 Hello friends, in today's session, I am going to deliver lecture on work energy principle, myself, Bipin Patil, assistant professor, department of civil engineering, Valchan Institute of Technology, Solapur. So these are the learning outcomes for today's session. So at the end of this particular session, student will be able to, first one, explain the work energy principle, few points we are going to discuss here, what do you mean by work energy power and this work energy principle and second one, proof for this particular work energy principle. See here, first, what do you mean by work? Now my dear friends, you just focus on this particular figure. What it indicates? Two blocks are present, okay? The distance between these particular two blocks, we consider here as additional load is present here, it acts in horizontal direction that is P. So means here, initially this particular box is present here, this is the present condition of this particular box. When we apply additional load in any one direction, so this particular block moves in the same direction having some displacement. So see here, what do you mean by work? Work is the product of force and distance. So this P is nothing but the force, S is nothing but your distance and the distance should be in the direction of force, means this particular distance should be in the direction of force, in which direction you are applying the force. That is, work is the product of force and displacement. So mathematically, in formulae, we say that work done is equal to force into distance. So this force P and the distance is S and the unit of this particular work is joule. Second one, what do you mean by power? The rate of doing work is known as power. So see here, power is nothing but work done per second. For example, you just consider one person is just transferring one material from one place to another one place. So for that particular, we require force to carry that particular force, to carry that particular material, then to transfer that particular material from one place to another place, we require distance. So during this particular, we require some time. So power, it is the rate of doing work, work done per second, mathematically, force into distance upon time. Now we just bifurcate force, distance upon time, that is nothing but your velocity. So in another way, we say power is nothing but force into velocity and the unit is VAT. Next one, energy. What do you mean by energy? There are different forms of energy. So the capacity to do work is known as energy. Capacity to do work, for example, one work if we consider, so the capacity of that particular person to do the work, that is nothing but the energy of that particular person to carry out this particular work. So basically it is a product of power and time and the unit of this particular energy is joule. Forms of energy, there are different forms are present. Basically I highlighted few sources. One is mechanical energy, second one, thermal energy. Sometimes we call that seat energy. Chemical energy is present. Light energy is the sound energy, nuclear energy, electrical energy and so on. These are nothing but the forms of energy. Potential energy and kinetic energy, we will discuss in this particular mechanical energy forms. Next one, the statement. Work energy principle. See here. It states that when a particle moves under the action of force, so you just remember the first figure, the particle or the block is present there, box is present there, it moves under the action of force. The work done by the force is equal to the change in kinetic energy of the particle. You can see once again, it states that when a particle moves under the action of force, when we apply the force to the particle, it moves. So work done by the force is equal to the change in kinetic energy of the particle. So work done is nothing but change in kinetic energy. Change in kinetic energy is nothing but initial final kinetic energy. The difference between these two that is nothing but the change in kinetic energy is there. Now see, we will discuss regarding the proof. We know that force is nothing but mass into acceleration, okay. So mass and acceleration, it is in a mathematical format. Force is nothing but mass. Now acceleration is just split into change in velocity with respect to time. That is dv by dt. So once again you just rearrange this particular term. Change in velocity with respect to time. So here in numerator and denominator, you just consider change in displacement that is ds. So multiply change in velocity with respect to time that is dv by ds and here ds by dt. So the mathematical format, force is equal to mass into change in velocity with respect to this change in displacement with respect to time. Once again rearrange the terms, force is equal to mass into dv by ds, you just keep as it is. Change in displacement with respect to time that is nothing but the velocity. So just consider this denominator part in left hand side, f into ds is equal to m mass velocity change in velocities there. So integrate on both sides, force into ds change in displacement is equal to this mass velocity into change in velocities there. Now here you just consider the limit. Here we are considering the limit for displacement s1 to s2 and for this velocity you just consider velocity v1 to v2 is there, right. So integrate on both sides, f the limit is s1 to s2 change in displacement ds is equal to m limit v1 to v2 vdv is there. Now just rearrange integrate on both sides, f is equal to s2 minus s1, m is equal to v square by 2 and you just consider limit v2 and v1 is there. Rearrange this particular term, f is equal to s2 minus s1 and after integrating you just put this particular limits 1 half mv square minus 1 half mv square. So v and u that is nothing but final kinetic energy and initial kinetic energy. So work done is equal to work done is equal to final kinetic energy minus initial kinetic energy. So sometimes we called as work done is equal to change in kinetic energy. So these particular limits are very very important s1 s2 that is nothing but the displacement is there and these are nothing but your kinetic energy means velocity we are consider here v1 to v2 is there. Now according to that this particular statement it states that when a particle moves under the action of force the work done by the force is equal to the change in kinetic energy of the particle that is work done is equal to change in kinetic energy. These are the statement this is the proof regarding this particular statement. So work done is equal to final kinetic energy minus initial kinetic energy that is change in kinetic energy is there. Now my dear friends you just go through this particular question pause the video and try to give the answer. According to work energy principle a particle of a mass m when subjected to unbalanced force system the work done during the displacement by all forces is equal to change in dot dot means here the options they are mentioned during the displacement. So we just try to identify the correct answers pause the video. So this is the answer of this particular question. So kinetic energy we are considering to prepare this particular session I refer this particular references thank you.