 I am Swathi Ghargay, Assistant Professor, Department of Civil Engineering from WIT, Swallapur. Topic for today's session is Impulse Momentum Method. Learning outcome of this session, at the end of this session, learner will be able to analyze force, time, velocity of a moving body. Impulse, it is a change of momentum of an object. When the object is acted upon by a force for an interval of time, that is, impulse is equal to force into time. We will see it diagrammatically. Let the body of mass m and several forces are acting on the body. The resultant of this body, let it be r, it is acting in a x direction. So according to D'Alembert's, the inertia force induced in the body due to the external forces acting and that inertia force is equal to the resultant force and it is acting in the opposite direction of that resultant force. That inertia force, it is the product of mass and acceleration. So according to D'Alembert's, we can write r is equal to ma. As we know that, derivation of velocity with respect to time is the acceleration. Put acceleration in the equation, we will get r is equal to m into dv by dt. So r into dt is equal to m into dv. Now we will continue with the previous equation, r dt is equal to m dv. Write the equation for time, the integration limit is 0 to t and for velocity, integration limit is initial velocity u to final velocity v because in that time interval velocity varies from u to v. After integration, we will get mv minus mu and the term integration of r dt is called as the impulse. It is a product of force and the time. Therefore, impulse is equal to final momentum minus initial momentum. Now we will solve one numerical here. There is a body of weight 1500 Newton and it is on the surface having coefficient of friction is 0.1. A force 300 Newton is acting on the block 1500 Newton and as a result, it is moving in the direction of force. So it starts with the initial velocity is 0. So this is the given data for the numerical and the question is, what time will elapse before the block reaches a velocity of 16 meter per second starting from rest? So in this numerical, there are total two forces 300 Newton and the 1500 Newton will draw for the free body diagram of the block. So for free body diagram, remove support and show the normal reaction offered by the support that is N. And there is a frictional coefficient. So frictional force will act in the opposite direction of motion and that frictional force will be mu into N. As the block is moving in the direction of 300 Newton block, so the work is done in the horizontal direction. So we can write resultant is equal to summation of fx or in another word we can say that summation of all the vertical forces is 0. And here in y direction, there are only two forces 1500 Newton and the support reaction offered by the support. So that N is equal to 1500 Newton and frictional force is the product of mu and N. So it is 0.1 into N that is 150 Newton. In x direction, see there are total two forces 300 Newton and the frictional force. As we know that resultant is the summation of fx. So resultant is 300 minus 150 that is 150. So we have calculated resultant here. We will continue with the same figure. As we derive impulse is equal to momentum or RT is equal to MV. Momentum is nothing but the final momentum minus initial momentum. In this equation R is 150 we have calculated earlier, T we have to calculate, M it is the weight of body divided by G that is 1500 divided by 9.81. And final velocity is 16 and initial velocity is 0. So in the equation only time is unknown you calculate the time. So calculate time it will be 16.31 second. So to gain the velocity 16 meter per second the block need a time 16.31 second. Now you pause video here, read the question and find the answer of the question. In previous question if 300 Newton force is then removed how much longer will the block continue to move? Here the solution it is asked that remove 300 Newton force. So there are total three forces will remain that is self-height of the block 1500 Newton, support reaction that is N and the frictional force that is 150 Newton. So with these three forces we will do the analysis of the body now. Now initial velocity is 16 meter per second after removal of 300 Newton force the body will stop after some time we have to determine that time. So we first we will calculate the resultant here there is only one force in the x direction. So resultant is equal to minus 150 Newton according to the sign convention for the direction of the force. Now use the impulse momentum method impulse is product of force into time that is resultant into time and momentum is product of mass and velocity that momentum you take a final momentum minus initial momentum. So put all the values here calculated are that is 150 m is body is remains same. So 1500 by 9.81 is the mass of the body and final velocity is 0 and the initial velocity is 16 calculate T again time is we get time 16.31 second. So the correct option is 16.31 second we will solve one more numerical here there is a vehicle of weight 20 kilo Newton and it is moving on the concrete road and the coefficient of friction between concrete road and the surface of tire is 0.75 and it is moving with the initial velocity 70 kilometer per hour. So first we will draw the free body diagram of the vehicle shows support reaction offered by the road surface that is that must be equal to the self-fit of the vehicle because no other force is there in the y direction. So that two forces must be equal so right here 20 kilo Newton. Calculate frictional force frictional force is mu into n that is 20 mu as the vehicle is moving in a x direction. So work is done in the x direction. So if we can write r is equal to summation of horizontal forces. So in horizontal direction there is only one force that is frictional force. So resultant is equal to minus 20 mu. Apply impulse momentum method RT is equal to MV RT is equal to final momentum minus initial momentum but here purposefully I have taken a numerical for the velocity is in the form of kilometer per hour. So we have to convert that kilometer per hour velocity in a meter per second. So here there is a conversion you have to multiply by 1000 then it will convert the kilometer in meter and we have to divide it by 3600. So the hour will get converted into second. So 70 kilometer per hour is 19.44 meter per second so that will be the initial velocity. Now you put all the values in this our impulse momentum equation it is minus 20 mu into T is equal to m is the weight by g that is 20 by 9.81 into final velocity is 0 and initial velocity is 19.44 in meter per second and find out the T. So T is 2.64 second so after applying a break and if the velocity is 70 kilometer per hour it will take 2.64 second to stop it to stop completely. These are my references thank you very much for the listening.