In physics, the normal force (or in some books 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 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 describing the stress state of the surface. That is,
In another case where the same object as mentioned above is on a 40 degree incline, we have to insert cos θ into the equation for normal force. Fnormal = mass · gravity · cos θ. So solving for the normal force, we get: FN = 40kg · 9.81m/s2 · cos 40° = 300.6 newtons
US Patent Issued to Robert Bosch on Dec. 3 for "Method for Controlling a Normal Force in a Frictional Contact of a Continuously Variable Transmission" (Dutch Inventors)
Dec 03, 2013; ALEXANDRIA, Va., Dec. 3 -- United States Patent no. 8,600,634, issued on Dec. 3, was assigned to Robert Bosch GmbH (Stuttgart,...
Publication No. WO/2010/036099 Published on April 1, Assigned to Robert Bosch for Normal Force Control Method (Dutch Inventors)
Apr 05, 2010; GENEVA, April 7 -- Francis Maria Antonius Van Der Sluis, Erik Van Der Noll, Antonius Adrianus Helena Maria Van Dongen and Robert...