 in Professor, Department of Civil Engineering from WIT, Swollapur. Topic for today's session is DLM words principle. Learning outcome of this session. At the end of this session, learner will be able to analyze the body, which is in motion, by using dynamic equilibrium equation discovered by DLM words. DLM word principle, it is a system of forces acting on a moving body is in dynamic equilibrium with the inertia force or a reverse effective force of the body. Hence, just by applying a reverse effective force, the moving body can be treated as a body in equilibrium and can be analyzed by using equation of static equilibrium. Here, there is one body of mass m and the pulling force P acting on a body, surface will offer a normal reaction and there is a frictional force between the surface and the body. So, that frictional force must be equal to frictional coefficient into the normal. So, there are total three forces acting on the body, P frictional force and the normal offered by the support. With these three equation, we cannot analyze this body by using a equation of static equilibrium because it is not at the rest position. It is in a motion due to the force P. So, DLM word says that whenever the body is in dynamic condition, it is also very easy to analyze such a body. Simply add one more force which is exactly acting in a reverse direction of the resultant force. So, that force is called as the MA or it is called as the inertia force, mass of the body into acceleration. So, these two equations are available for the analysis of body. So, these two equations are called as the dynamic equation of equilibrium discovered by the DLM words. Remember here, summation of moment is equal to 0. That equation we are not using because it is a concurrent force system. All the forces are supposed to act on the center of gravity. So, summation of moment is equal to 0. That equation will not be useful here. Now, you think and answer the question, which is the alternate law for the DLM word principle? We have seen DLM word principle we discuss. Your options are Newton first law of motion, Newton second law of motion, Newton third law of motion, and Newton's law of gravity. Answer is the alternate law for the DLM word principle is Newton's second law of motion. Because Newton's second law of motion says that the external force acting on the body, it is equal to the mass of the body into acceleration. So, f is equal to ma. Use that equation in the DLM word principle. So, this is the alternate law for the DLM word principle. Now, by using DLM word principle, we will solve one numerical here. In the numerical, there is a one block of 1200 Newton is on the inclined plane. It is connected with the rope. And the rope is passing over a frictionless pulley. And to the another end of the rope, there is another block attached of weight 800 Newton. And inclination of the inclined plane is given 12 degree. Your question is, find the tension in the rope and acceleration with which the body moves of the plane. And it is given coefficient of friction for the plane and the body is 0.2. Here, for this case, coefficient of friction is not given with the vertical wall and the 800 Newton. So, it is not in the contact with this vertical wall. We'll solve numerical step by step. First, draw the free body diagram of 1200 Newton block. 1200 Newton block, it is on an inclined plane. So, draw it as it is in an inclined nature. Many times, students have a fear of the problem of inclined plane. So, my suggestion is, you keep it as it is. We will change the axis itself. So, show here x axis parallel to the plane and the y axis perpendicular to the plane. So, it is a very easy method. And analysis of such a case is also very easy. The self-heat of the block is 1200 Newton and it will act vertically downward. And the rope is pulling the block. So, there is a tension in the rope. It is acting vertically upward along x axis. And it is in contact with the plane. So, plane will offer a normal reaction in vertical upward direction along y axis. As the block is moving up the plane, so frictional force will act in the opposite direction. And that will be equal to mu into n. Here, there are total four forces are acting on the body. Self-heat, tension in the rope, normal reaction, and the frictional force. With these four forces only, we cannot apply the D'Alembert's principle. According to D'Alembert, add one inertia force in the opposite direction of the motion. So, inertia force is M A. M is the mass of the body. It is W by G. W is given 1200 Newton and G is 9.81. And here, A is the acceleration. So, M A force will be acting in the opposite direction of motion. Before going for the analysis, see here. T force is in the x direction. F is also in the x direction. N is in y direction. And M A force is in x direction. But only one force is there, 1200 Newton. It is not in either x direction or either y direction. So, we will find out the component of 100 Newton in x and y direction. And inclination of the plane is given 12 degree with the horizontal. So, it's normal. We'll make 12 degree with the vertical. So, vertical component will be 1200 into cos 12. And the horizontal component will be 1200 into sin 12. So, like this, we resolve the force 1200 Newton in a x and y component. Now, in y direction, there are only two forces. 1200 cos 12 and the N. We have applied M A force. So, now we can use the equations of equilibrium. So, use the equation of equilibrium. Summation of F y is equal to 0. Only if two forces are there in y direction, so we can write N is equal to 1200 into cos 12. So, N is equal to 1173.77 Newton. So, calculate F. F is equal to mu into N. So, it will be 234 into 476 Newton. Now, go for the summation F x. First, calculate the forces in x direction T, F 1200 sin 12 and the M A. Total four forces are there in x direction. Do the summation of four forces and equate with 0. Simplify the equation. So, the equation will be in the form of A and T. So, it is 122.32 A minus T is equal to minus 484.25. So, let it be equation 1. Now, go for the analysis of second block. Second block is of self-height 800 Newton. Self-height always act vertically downward and the second block, it is connected with the rope and so there is a tension in the rope in vertically upward direction. So, here the block which is on the inclined plane which is moving up the plane. So, obviously that 800 Newton block will move down. So, in the opposite direction of motion, we have to add M A force. So, I hope you understand why it is in vertically upward direction because the 800 Newton block is moving downward. So, in the opposite direction of motion, we added M A force. Now, apply equilibrium equation. So, summation of all these three forces equal to 0. We will get the equation T plus 800 divided by 9.81 into A is equal to 800. Now, from the first block equation 1 is there, from the second block equation 2 is there. These two equations solve simultaneously and find out the value of T and A. So, we will get the value of tension in the rope is 673.68 Newton and the acceleration is 1.549 meter per second square. These are my references for this video. Thank you very much for listening.