 Normal contact force

The normal contact force is the component of a contact force perpendicular to the local contact surface. If $\mathbf{n}$ is the outward unit normal vector, a nonadhesive support exerts $N\mathbf{n}$ with $N\ge 0$; the remaining tangential component is associated with friction. Over an extended patch, the resultant follows by integrating the local contact pressure and allowing for changes in normal vector.

For a block at rest on a horizontal table with no other vertical loads, Newton's second law gives $N=mg$. On a stationary incline it gives $N=mg\cos \theta$, while in an accelerating lift $N$ changes with the lift's acceleration. Thus the normal contact force is a response required by the mechanical constraint, not an independently fixed multiple of mass. If maintaining contact would require a negative $N$ in a nonadhesive model, the bodies separate.