Lecture 05 : Statics, Kinetics and Kinematics

[Music] [Music] welcome to the next lecture on Statics kinetics and kinematics in this lecture we will try to cover the introduction of Statics kinetics and kinematics then we will try to see introduction to engineering mechanics we are slowly getting into the application of the fundamentals what we have seen here into engineering then Statics definition and Concepts kinematics definition and Concepts kinetics definition and Concepts then under kinetics we will be seeing work energy and moment of inertia then impulse and momentum will be seen finally like every time we will try one or two numerical problems we will have a recap then references so Statics Statics is concerned with objects at rest or in a state of equilibrium in the simpler term it analyzes the condition under which a body remains stationary for example a bus standing a dam erected a bridge constructed a big shopping complex constructed a tripod where a camera is located while shooting is stationary right so these are some of the examples this branch of mechanics focuses on the forces acting on an object and how these forces balance each other out preventing any motion so if there is any stability problem so then what we do is we first try to come to static analysis and find out what are the forces coming and how are the forces getting balanced so that's very very important for Statics kinetics k itics on the other hand deals with the relationship between the forces acting on an object and the resulting motion for example when the plane is flying when the windmill is rotating when the car is moving a boy is playing football and kicking the football right so these are all where there is a force acting on the object and there is a resulting motion it explains how these forces cause the object to move accelerate or decelerate for example if you are playing a wall tennis game so you are trying to strike or hit the ball as against the wall so the force what you apply hits on the wall and the ball bounces and come back what will be the force will it be same will it increase will it decrease right you try to take a dry ball and then hit it against the wall a dry tennis ball you try to hit it against the wall then you try to take a semi moist or a wet ball try to heat it against the wall then you try to soak the ball in water and then try to uh ball against the wall so when you try doing all the three you will try to see different forces are required if you want to maintain the same uh force with which the ball comes back so these things explain how these forces cause the object to move accelerate or decelerate kinetics considers the object mass and how it interacts with the applied force right even when you are trying to use a spoon while eating that is also a force which is there how does mass Force interacts and what happens to the motion kinematics kinematics describes the motion of the object without considering the forces that causes it so here you should be very clear the motion of the ball without considering the forces so in the last two cases what happens it is the kinetics is the relationship between the force acting on the object and the resulting motion the first one is it is focused towards the concern of the object at rest or in a state of equilibrium okay how forces balance each other in order to prevent motion is Statics right so three different be very clear in the definitions it forces on how an object moves characterized by its position displacement velocity acceleration by this time you would have learned what is the difference between position displacement velocity acceleration I can just give you a small lead this is m/s square this is meter per second and this is meter I hope you can go back revise in the first lecture and get this so it also provides it provides your geometrical description of motion independent of the object mass or the forces acting on it okay so you can see the car with what velocity go a person who runs at the speed your boy trying to bounce the ball your boy trying to throw the ball ball follows a projectile motion and he's trying to throw the ball in air so all these things lead to usage in engineering mechanics and it these concepts are very much used in Aerospace chemical engineering Electrical Engineering also they use it right so all areas of of engineering Civil Engineering also they use it in a large extent so in all areas of engineering they do static analysis kinetic analysis and kinematic analysis depending upon the requirement so now let us see the introduction of engineering mechanics so engineering mechanics is the Cornerstone discipline that underpins the analysis and design of an engineering system what is an engineering system system for example wheel axle is an engineering system a lever which is used to lift wheel and axis XLR you have two wheels these two wheels are connected by a rod so that Rod is called as axle okay in automobile it is exhaustively used in train also it is used uh so inclined plane a block placed on an inclined plane is an engineering system then you have lever pulley for lifting so this is exhaustively used today in jcbs that is or folk lifts and even if you see that it is exhaustively used in your elevators right they use a pulley mechanism then a screw which is used to fasten two blocks or whatever it is so then you also have a wedge system right so all these things are Engineering Systems where in which applied mechanics finds a very important role so if you go back here I would like to recollect what we saw in the initial days we saw push pull so in that way if you go this is a push Force right this is a torsional force if it slips down it is either a pull or a push whatever you are trying to do right liver based and then this again uh we will have pull or push so here everywhere the MU dominates we saw the friction also dominates see as in when you start reading such courses you have to correlate with real time and you have to correlate back and forth knowledge such that you will start enjoying the course as and when it proceeds it serves as the bridge between the fundamental principles of physics and their practical application in various engineering field in essence it equips Engineers with the tool to understand and predict how objects structure behave under the influence of force and motion for example a tree when there is a strong wind blowing the tree will swi swing right or it moves so that is nothing but tree an object interacting with the force and then what is the motion it has I try to push an object object is stationary it's a structure or an object you can say it is a stationary one I try to apply force and while applying force it tries to fall down or sometimes it moves so all these things can be figured out in engineering mechanics so if you go by uh definition engineering mechanics leverages classical mechanics to analyze Force moments motion of rigid body in engineering context for example you can see here it is a system a wall in which you have put two hooks the Rope is attached uh to a weight which is there which will try to slide or swing so just by playing with this tension and then playing with the distance the ball can be moved up or down or left or right to uh meet out the real time requirements so it integrates principles from mathematics physics calculus for problem solving in Statics Dynamics and strength of material we'll see what is strength length of material later so what are the important terminologies which are generally used in engineering mechanics they are first is equilibrium so equilibrium will have a body this can be fub1 FS2 and F3 so this can move with a velocity V so here this is an object where forces are there it is moving it is moving stably so that is we can say is equilibrium equilibrium determines the condition under which a body remains at rest or in uniform motion what is motion analyzing the kinematics and kinetics of the object is motion so in kinetics relationship between the force and motion of the object strength of materials are nothing but understanding how materials deform and fail under the various loading conditions are nothing but strength of materials so applied mechanics when it is extended to a material it gets into strength of materials for example you have a ball now the forces are going on so it is in a equilibrium state it is moving now let us assume if there is a hold there so for example I hold it grip it here now there is a material so when the forces are applying what is the response of this material such that it will try to respond to the requirements so that is nothing but strength of materials right safe design then effective design problem solving framework so these are some more important terminologies which you should know what is a safe design it equips engineer with the ability to analyze stresses strain and deflection in structure ensuring their safety and functionality under various loading condition for example you try to buy your a shoe with using the shoe you try to walk you wear the same shoe for running jogging jumping all these things you do but your shoe never gives away so here what has happened is nothing but there is a safe design done on the system and then you can same way for example you take a cart where you sleep so sometimes what happens you go there sit in a cart and sleep a 60y old man or a 50-year old man does it when a 20year old adolescent boy or your 12y old old child if they go to bed they jump on the bed still the CT has to withstand the impact load and it also has to withstand the sliding load whatever it is so that is safe design so naturally what happens is the leg strength the cart base the uh the Fastener which is used their torque everything is to be considered such that you make a safe design efficient design by understanding how the forces act on the affect the object Engineers optimize designing for strength weight and material use is effective Design One Is Safe design the other one is effective design effective design is predominantly used in Aeroplane rocket automobile see even in your automobile car you can increase the safety to a large extent but when you increase the safety you try to add more and more material when you add more and more material the weight goes High the mileage goes down so now what you do is you try to have a compromise by reducing the the weight of the uh sheet metal body which is around or reducing the weight of the material which is used uh such that the efficiency mileage efficiency can be improved and when you are doing so if you go back and see we do crash test so in Crash Test we try to do a little bit of optimization and try to gener generate a efficient design what is problem solving framework the core principle of engineering mechanics provides a structured approach to solve complex engineering problems you try to take a system in that system you try to divide several small subsystems and each of the subsystem you try to have a framework and from that framework you start working when we are looking at the definition in Statics Statics a fundamental branch of engineering mechanics meticulously investigates the behavior of rigid body at rest or in state of equilibrium if you look at this this tries to tell you a simple application or a simple system where in which your block a wooden block or a stone block is there so first you see when the stone block is at rest you have a spring which is applied or you try to have a hydraulic system or a pneumatic system or your motor attached with a screw whatever it is you try to pull so when you try to pull you see the the block is in stationary motion and the spring keeps on increasing the load after a certain point of load the the spring so that means to say so much of weight is getting applied this block starts moving once it starts moving so from static friction to sliding friction it goes you see there the load what you apply has reduced so this is a a simple example this is very much used in any of the realtime application where there is a moving body right you can also understand that when you have a wooden rack where in which it is loaded with books it has a heavy Mass so now when you try to drag it initially you will have so much of resistance you keep on increasing your pushing force on it at some point of time it slides if your pushing force is instantaneously very large the object is at stationary it topples for example I will try to draw a situation so you have an rack so you are trying to push so the mass is here weight is here right you are trying to push with the force sometimes it can slide sometimes it can topple so how does it topple the force is large the bottom one which is holding the weight is resisting the force to help in movement if the force keeps on increasing it topples see now you see it is a typical situation which you see in real time in order to analyze that we try to use this Statics so it is nothing but a foundational branch of engineering mechanics where in which meticulous investigation are done on the behavior of rigid bodies at rest or in the state of equilibrium its primary focus lies in analyzing the intricate interplay of forces acting on a body and the conditions that ensures the forces perfectly counter balance one another preventing any motion is Statics and why do you want to two St because many a time you are in motion by doing static analysis you can try to have a fir hand approximation to how the system will react what all has to be there in the system what should be the weight of the system all these things can be thought off so there are two things which are there weight is there the shape is also there we call it as shape Factor so weight is in we will try to do everything in the Statics and once it is done when we have to improve the efficient design we start playing with the shape Factor so you can see in the previous example a man trying to push your block so here is the force fa which is there here is a frictional force which is going against so why is that friction coming no surface is flat so you will have several interlockings on the floor and with the object this tries to increase the friction the next fundamental uh concept is going to be equilibrium the key concept is an object is at rest if the sum of all the forces summation F equal to zero and the sum of all the momentum summation m is equal to zero acting on it are zero so it is something like this you have a car on one side you have a car on one side equal weight so it is at equilibrium so equilibrium means summation of all the forces this and sum of all the moments acting on it must be zero so what we do is we always try to make a draw a system with simple system we convert a realtime situation into a simple system mass force and other things then we will try to see whether the system is in equilibrium for which we always try to use this rule summation F equal to0 or summation m equal to Zer and both are to be used forces interaction that can cause an object to move or deform static focuses on concentrated forces and distributed forces acting over an area so what we are trying to say is we in order to simplify the problem we will always try to see okay there is a body in this body there is a concentrated load so here what has happened the load has been shifted to a single point and this is a body this can be a ball or whatever it is there is a body there is a force single point acting on it so this uh can be thought of or you can try to have a body where in which you try to apply it over an area so let us take a simple example you take a blunt knife and a sharp knife so why is the force always very high in a blunt knife as compared to that of a sharp knife why because the load which is applied gets distributed over an area yes sharp knife yeah blunt knife so now you apply a force of 10 kg right you apply a force of same 10 kg so here it is getting distributed over an area moment it is distributed over an area so then what happens the for cutting you will always try to use a larger Force so this is what is the distribution of Force effect which comes sharp and distribution so single point and distributed over a area so Statics focuses on concentrated Force single point or distributed area the force acting also can be that right so force can be on a single point force can be on an area moment moment is nothing but a torque a force tendency to rotate an object around a point is called as torque the body which is mounted so you are applying Force so it topples so it is nothing but moment it is calculated by multiplying the force magnitude by the perpendicular distance from its line of action to the rotation point that is moment so the important terminologies are multiply force magnitude by perpendicular distance from its line of action to the rotation point so this is important so when we discuss more it is moments are crucial for achieving rotational equilibrium so this is very important you remember we were looking into summation of f equal to0 summation of m equal to0 so this is for a equilibrium State let's see some of the definitions of kinematics kinematics is a Corner Stone branch of mechanics dels into the fascinating relim of meticulously describing how objects move through space and time independent of the forces causing that motion so here we are more worried about how objects move through space and time that's kinematics right so unlike its counterpart kinetics kinematics focuses solely on the geometrical aspects of motion dis regarding the forces that may be responsible so examples are a boy standing on your a rooftop and playing or throwing a ball or a boy trying to throw a ball on the in the air and he sees how does the fall happens a projectile motion distinction from Kinetics is while both kinematics and kinetics deals with motion a crucial distinction exist in kinematics a cl to a detailed map that meticulously chart the path and the speed of an object without explaining why the object takes the specific route or how fast it travels it only looks at the path and the speed of an object conversely kinetics dels into the Y aspect analyzing the forces that causes the motion described in kinematics so you should clearly understand the distinction between kinetics and kinematics kinetics is y aspect is kinetics kinematics is path and speed of the object is discussed here so the other key concepts are in kinematics are displacement displacement is Delta X is the change in position of an object from its original X KN to a final X1 Point expressing both magnitude and Direction so Delta X is nothing but X1 - x velocity measures the rate of change of displacement over time so velocity is nothing but Delta X by delta T right displacement ment velocity right with respect to time then acceleration represents the rate of change of velocity over time indicating whether an object is speeding up slowing down or changing direction is called as acceleration please try to understand the difference between displacement uh velocity and acceleration it is rate of change of displacement is velocity rate of change of velocity is acceleration so in acceleration you only say whether the car is speeding or slowing the next concept is partical kinematics it is a subfield of mechanics where in which it dissects the motion of idealized Point like objects Point like objects or particles through a space and time its focus lies solely on the geometrical description of this motion independent of the forces that may be causing it is a very important statement its focus lies solely on the geometrical description of this motion independent of force that may cause it so there are two main types of motion particle motion one is rectilinear the second one is curvy linear rectilinear means an object moving along a straight line so its simpler description with scalar quantities is magnitude only for displacement velocity and acceleration when we talk about curvy linear it requires vector quantity also with both magnitude and direction for a complete description of displacement velocity or acceleration the two things are very very very important rectilinear and curvy linear rectilinear is predominantly is a scalar quantity curvy linear is a vector quantity so when we see the definition of kinetics kinetics is a Cornerstone of mechanics dwells into the profound influence of forces on the motion of the object it establishes crucial link between the applied forces and resulting changes in an object's state of motion okay it establishes the object's state of change of motion so now let us see some of the uh Newton's law of motion okay Newton's first law of motion it states that everybody continues in its state of rest or of uniform motion in a straight line unless acted upon by some external force is Newton's first law of motion this is also known as law of inertia okay the second law of motion it states that the rate of change of momentum is directly proportional to to the impressed force and takes place in the same direction in which the force acts so this is the second law of motion first law of motion the third law of motion is to every action there is always an equal and opposite reaction now let us see work and energy principles so energy watts or it can be Jewels per watts are Jews per second right so energy can be heat energy as I told you it can be energy what you consume in the house Force right work is the another thing so work and energy principles this principle establishes a crucial link between the work done by a force and the change in an object's energy so I am trying to push or I am trying to keep a ball hit it with a hammer so the work done by force and the changes in an objects energy in simpler terms the work done on an object translates to change in its energy mathematically the work W done by a constant force F acting on an object under goes a displacement D is expressed as w = f into D into cos Theta Theta is the angle between the force and the displacement Vector so work this is very important work can be expressed as W = to FD cos Theta Theta is the angle between the force and the displacement Vector so the mechanical energy can come in in two forms or it can come in uh maybe three forms I can say but predominantly we talk about only two forms so what are they they are nothing but kinetic energy and potential energy kinetic energy is the energy of motion determined by an object's mass m and velocity so this is expressed as half M v² so potential energy is this kinetic energy is this potential energy means an arrow getting loaded to a string right or you are trying to pull a rubber band and then you keep a paper and release it you see what is the projectile motion of the paper whichever is used so kinetic energy is nothing but half MV squ which is uh here this is uh released and potential energy is the energy which is getting stored potential energy arises from an object's position or configuration gravitational potential energy depends on mass gravity and height while elastic potential energy comes from deforming elastic objects so PE can can be found out as MGH H so this is for kinetic energy and this is for potential energy in many of the manufacturing problems we will try to use potential energy and kinetic energy for example what is the load required to split a material by water so now where is the application it is water jet or I will put it this way there is a waterfall which comes the waterfall what is the energy required to erode The Rock from the particular place right so now what is the force required to break the rock so that depends on waterfall so in waterfall you try to change the uh increase the potential energy when you try to increase the potential energy what happens is you try to play with the H so what is the height from where the water Falls and uh what is the mass of it then what is the gravity so all these things try to play for potential energy and then it tries to hit at the object its kinetic energy so next is impulse momentum principle which is part of kinetics so the impulse momentum principle states that the impulse J produced by a force F acting over a Time delta T equals the change of momentum Delta P of an object so this is nothing but J equal to Delta P the principle states that the impulse J right you use a baseball or you use a football or you use a cricket or you throw a basketball so impulse J produced by a force F acting over a time period delta T equals the change of momentum Delta P of an object so momentum p is a product momentum p is a product of mass into velocity this is momentum force is nothing but Mass into acceleration momentum p is a product of mass into velocity so when you are trying to play a caramboard or when you're trying to play a bots so you can see the Striking ball hitting the other ball and then moving right so what is conservation of linear momentum the conservation of linear momentum is a powerful principle which states that in a closed system no external force acting the total linear momentum of an object remains constant before and after an interaction in simpler terms the momentum gets redistributed around the object itself but the total amount stays the same same the amount whatever you apply in your closed system that the total linear momentum of an object remains constant before and after an interaction so the moment gets redistributed among the objects involved but the total amount stay is the same so applications of ctions we will see the impulse momentum principle is essentially used for analyzing collusions collu means a ball hitting a ball a caramboard coining hitting another carambot coin a bat hitting a ball a tennis racket hitting a tennis ball it helps to predict post custion velocity by considering impulse from the force and changes in momentum this knowledge helps in aiding safety features like car airbags and understanding phenomena like planetary ctions so everywhere we use the application in collu moment of inertia moment of inertia I emerges as a crucial concept analogous to mass in linear motion so mass in linear so you can see here this is I moment of inertia the quantities an object resist to change in its rotational state is moment of inertia just like a heavier mass is harder to accelerate linearly a large amount of inertia signifies greater resistance to the rotational acceleration you keep a coin you keep a paper you pull the paper in such a way such that the coin slips inside the glass tumbler or inside a closed volume right so moment of inertia is very important many at times in later uh part of the course we will use this concept of moment of inertia which is it quantifies an object's resistance to change in its rotational state so when you have a a pen when you have to spin the pen it's moment of inertia is there how to calculate the moment of inertia several ways are used to calculate the moment of inertia of your rotating object they are for uniform objects the moment of iner I is calculated by taking the product of mass with the square of its distance from the axis of rotation so it's m r² This Is How They calculate for a uniform object what is a uniform object axis symmetry part right uniform objects the moment of inertia is calculated by taking the product of the mass with its square of the distance from the axis of rotation right for a non-uniform object we calculate the moment of inertia by taking the sum of the products of individual Point masses at each different radius so this is written as I is equal to summation of m i r i² it is m i is nothing but summation of m i r i s so it is the sum of the product of individual Point masses now let us try to solve a simple problem and use the concepts whatever we have gone through in the tutorials you will have minimum 10 problems in each lecture we will try to post the problem and you will have to solve it then we will release the solution also what work is done in dragging a block 10 m horizontally when a 50 Newton force is applied by a rope making an angle of 30° with the ground so how do you solve the problem what is the force available 50 Newton what is the uh horizontal uh distance it has to drag 10 m what is the Theta which it make 30° so how do you what what do you have to find out what is the work done work so what is a formula for work it is F into s into cos Theta so that is nothing but 50 into 10 into cos 30 which is nothing but which is 51 2.4 jewles okay now let us see one more problem how large a torque is needed to accelerate a wheel the means to say in a car wheel for which I is equal to 2 kg M squ from rest to 30 rotations per second in 20 seconds what how large a torque is needed to accelerate a wheel for which I equal to 2 kg M Square from rest to 30 RPS in 20 seconds so moment of inertia they are asking moment of inertia is nothing but I which is 2 kg M squ so R PS after 20 seconds is n equal to 30 so initial velocity Omega is equal to0 final velocity is nothing but Omega Omega 2 is = to 2 < into 30 which is 1884 radians per second what is angular acceleration angular acceleration is nothing but Omega 2 - Omega 1 by T which is nothing but 1884 - 0 by 20 which which is nothing but 9.43 radians per second so now if you want to find out what is torque torque is nothing but to is I into Alpha so which is 2 kg M squar into angular of acceleration Al 9.43 radians per second is equal to uh 18.86% uh and then what do you do is now to is nothing but I into Alpha which is nothing but 2.89 M squ into 9 so we get answer is 18.86% then explaining the definition and concepts of kinetics then elaborate the principles of work and energy then we studied about impulse momentum principle what is momentum and its application in ction and finally we saw a brief moment of inertia introduction and we solved two problems here are the references which we have used for this lecture thank you very much [Music] [Music] [Music]