 Good morning to all of you. So, we are in this two week ISTE workshop on Engineering Mechanics and we had conducted this workshop in September that was the co-ordinators workshop that we have conducted. Myself is Souvik Banerjee and my colleague is Professor Mandar Inamdar who is not here due to another academic commitment. So, as you have seen specially those co-ordinators those who were there you know we tried to you know basically cover the statics in engineering mechanics and with some touch on dynamics, but then after the discussions we have actually modified our schedule a little bit and just to start off with quickly about our background you have probably looked at our websites also. So, I did my you know bachelors from Bengal Engineering College and then my masters from this institution in the civil engineering and then went abroad at University of California Los Angeles did my PhD over there and my colleague Mandar he did his B.Tech from IIT Bombay itself and then went abroad again at California Institute of Technology to do his PhD. So, we have been teaching this course for over 5 years now and we had a very good experience specially you know jointly we taught more than 700 students at IIT. Therefore, we decided to go online with this course and see what kind of response actually we get, but as you all know that we are all teachers. So, we are not really preachers and we try to look at you know different angles from both the students perspective as well as from the teachers perspective that how we can make an impact on the student. So, as such as you will find here that I am really not going to make much movement as I will do in a course setup because I am totally bounded by lot of communication technologies here and as such that happened in coordinator's workshop also we are able to make lot of interactions. So, I am afraid that those kind of interactions can be made or not. So, what we can do at best may be if we just quickly go to the course schedule and I hope all of you have that schedule with you as well. So, we will just try to go through very quickly. So, in the schedule now you see in the coordinator's workshop we have only 5 days. So, we had to squeeze many stuff there and more or less we went to very depth you know of the topics that we have covered and therefore we could not accommodate the dynamics part in detail. So, only change that you will see that now we have dynamics as well included and dynamics will include both kinematics as well as kinetics in particles as well as in rigid bodies. So, as I said before that we are going to slow down the pace in this workshop and we will try to be more interactive and try to solve some problems together. Although we did that as well in the coordinator's workshop and the response was very good. More or less after every session that we will take we will also have a small quiz. So, as you will find here that in the afternoon slot let us say you know today itself around 5.30 after the tutorial of lecture number 2 we are going to have a small quiz. So, all the coordinators are really requested to have the you know tablet, a cast tablet so that we can use the clicker you know to get the quiz results that you can also send us for evaluation. So, with this what I am going to do now we are going to you know quickly go again back to the introductory part of the lecture. So, in the introduction so we will just go through this you know about the definition of mechanics as such. Then we are going to look at some of the fundamentals that are required and we will expect that our students are already familiar with that. So, mechanics as we know you can see now if you just type in medium wave dictionary or maybe in the Wikipedia you will quickly see that what is the definition of mechanics. So, it is a branch of physical science that deals with energy and forces and their effect on bodies. So, we are mostly going to look at you know how the body different forces on the bodies that you know lead to the condition of rest or condition of motion of the bodies. And as you will see that mechanics is going to be very important to the design construction or operation of machine or tools in the latter stage. Now remember the third point is also very important mechanical or functional details or procedure. So, the mechanics of the brain so the term mechanics is used to describe you know various aspects of procedure. So, here mostly you know we can also think about the methodology of the teaching aspect that can be also mechanics of teaching that we can actually look at how we can make some impact towards students. So, as such mechanics can be broadly described into you know two branches one is the statics and another one is the dynamics. So, statics deals with the bodies at rest under the action of all forces and all the quantities are time independent. Whereas in dynamics body is at motion under the action of all forces and all quantities are time dependent. So, although as we see that mechanics as such you know deals with mostly force balance and moments balance in general we can think that way if you leave the you know kinematics part apart all the force will come into play based on the kinematics when you are working on the dynamic side of it, but then why do we need a such an elaborate course. So, we know that there is a multi-body interactions that are coming into play and during the multi-body interactions how the force is transmitted from one body to the other body that is going to play a significant role and we have to analyze those kind of multi-body system which can be very complex in nature. Therefore, a good understanding of the fundamentals goes a long way in solving such complex problems. So, basically what we are going to deal with in mechanics that we are we will try to draw the free body diagrams as much as I can and we will try to use the equations of equilibrium or motions in case of dynamics that will be really important in the latter stage of different courses that we are going to you know students are going to take at a latter stage such as strength of materials is one structural analysis it could be machine design and so on so forth. So, mostly we are going to look at the free body diagrams in details as well as we should not forget that kinematics is going to play an important role when we talk about the dynamics. Regarding the books that we are going to follow or rather we tell the students in IIT see in this lecture sets that we are going to use in this workshop we are referring to vector mechanics for engineers that is by B. R. and Johnston. In fact, major chunk of lecture materials will be taken from these books we are going to use lot of slides those are provided to us by McGraw Hill and we believe this is a very standard and textbook that is used worldwide beyond that we are also going to follow engineering mechanics statics and dynamics by Meriam and Craig and as well as for the dynamics we are also going to use the book by Heabler. Some of the useful links that we encourage students to look into those are howstuffworks.com this is a very useful website to look at behavior of you know different machines tools or even you know different bodies how they are performing under the action of forces. So what it does basically it illustrates very fundamental you know mechanics of different types of bodies as well as there is another website that is Carnegie Mellon University there you can actually log in to have some interactive session as well. So what we are going to quickly go through are basically some of the fundamentals and we assume that students would be familiar with these fundamentals when they are entering engineering mechanics course. So these fundamentals will be dimensions that are dealing with space, time, mass, vectors and scalars their definitions, parallelogram law that will be used for vector additions then Newton's law we have three different laws that are going to be very important for solving mechanics problem principle of transmissibility of the forces and the system of units. So we are going to take one at a time and just go through this. So dimensions as you all know that space, time and mass these are absolute concepts and they are independent to independent of each other. So in such space that is associated with the motion of the position of a point P given in terms of three coordinates that means that if we want to define the position of a body at a point P then that concept comes into play. Similarly for time that defines an event. So that event will require specification of the time and position at which it occurred. Mass used to characterize and compare bodies that means response to earth's gravitational attraction and resistance to changes in translational motion. So that means we can compare how two different bodies will have two different mass based on the gravitational attraction that means gravitational force that we call m times g. So what kind of resistance they are going to put in? Force again represents the action of one body onto the another and as we all know that force is not an independent concept rather force will be dependent on mass as well as the acceleration that means variation of velocity with time. For vectors and scalars what are vectors that has both magnitude and direction? However that is not the sufficient condition we have to also say that vector should be added according to the parallelogram law. So that means if I have P and Q two vectors and if I draw a parallelogram then the diagonal should give me the resultant. So it will be added based on E plus Q and the vector quantities are displacement, velocities, accelerations and forces. So what is a scalar quantity? Scalar quantity that only possesses magnitude but not direction such as mass, volume and temperature. So next we will take up the Newton's law. What is the first law? The first law states that every particle continues in a state of rest or uniform motion in a straight line unless being interrupted or compelled to change that state by forces imposed on it. So Newton's first law is going to play an indispensable role when we talk about the equilibrium in statics as well as when the body is in constant velocity. So Newton's second law that states that the change of motion is proportional to the natural force impressed and is made in a direction of the straight line in which the force is impressed. So we can get the concept that force is equals to mass times acceleration. So the particle will acquire more acceleration if the force is large. It is going to acquire small acceleration if the force is small. So remember that Newton's first law can also be derived from the Newton's second law. If we assume that acceleration is 0 or the body is either at rest or moving at a constant velocity then we can say that some of all forces in the body should be equals to 0 and that will bring in the concept of equilibrium. And Newton's third law is that the forces of action and reaction between two particles should have the same magnitude and line of action with opposite sense. Now this is very important and it is going to play fundamental role when we are going to look at multiple bodies that are jointed together. So when we are going to draw the free body diagram then we have to take one body isolate one body and we have to see that how the forces is transferred from one body to the other body. Newton's law of gravitation so two particles are attracted with equal and opposite forces and these are again from the experimental evidences. So if we consider that a particle is actually at the earth surface then we must have the force should be equals to the mass multiplied by the gravitational constant so that gravitational constant will be 9.81 meter per second square. Next would be the principle of transpisibility. So why this is very important the reason being is that when we want to solve for the equilibrium the force can be taken anywhere in its line of action. So that means without affecting the equilibrium or motion I can transmit the force anywhere in the line of action of it but remember that this is fine as long as the equilibrium is concerned. But when I want to look at the internal deformation of a body then that rule cannot be applied. So for example we can clearly see that if I take this pen and I am concerned about what kind of deformation these two forces that I am applying at the extreme end is going to give then the deformation that we will get from this will not be equal if I just consider the force at the middle. So that means if I pull like this by holding the pen at one end and at the middle and if I hold the pen at the two ends the deformation is going to be absolutely different. However if we take the equilibrium it does not matter my equilibrium will always tell that the forces are equal and opposite in nature. So now coming back to the units this is very important specially for the students because in most of the books they try to refer to both the SI units as well as the FPS units. So as we all know that in SI units mass would be in kg, time will be in second and length will be in meter whereas in the FPS units the mass will be in slug, time will be still in second and the distance will be in foot. So remember that length, time and mass as we said these are the basic units but force needs to be derived from these basic units. So force will get a value of kg meter per second square which we will say in Newton and in case of FPS unit it will be in pound as we see here. Now why that is very important so I just put a quick example here which is related to the NASA Mars climate orbiter that was their first interplanetary weather satellite designed to orbit the Mars and you can see that two different groups were working on that. One group was working was working in SI units another group was working in the FPS unit. So what happened that one group actually forgot to convert the unit of FPS to SI and that actually created the disaster. So it is very important that we should convert the unit whenever required. However usually we prefer to continue working on the SI units as you will see also in this workshop but whenever required we will try to convert the SI units to FPS or FPS to SI. So once we are done with the fundamentals now another important aspect is what is the idealization of mechanics. So in the mechanics we actually make a rigid body assumption. So what is the rigid body assumption that means the body should undergo pure translation and pure rotation and it should have no internal deformation that means assumes original geometry. So a simple illustrative example is presented here for example if we consider this beam let us say we have a support let us say this is a fixed support in one end another one is the roller support. Then what happens when we are taking the equilibrium of the body we are not concerned about the small deformation that is taking place or how would rather let us say if our objective is to calculate how the forces are transmitted into the supports then we are not reanalyzing the fact that how this force is probably affecting the support reactions as we keep applying the load. In other words as long as this deformation is very small then we can always assume the original geometry of the body and we can ignore the deformation of it. Therefore a particle now will idealize a body by placing its mass at its center and neglecting its physical size. So what are the procedure we are going to follow when we are going to solve the mechanics problem as such will be given with the you know data specifications and a figure showing all the quantities involved. So the problem is given with the proper data and the specifications. So what would be the most important part that we want to come up with is the free body diagrams. So remember this is very fundamental because in the free body diagram we have to indicate all the forces that is acting on each and every body. So there could be multiple bodies but when we are going to separate it we have to take care of the transfer of forces from one body to other body at their connection based on the Newton's third law. And then we are going to apply the fundamental principles. So fundamental principles are either Newton's first law or Newton's second law that means if we are you know using let us say we are just talking about equilibrium problem then we will set some of force and moment equals to 0. And if we are talking about dynamic problem then we will say that some of forces should be equals to mass times acceleration and some of moment should be equals to mass moment of inertia multiplied by angular acceleration. So remember what is most important that we should give the proper reasoning because each and every problem will follow a logic. So how do I ensure that my answers are correct that can only be done based on the physical intuitions and when your logic or the reason that I am putting in when that meets the intuition then I know that my answers are correct. So I am not talking about the numbers here but let us say do I get the correct sign that is very going to be very very important when we are solving the mechanics problem because as we will see the directions of the reactions, directions of the moments those have to be understood very very clearly. So now as we know that there are so many problems basically mechanics is all about solving real life problems. So we are trying to deliver the ideas to the students that how a problem can be simplified. So any physical or mechanical models is simply a caricature of a real world problem. So we are trying to define simply a bare bones model of the physical system that we have. So therefore we may not get the most accurate solution but with some accuracy we can always find the answer. So what is shown here in this picture is that of a handy crane. So in the handy crane as we see that we have a hydraulic cylinder here that is allowing for the adjustment of this arm right here and we can clearly see in absence of this hydraulic cylinder then if we put a weight here it is going to simply collapse. So what will be most intriguing in this case to say how should I consider the force in this hydraulic cylinder? Is it going to be axial force? Is it going to be some other type of forces that we should consider? Similarly there are variety of problems that we will see in nature and I will just briefly go through different types of problems how we prepare the bare bones model which we treat as a reasonably accurate model to represent the physical system. So for example it is a draw bridge and you will see that you know most often in UK or in Europe rather where these bridges will help to maneuver small ships and boats as they you know go from one part of the city to the other part of the city but this bridge as you can see here can be modeled in a very simplified form. So as such we will see that there is a lever right here and as you apply the force it is basically going to go up. So the main question that could arise here that can I actually get the value of this cable force by knowing how much force I am applying. So this kind of questions will come up similarly can we get the reactions and so on so forth. So in robotics we will also see the you know application of mechanics. So how do I you know simplify the problem? So here what is happening basically in the competition it was given to the students to design an eliminator which will be able to kill as many good guys as they can. That means ultimately you know we have to design some kind of mechanical system that is able to held the you know these people on the neck. So you can see that mechanical device here. So ultimately what is most important here that as soon as you lift the you know guy then we can assume that your sea is dead. So we can just lift the human being the good guy and as soon as it is lifted then we say the ok the game is over or at least the eliminator wins. So therefore we can see that friction is going to play an important role. So depending on the friction between the you know net and the mechanical device if we consider these two metallic surfaces then we have to decide on the force that is required to pull this object or to you know uplift the object. So again in aerospace engineering we see that the main you know aerodynamic load is going to be taken by the main spar. So we have the spar in the wings. So basically on the conservative side we can see all the uplift forces and how we are going to actually model this spar under the action of the load. So we can see here it is a very simplified model we have assumed that ok it may be you know fixed between the fuselage that is the body and the wing here and then we can calculate what is the force transmitted from the spar to the load. So that means can we get the support reactions here. So these are the type of problems we are going to see. Similarly if we go to the civil engineering applications we are also going to see that different supports are there you know bridge will be resting on the bearings some other piers and so on so forth. Also there could be some connections here. So we have to model this connection and we have to understand that how the force is transmitted from one body to the other body through this connections. So if you look at the dynamics of it. So once we go to the dynamics so one aspect is definitely the kinematics. So whereby we have to discuss you know rectilinear motions, curvilinear motions and so on so forth and then suddenly we have other component that is the kinetics. So knowing the you know kinematics part can we really come up with the force system that is acting on the body such that we can derive the equations of motion and solve the problem as required. And last but not the least I have put one more example of a car vibration setup. So this one was actually taken from howstuffworks.com and we can clearly see that suspension system is very important. And this can be actually modeled as a mass spring damper system and we will take this problem towards the very end when a car is actually riding on a bumpy road. Can we derive the equations of motion from the by assume the mass spring and damper system. So another important aspect that I must mention is numerical accuracy. So remember in engineering mechanics you know accuracy of the solution is important but these days you know with the advent of let us say computers and calculators as such the numerical accuracy you know can be maximum numerical accuracy can be achieved. So it will be always preferred to keep certain digits after the decimals at least 2 to 3 digits should be kept so as to avoid the issues related to numerical accuracy. So with this I would conclude the introductory part of the engineering mechanics.