Hello, in this lecture, we will see how a man, standing on Earth is in equilibrium. We will use a new construction, called a free-body diagram, which will enable us to identify all the forces which act on this person, and we will determine how to define equilibrium on the basis of precise criteria. When a man is in equilibrium on the ground, it is obvious that, due to universal gravity, his mass induces a weight which is activated by Earth. Earth itself acts on this person, so that he is in equilibrium, and, under the person's feet, acts a contact force. We are going to use this construction of a free-body diagram to evidence these effects. Let's look at a man on the ground. The first force which acts at his center of gravity, which is approximately at this height, is his weight G, which acts vertically downwards, and this weight has a value of approximately 800 Newtons in this case. We can see lots of other things around this person, which do complicate our thinking. Are there some effects induced by the red construction behind, or by the benches, or by the flower display cases ? It is not clear. So, what we want to introduce is the principle of a free-body, which will enable us to isolate what interests us, it will often be a structure, here it is a person, from the environment, to only focus on what is significant. I then draw a free-body which surrounds the person, which includes everything which is significant, and then which cuts, however, just under the person's feet, since we want to reveal what happens under the feet. What happens around him, however, is not very significant, and thus disappears. Thus if we look at this sky blue free-body edge, inside this free-body acts a force of 800 Newtons downwards, and if it was the only force which would act, well, the man would go down, would fall down. There is necessarily another force, it is neither on the left, neither on the right, the man is not borne by air, it is not either on the top, the man is not borne by his hair, but it is under his feet. I draw here a force which corresponds to the effects of both feet together, and which is the effect of Earth on the man. Just where our free-body passes under the feet, it passes at the boundary between the man and the ground, and this kind of force is a contact force which always acts perpendicularly between two bodies which touch one another. We now want to know how this body can be in equilibrium, how this free-body can be in equilibrium. Well, for it to be in equilibrium, it is necessary that the ground has enough capacity to bear the person. We can easily understand that this force must be equal to and in the opposite direction that the person's weight, that is to say to be equal to 800 Newtons. What happens if this person, instead of standing on a firm ground, stands on quicksand ? Well, the quicksand can exert a force upwards of, let's say, only 300 Newtons. So, the result of this is that there is a force of 500 Newtons which pushes the person downwards, until, once the friction acting along his legs increases, the force which can be transmitted by the quicksand is significant enough to equilibrate the 800 Newtons of the person, it is thus necessary for the equilibrium that the contact force of the ground on the person should be able to be equal to the person's weight. We can also express it saying that it is necessary that the sum of the forces acting on the free-body should be zero. We can represent this graphically, we have here the weight of 800 Newtons, weight G, and then we have here the contact force which is also equal to 800 Newtons. Then, we can see that it is... so, I drew these two vectors a little bit staggered from each other so that we can see them, actually they are really layered over each other. We can also say, since they are two vectors, that the vectorial sum of the forces must be zero for a body to be in equilibrium. Let's consider another case, the one of a person who leans forward. I draw a free-body which surrounds this person, we pass just under his feet, the forces which act on this free-body are on the one hand inside the free-body, the weight G of the person and then, on the other hand, under the free-body, there, the bearing force, the contact force of the ground on the person. What we notice is that these two forces share the same line of action, that is to say that they are aligned. If we look at the person's feet on the right, we can draw here the path of the free-body, well, I am only interested in one of both feet, but the reasoning I am doing is also valid for the sum of both feet, well, we can see that in this configuration, the sum of, the contact force, it acts somewhere just at the front of the feet, but it is still possible. If the contact force, however, had to act even more on the left, it would cause a problem, we could arrive at the end of the big toe, and then after, there would be a problem about the strength of the foot, and then, if we go further, this is the case of someone who leans forward too much, this person here have a center of gravity which is situated on the left of the line of action of the contact force, In the first picture on the left, it is located slightly to the left, whereas in the picture on the right, much more, in this case here, we deal with a loss of equilibrium since the ground is still ready to provide 800 Newtons to resist to the weight of the person, but however, it is impossible that the line of action of the weight of the person coincide with the line of action of the contact force. The person who loses his balance is a case that does not interest us anymore in this course, since we want to focus on the structures in equilibrium, but it is obvious that it also means that, if it happens to a man, it can also happens to a structure, and then we need to be very careful not to get structures which are not able to be in equilibrium. In this video, we have seen how to use a subsystem, to evidence, not only the weight of the person, but also a contact force between the ground and the person, we have seen that the equilibrium of two forces is conditioned by two conditions ; the first one is that the vectorial sum of all the forces which act on the free-body must be zero, and the second one, is that the forces have an identical line of action. And finally we have seen that a loss of equilibrium results from a violation of one these two conditions.
