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Normal force
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the normal force (or in some books N) is the component, perpendicular to the surface of contact, of the contact force
Contact force

In physics, a contact force is a force between two objects that are in contact with each other. This is distinct from a non-contact force , such as gravity or magnetism attraction/repulsion....
 exerted by, for example, the surface of a floor or wall, on an object, preventing the object from entering the floor or wall. In a static situation it is just enough to balance the force with which the object pushes, e.g. its weight on the floor, or a smaller force if somebody leans against a wall.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the normal force (or in some books N) is the component, perpendicular to the surface of contact, of the contact force
Contact force

In physics, a contact force is a force between two objects that are in contact with each other. This is distinct from a non-contact force , such as gravity or magnetism attraction/repulsion....
 exerted by, for example, the surface of a floor or wall, on an object, preventing the object from entering the floor or wall. In a static situation it is just enough to balance the force with which the object pushes, e.g. its weight on the floor, or a smaller force if somebody leans against a wall. If an object hits the surface with some speed, the normal force provides for a rapid negative acceleration, depending on how flexible the floor/wall is (and, of course, if it can provide enough force for stopping the object instead of breaking). Also, if the object is soft, only the outer part needs to decelerate rapidly, the inner part can do that more gradually, while the layer in between is compressed.

In general, the magnitude of the normal force is the projection of the surface traction, T, in the normal direction, n, and so the normal force vector can be found by scaling the normal direction by that force. The surface traction, in turn, is equal to the dot product of the unit normal with the stress tensor
Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
 describing the stress state of the surface. That is, Or, in indicial notation,

Frictional force


The parallel shear
Shear

Shear as a noun may refer to:*Bias , in clothing design, fabric may be cut on the shear*Cosmic shear, an effect of distortion of image of distant galaxies due to deflection of light by matter, as predicted by general relativity ...
 component of the contact force is known as the frictional force
Friction

File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
 .

Example

In a simple case such as a 40 kg object resting upon a table, the normal force on the object is equal but in opposite direction to the gravitational force applied on the object i.e. the weight
Weight

In the physical sciences, weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the Earth's gravity is approximately constant; this means that an object's weight is roughly proportional to its mass....
 of the object. In this case the normal force is given by, 40 kg · 9.81 m/s2=392.4 newtons where 9.81 m/s2 is equal to the acceleration due to gravity
Standard gravity

Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to Earth's gravity at the Earth's surface at sea level....
 (near the Earth's surface).

In another case where the same object as mentioned above is on a 40 degree incline, we have to insert cos ? into the equation for normal force. Fnormal = mass · gravity · cos ?. So solving for the normal force, we get: FN = 40kg · 9.81m/s2 · cos 40° = 300.6 newtons

Real-world applications

For a person standing in an elevator moving with constant velocity (including stopped), the normal force on the person's feet balances the person's weight. In an elevator that is accelerating upward, the normal force is greater than the weight and so the person's apparent weight increases (making the person feel heavier). In an elevator that is accelerating downward, the normal force is less than the weight and so a user's apparent weight decreases. If a user were to stand on a "weight scale", such as a conventional bathroom scale, onto the elevator, the scale would read either more or less than the person's actual weight when the elevator is accelerating up or down (respectively) because weight scales measure normal force (which varies as the lift accelerates), not gravitational force (which does not).