# What does normal force equal?

## Inclined planes¶

If a body is placed on an incline, it becomes due to its weight accelerated down the slope along the incline. This can be explained if one thinks of the weight force divided into two partial forces (along the inclined plane and perpendicular to it):

• The force perpendicular to the inclined plane becomes the normal force called. This part of the force would cause the body to sink into the inclined plane, but if the ground is solid, the ground works against it due to its rigidity.
• The force parallel to the inclined plane becomes the downhill force called. This force component causes the body to accelerate along the inclined plane.

If the downhill force is large enough to overcome the frictional force acting between the body and the inclined plane, the body begins to slide.

The weight is on a horizontal plane equal to the normal force , the amount of downhill force is zero. Conversely, along a vertical wall, the downhill force is equal to the weight, and the (pressing) normal force is equal to zero. At any angle of the inclined plane, the following relationships apply to the amounts of normal and downhill force:

This was used to be the angle between the weight force and normal force equal to the angle of the inclined plane, because there are two perpendicular angles. One also denotes with the length of the inclined plane, the similarity of the two force triangles and the triangle of the inclined plane results in the following relationship between the downhill force and the weight of the slide:

The longer the inclined plane, the smaller the downhill force acting along the plane. For this reason, roads and paths are laid in serpentines in the mountains.

The size of the angle can be based on the ratio of the height to the (horizontal) width calculate the inclined plane. This applies to the angle :

So the smaller the angle is, the longer it is at a certain height of climb the horizontal width or because of also the length the inclined plane.

Inclined planes with friction

If an object is placed on an inclined plane, it is caused by the downhill force accelerated down the incline. If the opposing frictional force between the object and the inclined plane cannot be neglected, it must be taken into account as follows:

Here referred to the coefficient of friction for static or sliding friction; in addition, was for the acting normal force the above formula (1) is used.

If the object is initially at rest on the inclined plane, it then begins to slide when the downhill force exceeds the maximum static friction force. For the borderline case, the following applies:

This equation can be on either side be shortened; one thus obtains:

If the coefficient of static friction for the pair of materials (object - inclined plane) is known, it is possible to specify immediately from which angle the object will start to slide:

The angle is also called the “maximum angle of approach”. It can be used, for example, to express the slope up to which a powder-like bulk material can be piled up before the material begins to slide.

If an object moves down an inclined plane at a constant speed, the downhill force is equal to the sliding friction force. Through an experimental determination of the associated angle can thus determine the coefficient of sliding friction can be determined between the material of the object and the material of the inclined plane.

Wedge effect

A wedge with a force on the back is exercised, the surrounding material can drift apart. This splitting effect, which is used, for example, with axes or chisels, can also be explained by means of the distribution of forces on an inclined plane, if one thinks of the wedge as divided into two right-angled triangles.

The power that is exerted on the wedge can be divided into two normal forces and divided perpendicular to the wedge surfaces. One denotes the width of the wedge back with , the length of an inclined wedge surface with and half the wedge angle as , then:

Because the length of the inclined surfaces is usually longer than the width of the wedge, the splitting normal forces are greater than the force acting on the wedge .