In physics, the normal force 
(occasionally N) is the component, perpendicular to the surface of contact, of the contact force 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 forces acting on the object, such as the force with which the object pushes against the surface and friction.
In another common situation, if an object hits the surface with some speed, and the surface can withstand it, the normal force provides for a rapid deceleration, with the speed depending on the flexibility of the surface. If the object is soft, the outer part will tend to decelerate more rapidly, the inner part can do that more gradually, and the layer in between is compressed, deforming the object.
The normal force is one of the basic concepts in mechanics, the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements.
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Equations
In a simple case such as an 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 (or the weight of the object), that is, Fn = mg, where m is mass, and g is the acceleration due to gravity (about 9.81 m/s2 on Earth). The normal force here represents the force applied by the table against the object that prevents it from falling, and basically means that the table is sturdy enough to hold the object up without breaking.
Where an object rests on an incline, the normal force is perpendicular to the plane the object rests on, the horizontal component representing its tendency to slide down the plane. The strength of the force can be calculated as:
- Fn = mgcos(θ)
where Fn is the normal force, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the inclined measured from the horizontal.
The normal force is one of several forces which act on the object. In the simple situations so far considered, the most important other forces acting on it are friction and the force of gravity.
Using vectors
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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 describing the stress state of the surface. That is,
Or, in indicial notation,
The parallel shear component of the contact force is known as the frictional force (
).
The static coefficient of friction for an object on an inclined plane can be calculated as follows:[1]
- μs = tan(θ)
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, while riding 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).
References
- ^ Nichols, Edward Leamington; Franklin, William Suddards (1898). The Elements of Physics. 1. Macmillan. p. 101. http://books.google.com/books?id=8IlCAAAAIAAJ.
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