# Normal Force

on . Posted in Classical Mechanics

Normal force, abbrevation is $$F_n$$, in physics describes the force exerted by a surface on an object in contact with it, perpendicular to the surface.  It is called the "normal" force because it acts perpendicular or normal to the surface at the point of contact.  The normal force arises as a reaction force to counterbalance the force applied by an object onto a surface due to gravity or other external forces.  It prevents the object from sinking into the surface or passing through it.  The magnitude of the normal force depends on the weight of the object or the force exerted on it, as well as the angle or inclination of the surface.  The normal force is equal in magnitude but opposite in direction to the force applied by the object on the surface, according to Newton's third law of motion.

In situations where an object is on a flat horizontal surface, the normal force is equal to the weight of the object, resulting in a net force of zero in the vertical direction if no other forces are present.  However, on inclined surfaces or in situations involving vertical acceleration, the normal force may vary accordingly to maintain equilibrium.  The normal force plays a significant role in analyzing and predicting the motion of objects on inclined planes, calculating contact forces, determining the stability of structures, and understanding the mechanics of objects in contact with surfaces.

It is important to note that the normal force is distinct from the gravitational force acting on an object. The gravitational force pulls the object downward, while the normal force acts upward to counterbalance it.

## Normal force formula

$$\large{ F_n = \frac{ f_k }{ \mu_k } }$$     (Kinetic Friction)

$$\large{ f_k = F_n \; \mu_k }$$

$$\large{ \mu_k = \frac{ f_k }{ F_n } }$$

Symbol English Metric
$$\large{ F_n }$$ = normal force $$\large{ lbf }$$ $$\large{N}$$
$$\large{ f_k }$$ = kinetic friction $$\large{ lbf }$$ $$\large{N}$$
$$\large{ \mu_k}$$  (Greek symbol mu) = kinetic friction coefficient $$\large{ dimensionless }$$

## Normal force formula

$$\large{ F_n = \frac{ f_s }{ \mu_s } }$$     (Static Friction)

$$\large{ f_s = F_n \; \mu_s }$$

$$\large{ \mu_s = \frac{ f_s }{ F_n } }$$

Symbol English Metric
$$\large{ F_n }$$ = normal force $$\large{ lbf }$$ $$\large{N}$$
$$\large{ f_s }$$ = static friction  $$\large{ lbf }$$ $$\large{N}$$
$$\large{ \mu_s }$$  (Greek symbol mu) = static friction coefficient $$\large{ dimensionless }$$

Tags: Force