= Normal contact force
{title2=$N$}
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 $N\geq0$; 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.
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