Draw Every Force on One Body, Then Apply F = ma

If a particle moves with unchanging velocity, the net force on it is zero, so the third force is the negative of the sum of the other two.

If instead the body accelerates, F_net = m a as vectors: a 2.0 kg box accelerating at 12 m/s² along a given direction needs a net force of 24 N along that direction, and the unknown second force is F_net - F1 as a vector difference. For a sphere hung against a smooth wall, the three forces (wall reaction R, tension T, weight W) sum to zero as vectors, which gives T² = R² + W² and R = W tanθ, but not T = R + W.

Action and reaction are equal, opposite and act on two different bodies, so they never cancel on a single body. A horse moves forward because of the force the ground exerts on it, the reaction to the horse pushing back on the ground, not because of the force it exerts on the wagon. If gravity disappeared suddenly, the weight of all bodies would become zero but their mass would not change. A monkey climbing a light rope over a frictionless pulley, balanced by bananas of equal mass, always pulls up the bananas by the same amount that it climbs, so the distance between the monkey and the bananas stays unchanged.

In a freely falling system everything has the same acceleration g, so a spring joining two masses is neither stretched nor compressed, whatever the masses. Two blocks pressed against a smooth wall with rough contact between each other cannot be in equilibrium for any pressing force, because the smooth wall supplies no upward force and friction between the blocks is an internal force that cannot support their combined weight.