So, a priori, we are going to say that there is a tension T one, and a tension T two.

But if we have a look on the equilibrium of the free-body in

the middle, we will see that there are, acting on this free-body,

only two forces, the force T one which pulls towards

the left, the force T two which pulls towards the right.

Thus, necessarily, T one must be equal to T two, and then, is equal to

T, which we will use in the following. So, we needed this

free-body anyway. If we extend the line of action of the

force T on the left and on the right, it

will cut the line of action

of the force of the weight.

And, to have the equilibrium, it will be necessary

that the force under the feet should be converging with these two other forces.

Then, that these three forces are converging.

And we thus get, that the force, under the feet

of the person on the left, S one, passes by this point.

And likewise,

the force under the feet of the person on the right,

S two.

Let's draw the acting forces, for the

free-body on the left in the Cremona

diagram. So, here, we have

the weight of 800 Newtons.

We are going to have the force T

which acts on the horizontal axis. We are not totally sure

until where. Then, we know, on the other hand,

the direction of the force S. I make the transition,

a little bit quickly. Excuse-me.

So, we get the force S one, and the force

T which express the equilibrium of the free-body on the right.

Thus, this person is in equilibrium, and we can read

graphically the value of the internal force in the cable, which is equal to T.

Let's now take a look at the equilibrium of the person on the right.

To do that, we are going to reuse the segment T that we have already drawn.

In this way, we are not going to introduce any mistakes.

So, we are going to introduce the new force of 800 Newtons.

We are going to reuse the segment T, in the other direction,

and we are going to close the polygon of forces expressing the equilibrium of the

person on the right, by the force under the feet, S two.

This construction, in which we combine two polygons of forces,

together, with one or several shared forces, is called a Cremona diagram.

This Cremona

diagram will be a construction that we will use very often, thereafter.

So, it is very important to understand well how we construct it,

and to see well the meaning of the various components of this diagram.

Let's now look at a tug-of-war

a little bit more realistic, between two persons.

The person of 800 Newtons, that we know

well, and another person evidently lighter.

It is quite clear that the lighter person was not able to stay

in equilibrium, when the heavier person,

on the left, began to lean back.

But let's try to see why, in the Cremona diagram.

We have, here, on the left, a person of

800 Newtons, and on the right, a person of indeterminate

weight, but clearly

lighter. We draw the line of action of these two

forces, since we will need them after. And we

draw the line of action of the internal force in the cable.