that will be displayed on slides because as I said all of us are teaching and we know what are the nitty-gritty details but we will just try to emphasize where students get stuck. So that is what we are going to do more that this is what we feel in IIT that students are having difficulties at this part you know of the lecture and this particular topic. So we are going to kind of focus on that and then what happens that we will we are going to have again as professor Fatouk also mentioned that we are going to spend time ourselves to solve some tutorial problems. So as such these problems are also given in IIT to our students and then we have to also solve the quizzes. So quizzes will be let us say five minutes or ten minutes quizzes that is what we are going to do and we just flash it on the slide and we have to answer those problems in five minutes time that is all. Now I just want to know one thing that all of you do you actually know all of you have direct experience teaching engineering mechanics all of you how many of you have you know taught directly engineering mechanics please raise your hand just want to get a feeling and how many of you have taught let us say structural analysis or let us say solid mechanics type of course little bit advanced level okay so great so we have a large number who have taught engineering mechanics. Now I will just quickly talk about the syllabus that has been proposed and this is what we tend to follow in IIT and predominantly we deal with statics problem with some focus on the structural dynamics towards the very end and the reason being that we mostly try to have you know our emphasis on the force balance and moment balance so it is the entire course as if a student has a feeling that he is looking at simply a force balance and moment balance and we can do that even for structural dynamics problem so that is what we tend to do okay. So even we can discuss it out later on how to modify this and so on so forth so we have a discussion session towards the I think it will be held on Friday so we will talk about that a bit more. So with that I think what we will do quickly we will start the lecture that is first lecture will be on the introductory part of mechanics and we are mostly you know going to look at the fundamental concepts that the student already have and we assume that students should have sufficient knowledge on this type of you know these concepts. So that is what we are going to start off with and if we go to Wikipedia so what is mechanics in general all of you know students are these days very advanced so they actually look at lot of internet and you can see there are large number of NPTEL courses there are some online courses in if you go to visit some US universities we see a large number of you know open learning initiatives are there. So therefore students are very very familiar with internet options and all that thing that we have. So as such mechanics it is pronounced as mechanics so and basically what it is it is a branch of physical science that deals with the forces and energy that is as for the definition of you know Wikipedia. Now the practical application of mechanics to design construction operation of machines or tools. Now what is nice is actually the third part of it mechanical or functional details or procedure that is you know they have just given mechanics of brains. So the word mechanics has been used to also describe the procedure. So you know our take is here could be also mechanics of teaching what is the mechanics of teaching ok how do I answer to the students to their satisfaction that is what I think most intriguing for us as such ok. So now as we know that mechanics is the science which describes and predicts the condition of rest or motion of bodies under the action of forces and we know that mechanics you know is going to be required for advanced studies such as we see the you know solid mechanics that is very fundamentally important then we are going to see structural design analysis and machine design and so on so forth ok. What are the branches of mechanics we have statics and dynamics these are the two typical branches where statics is mostly going to deal with forces that is under rest that means all the variables are time independent whereas in dynamics all the variables are time dependent. So these are the broad ways to think about mechanics to discipline some mechanics, statics and dynamics remember so why do we need an elaborate course on mechanics and as I said the rules are very very simple and we give a flavor to the students that ok look this is simply going to be force balance and movement balance. However things are very complex because most of the mechanics problems deals with interaction multi body interaction that is interaction of forces ok. So therefore we need to really tell students that how we typically solve the problems by taking into account the multi body interaction. So this is what we have to you know ensure that we give them a good understanding on how to deal with the complex problems remember one of the important aspects would be concepts of appropriate free body diagram. So whenever we are solving we have to make sure we tell them that the free body diagram is the most important thing that they should do ok. And the type of books we follow we basically follow three books first one is B. R. N. Johnston second one is by Shames and the third one is by Meriam and Craig. So these are the three books that is followed that are followed in IIT and we have to acknowledge these books because what happens is that we also have taken many problems in fact some of the lecture slides are directly taken from you know these authors. So we have to acknowledge those and some of the useful links that we give it to our students is howstuffworks.com very important link they are actually you can see you know all the animations are there how things are moving how things are behaving lot of practical problems are there that gives an instant feedback visual feedback that what is happening with this problem. So this is a very important website the other website is it is actually open learning initiative by Carnegie Mellon University in US. So they have a very nice website where you know both teachers and students can actually enter so they have to register and you can see large number of you know problems are there. So we have taken also some help from this particular website. So the first thing that I will be doing very quickly is that going through some of the fundamentals as an as I said that all of us have to ensure that students are actually these are these are kind of prerequisite for this course. So we make sure that students know you know already aware of water dimensions water vectors and scalars they are familiar with parallelogram law Newton's law principle of transmissibility and system of units. So these are the six things that we expect that student have a good grasp of it. Now as far as dimensions are concerned we all know that there are three independent dimension that is related to space, time and mass. These are three independent quantities that we have these are actually absolute concepts and we have also force now force is not an absolute concepts rather these are related to mass and time right. So they are actually dependent on the other three dimensions that we have ok. So vectors and scalars so we know that vectors will should possess both magnitude and the direction and as well as vectors should be added according to the parallelogram law ok. So ultimately if we look at p and q two vectors then the diagonal that it forms right. So that will be the diagonal of the parallelogram similarly scalar so scalar has only magnitude no direction then we come to the Newton's law we have Newton's first law. So Newton's first law is state that every particles continues in a state of rest or uniform motion in a straight line unless it is compelled to change that state by forces imposed on it ok. And the second law is basically force equals to force is proportional to acceleration. So we have that proportionality constant which is mass. So this one this first law actually brings in the essence of statics. So we can also restate as that if the resultant force on a body is zero then the body should be addressed or it will be under uniform motion ok. And the second law brings in the concept of inertia right. So we state that there is inertia force that is mass times acceleration. Now when we look at also in a you know in structural dynamics type of problem that inertia force we say that this is going to actually oppose the motion. In fact we can treat the dynamic problem as an static problem by simply in the free body diagram we can say that the force is taken in an opposite sense to that of a motion and we can handle the problem in a static way. In Newton's third law every action has equal and opposite reactions and finally we have Newton's law of gravitation that is coming into play and through that we actually know that there is a gravitational constant right. So now next comes to the principle of transmissibility. So that is another important concept that we have. So what it is is that conditions of equilibrium or motion will not be affected by transmitting a force along its line of action right. So that means if I have a body and I have force F I can actually transmit it anywhere along its line. So force as such has a infinite line of action and there is a very nice example here. So just to you know demonstrate that let us say we talk about this truck in a simplified manner we apply does not it does not matter whether I apply the force in this way in the front of the truck or rather I pull the truck from the front or I push it from the back. That means my line of action remains same and force can be transmitted anywhere in the line of action. Now once we tell that then what comes into play as long as equilibrium is concerned it is absolutely fine. But when we are actually interested in the deformation of the body which we tend to do in mechanics of solids let us say then can we apply that rule the answer is no. So what it is that if I take a pin and if I really pull it at the two ends of it what is my total deformation the internal deformation that is taking place will not be equal if I apply if I just put this force in the middle and try to pull it. The two deformation will be absolutely different and that is what we have to you know keep in mind we have to tell students look you can do this absolutely fine. As long as you are simply interested in the equilibrium but when it comes to the internal deformation that is not allowed. So the units very important you know we tend to emphasize again there are two system of units one is the SI unit another is the US units. So here we represent it by kg, mass and second and here it is going to be slug, foot and second. Now why we tell this repeatedly to the students that try to be very consistent with the conversion between one unit to the other unit if it is required in the problem. However in general we give the problems in SI units but you look at any authors in US actually they will have the books in FPS units. So therefore in some cases we may have to convert this FPS unit to the SI units and remember this was a very interesting fact that happened this NASA Mars climate orbiter this was the first weather satellite now two teams are working actually one was using SI unit another one who is in FPS units. What happened that when the you know satellite was launched it actually crashed because one team forgot to actually convert the FPS unit back to the SI units. So we again try to kind of emphasize this effects that how important these are when it comes to solving the problem. So what is the idealization of mechanics that is most important that we all know that we are actually going to look at rigid bodies. So we assume it as a rigid body why is that. So for example first of all assume that this is a beam on a support I apply a force. Now what I do I only consider that there is a pure translation and pure rotation to the body that is only possibility. Now we do not actually consider the actual deformation that can take place or we rather assume that the deformed geometry and original geometry they remain same as long as we try to solve for the forces to the equilibrium. So here my intention would be to really solve for the support reactions let us say. So it is not necessary that we have to calculate in each step how this force is actually changing its direction as the body from its original geometry assumes the deformed geometry that is going to create very big problem for us as such in non-linear mechanics that is done in practice. Ok but here we assume the deformation is very small therefore the body preserves the original geometry and we make a rigid body assumption. So how do I solve the problems? So first of all a problem will be given with a data with the proper geometry and a figure that shows all the quantities. We are really going to tell that this part is the most important part that is as soon as I have the problem in hand we should draw a free body diagram which will clearly show all the forces both known forces and the unknown forces that has to be done at the very beginning. And next would be just to apply the fundamental principles that means we are going to you know use the equations of equilibrium or equations of motion to get the forces. Solution check one of the important point that I discussed is that units. Students can easily look at am I getting the correct units back or not that is the first thing. Second thing is that every problem should have a logic and what we feel that students should be able to examine the answer whether they got it correctly or not through the intuition. So they have to really examine the answer with the intuition it is not that they have to make sure that ok my final number is correct let us say but the direction direction is very very important am I getting the direction correctly am I getting the position of the you know let us say resultant force correctly and so on so forth. So logical conclusion has to be there for each and every problem ok and therefore this is most important thing that can only be learned by solving a large amount of problems different types of problem we have to solve to get this experience and skill as the as we go through you know this topics. So again I will just quickly go through different types of problems that we will see actually in this course and remember why we are doing engineering mechanics as I said that this is basically modeling of real life problems. So there are many you know we are really trying to make a backbone you know model of the actual problem. So we are trying to simplify that model therefore what is most important is that to get the you know supports connections those things very accurately in the free body diagram. So in that way you can also think of you know in a reverse way we can tell students that ok I have a problem I really want to create a very simplified model of that that will give me the solution of the problem in a reasonable manner. It can be other way around engineering mechanics can help them to design actual and experiment for example what is a roller let us say what is a hinge how do I make those in the lab. So these are also important aspects so they are actually kind of contemporary to each other solving a real life problem and going from engineering mechanics to the demonstration in a laboratory environment. So for example we can quickly show here this is just a handy train can I actually solve the force in this hydraulic cylinder first of all why this hydraulic cylinder is here and second how do I go about solving this problem ok. Finally we can look at a draw bridge you see lot of you know places in Europe actually they have this kind of draw bridge what it does actually help in maneuvering the boats or small ships once they come once they passes you know through this small channels or river. So ultimately see again this is a bare you know backbone model very simplified model of this draw bridge ultimately we are going to apply a force and therefore through this force depending on the amount of this force we are going to get equilibrium configuration back. So for example can I get the force in this cable in this model again right or how much force is required for example to hold this body in equilibrium configuration given equilibrium configuration ok. So like that we can see that this is another problem these are some of the real life examples that is a ladder climbing how do I approximate this problem ok. So again supports and connections plays an important role and how we are going to take the effect of the forces on the body that is what we tend to demonstrate to the students. When it comes to robotics this is a very nice problem you know students are given to come up with a model of a arm it is a robotic arm. So what it is actually there is a competition that kill as many good guys as you can ok. So there is a eliminator who is actually going to kill as many good guys as you can. So ultimately I have to design this robotic arm to help the good guys in the neck as long as I can lift them up it is fine competition is over. So ultimately what is happening the force that is required that is really this is called the pincer force. So that force that I am going to apply depends on the friction force that is coming at the interface. So students can actually you know think of this way that ok these are the type of problems I am going to solve in this course. Remember this is a very nice website because there are a lot of robotic competition even IIT also have you know one good competition that is tech faced you know robotics competitions comes into play. Some of the you know aerospace side we can just say ok what is the aerodynamic lift force that we have in this wings part how do I actually approximate that aerodynamic force. So ultimately again this is a very simplified demonstration to tell that ok as long as I can I know what kind of supports are there in the wing which is connecting the body with the wing then if we know the loading pattern on it can I actually solve for the support reaction. Similarly how to model a bridge problem let us say we have you know these are actually supports we take these supports right here then we can also have the connections. These connections are also modeled here and we have the distributed uniformly distributed load that is placed on the wing. Some other examples are on the vibration side and probably car is a very good example on when it comes to the vibration basically what the intention here to tell that ok we have the you know suspension system that suspension system can really be modeled as a mass spring and damper and from there if we really look at those problem that is what we are going to learn in this course. So the mass spring damper system can we derive the equation of motion can I get the natural frequency if there is a forced vibration can I get the displacement velocity acceleration and so on so forth ok. So the idea is that give a large number of problem just at the very beginning of the introduction to give them a flavor is what we are actually going to see in this course. Important thing numerical accuracy see numerical accuracy of a solution will depend on two things one is the accuracy of the data given and the another one is the accuracy of the computations performed. See the solution the actual solution cannot be more accurate than less accurate of these two I am given with a data. Now data is usually given in the book I do not know how it is transferred from the field to the let us say book but some random number is given let us say data is correct ok. Then the choice is whether we have the computations performed correctly but in these days we use the calculators with a large number of decimal places. So as such computations are not going to give any truncation error. So whatever error that we see in engineering problem is coming from the data actually how we data is taken to the real life problem. So we see that we tell that the you know appropriately we just record the parameters beginning with one with 4 digits and with 3 digits in all other cases. So these examples are given here. So just to avoid the truncation error we have to take into account certain number of decimal places when we are solving the problem.