Hello. In this video, we will introduce the concept of resultant, and we will see how to get the resultant of two converging forces. The resultant of two or several forces, is a force whose effect on the structure is the same than the one of the group of force which we consider. That is to say that this force, it will have as magnitude, the vectorial sum, the magnitude of the vectorial sum of the forces, and we will see how to determine the position of its line of action. We have here an example of a real system with two forces, force one, and force two. We also want to draw to better see it, the line of action of each of these two forces. I drew, on the left, these two forces with their accurate position, and their magnitude, although the magnitude does not need to be necessarily accurate in the real system. And then, on the right, in the polygon of forces, I am going to copy these two forces with their accurate magnitude, to construct their vectorial sum. So, force number one, first, then force number two. The resultant of these two forces, is simply constructed like the vectorial sum. And, we denote, usually, the resultant by R. For the rest of this course, I will use very generally, the color orange to identify the resultant. Now, we have got the magnitude of this resultant. We can measure it in centimeters, since we actually have a scale drawing in the polygon of forces on the right. But now, the question is, where does this resultant act ? Well, we want it to act so that it produces the same effect than the two other forces. Thus, we cannot make it act anywhere, we have to determine where its line of action is located. So, I am going to draw the direction of the line of action in the polygon of forces. And now, we want to copy this line of action in the real system. And for these two forces to have the same effect on the system, it is necessary that this line of action should pass by the intersection of of the lines of action of forces one and two, in the real system. Thus, we have, here, this intersection, between the lines of action of force one, and force two. And we get, in this way, the line of action of the resultant. And we can, of course, copy this resultant with its magnitude, which we will have measured in the polygon of forces. So, but as we do not need to draw it to scale, here, it is enough to copy it in this way. Of course, you can see that there is a limitation to this construction. It is that both forces should be converging. That is what we had in the title of the lecture. We will revisit several times the theme of the resultant, particularly for the case of several forces, and for the case of forces which are not converging. For example, forces which are parallel, or else which would cross, let's say outside of our sheet of paper. We have seen in this video, that the resultant is obtained by making the vectorial sum of the forces. But, for the resultant to have the same effect, we also have to take into account the intersection of the lines of action of the forces, which will enable us to determine, one point on the line of action of the resultant, with which we will be able to trace in the real system. I repeat, in the real system, we draw the position of the forces to scale, but the forces do not need to be necessarily to scale. In the polygon of forces, the forces must be drawn accurately to scale, and obviously, with the good orientation.
