What is the balance of forces

Equilibrium of forces and moments of equilibrium

This post is about that Equilibrium conditions in statics. We'll deal with that Moment equilibrium and the Balance of forces. To do this, let's go first to the force and the moment briefly, then the Equilibrium condition derive. Then we'll explain that to you Superposition principle and calculate a example to the equilibrium of moments.

Equilibrium conditions in statics

In the Statics most calculation methods, derivations or assumptions are based on the so-called Equilibrium condition. In simple terms, this means that a body is under load not moved. Both moments and forces can act as loads on the body. Add the forces or moments acting on the system are zero, this is how it arises Moments- or also Balance of forces.

Formula of power

The basic Connections you will learn about force in our video for Newton's axioms. In general, a force is over that acceleration of a body and its Dimensions Are defined. Unfortunately, measuring is a force not as easy as possible and is therefore about the following formula calculated:

The Vector arrow on the symbol of force means that it is a directed size acts. so has a so-called Line of action. Put simply, the force acts in one direction, which in turn is dependent on the acceleration.

Formula of the moment

Perhaps you already knew what a force is, but you are now wondering what is meant by one moment understand? You might also be familiar with this from school, but not by this name. This is also used for the Law of leverage, only in a simplified form.

It is important that one moment only in terms of one Point is defined. In general, a moment is described by the following formula:

This corresponds to the Position vector from any point to Line of action the power. It doesn't matter which point on the line of action is chosen. Usually, however, it is the point of application of the force.

Equilibrium of moments and equilibrium of forces

You are probably wondering what such a moment does exactly. The law of leverage is also a special case of Moment calculation. So let's look at one now Seesaw: at one end there is a force, e.g. in the form of the Weight force of a child. Our Reference point is the suspension of the seesaw. Now let's imagine that the suspension has been placed high enough so that the seesaw cannot touch the ground. Then the seesaw would rotate around the suspension. So create a moment just one rotation around the selected reference point. In principle, rotation around any axis is also possible here.

You are probably thinking to yourself now: It's nice that there are forces and moments, but what does that have to do with themEquilibrium conditionsto do the equilibrium of moments and the equilibrium of forces? As you may have noticed, both force and moment have something to do with it Move to do. In the Equilibrium condition the point now is that there is no movement, i.e. that the observed object is in equilibrium. It follows that in the end on the body no resulting force and no resulting moment may work.

Superposition principle: addition of forces and moments

By the Superposition principle the mechanics, the entire moments and forces can each by simple addition calculate. If you want to know more about this video, we have linked an extra video here. Therefore the following formulation can be drawn up for the equilibrium conditions:

Here is the resulting powerthat arises from the addition of the forces. You have to keep in mind that both force and moment vectorial must be added. This leads to the following, component-wise representation:

So it arises 6 equationsto find 6 unknowns. This equilibrium condition applies at every point within a system that is in balance is located. It should be noted that the moments include both externally introduced moments and moments resulting from the forces.

Calculation of the equilibrium of moments

Of course, that looks very abstract now. So let's look at those again Seesaw: each side of the seesaw is now long and on one side sits a child, which one Weight force of 400 Newtons. Another child is sitting on the other side, but only in Distance to pivot point the seesaw. What force must act there so that the seesaw in the balance is?

To solve that, we're hiring Moment equilibrium around the suspension on:

So that the seesaw doesn't move, we need one Counterforce of 600 Newtons. The attacking forces must become too zero add.

As you can see, this is easy principle to be found everywhere. For example in the tug of war. There is one too Balance of forces Observe: Two people pull a rope with the same force, which is why neither person moves. Only when a person is stronger, i.e. exerts a greater force, does one set one Move one and there is no longer an equilibrium of forces.

The Moment equilibrium can also be found in very simple things. Let's just pick up a pen and try it on one finger to balance. In doing so, we intuitively try to establish a balance of moments so that the pen does not fall off.