= Contact force
A contact force is an interaction transmitted between bodies through a region where their material surfaces meet. A support pushing on a resting object and <friction> acting along a sliding interface are examples. This macroscopic classification does not mean there is a new fundamental interaction of exactly zero range; the underlying material response involves electromagnetic and quantum interactions.
At a surface, resolve the force into a normal contribution and a tangential contribution:
$$
\mathbf F_c=N\mathbf n+\mathbf F_t,\qquad \mathbf F_t\cdot\mathbf n=0.
$$
For a stipulated nonadhesive contact, $N\geq0$ describes compression. In a dry <static friction> model, $\|\mathbf F_t\|\leq\mu_sN$ is a bound, not a claim that friction always equals its maximum. The contact force adjusts to the force and moment balance while that bound and the other model constraints can be met.<University Physics Volume 1 by William Moebs and others>[Section 5.6, normal force and friction; contact-force decomposition]{ref}
For an original inclined-plane example, a $2\,\mathrm{kg}$ block rests on a plane at $20^\circ$. With $g=9.81\,\mathrm{m\,s^{-2}}$, the required normal and tangential forces are
$$
N=mg\cos20^\circ\approx18.44\,\mathrm N,\qquad
F_t=mg\sin20^\circ\approx6.71\,\mathrm N.
$$
A chosen $\mu_s=0.40$ permits up to $7.38\,\mathrm N$, so this static balance is feasible in the stated model. The actual friction is $6.71\,\mathrm N$, not $7.38\,\mathrm N$. The resultant contact force balances <gravitational weight>, although its normal part alone does not.
<Nonpenetration constraints> describe a further feature of rigid contact. If the gap is $g_n\geq0$, a simple unilateral model imposes $N\geq0$ and $g_nN=0$: separated surfaces do not push on one another, while touching surfaces may carry a compressive force. Adhesion, finite deformation and fluid films require different or extended assumptions.
A force sensor between two bodies can measure the transmitted interaction while motion tracking tests the resultant-force balance. The equal and opposite contact force on the other body belongs on that other body's <free-body diagram>. Those two forces do not cancel within the force sum for just one chosen body.
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