What is the formula for normal force

Friction and locomotion

In the following animation you can see a wheel resting on a surface. For example, it could be the wheel of a locomotive on the rails or a bicycle tire on a road. You can use the Surface materials choose from wheel and pad. It doesn't matter which body has which surface.

Weight force and normal force

The black cross in the middle of the wheel marks the center of gravity of the wheel. In this focal point, two forces initially attack:

  • The Weight \ (\ vec F _ {\ rm {G}} \) of the wheel. The weight forces the wheel against the base. The Amount \ (F _ {\ rm {G}} \) of the weight force you can change it with the slider on the left.
  • The so-called Normal force \ (\ vec F _ {\ rm {N}} \). The normal force is the force with which the base "normal" (Latin norma "Measure", in the sense of the right angle), i.e. acts on the wheel perpendicular to the surface. The normal force arises from the fact that the base is slightly deformed downwards by the weight of the wheel, which, according to HOOKE's law, causes an upward force. The base deforms just enough that the normal force has the same amount as the weight. Thus weight and normal force compensate each other and the wheel rests on the base.

Pulling force and rolling friction force

If you start the animation with the button below, two other forces will attack:

  • The Tensile force \ (\ vec F _ {\ rm {Z}} \). They pull the wheel in the direction of movement.
  • The so-called Rolling friction force \ (\ vec F _ {\ rm {RR}} \). It arises from the fact that the surfaces of the materials, viewed with a microscope, are never completely smooth, but rather rough. As a result, the particles "hook" to each other on the two surfaces. The wheel also deforms very easily when rolling and no longer stays completely round. All of this then appears macroscopically as a force that acts against the direction of movement. The Amount \ (F _ {\ rm {RR}} \) of the rolling friction force you can read off on the left.

In the animation, the tensile force is automatically set so that it has the same amount as the rolling friction force. Then the tensile force and the rolling friction force compensate each other and the wheel rolls over the surface at a constant speed.