Newton’s Third Law of Motion (the law of “action and reaction”) states:
“To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts.”
Newton’s third law asserts that action and reaction motions (caused by a force) occur in equal (or equivalent) and simultaneous pairs, and in opposite directions. When an impressed (applied) force accelerates a body in one direction (the action motion), an equivalent motion of reaction occurs in the opposite direction. This equivalent motion or force of reaction is exemplified by the backward “g force” that a passenger experiences during the acceleration and take-off of an airplane, the recoil when one fires a rifle bullet, or the lurch of one’s body toward a wagon when one sharply pulls on a heavy wagon with a rope.
The impact force and acceleration motion of the relatively small mass of a bullet out the barrel of a rifle in one direction is equivalent to the force and acceleration motion of the more massive rifle in the opposite direction. As Young puts it, “[T]he ratio of bullet speed to recoil speed is the inverse of the ratio of bullet mass to rifle mass.” In other words, m2/m1 is equivalent to a1/a2. Likewise, when a bazooka is fired, the explosion (force in the barrel) causes the action motion of the projectile out the front of the barrel and the equivalent reaction motion and force of the exhaust out the rear of the barrel.
Newton’s third law also empirically implies that the equivalent action and reaction motions of two bodies pulling against one another are inversely proportional to their masses. In Newton’s words, “[T]he changes of the velocities [acceleration motions] made toward contrary parts are inversely proportional to the [masses of the] bodies” (Figure 9).
For example, when a 100 kg astronaut applies a continuous or impact pulling force (action) with respect to a 500 kg barrel in empty space, the 100 kg man will (react) accelerate forward toward the barrel five times as fast and as far as the 500 kg barrel (acts) accelerates in the opposite direction toward the astronaut (during the same time period) (Figure 10). The 500 kg barrel itself does not exert an energy related force or pull with respect to the 100 kg astronaut, but the innate inertial “power” or force of resistance of the barrel’s mass to any change in its state of motion or rest is equivalent to an energy force applied against the astronaut.
The magnitude of relative intensity of the inertial force imposed by the 500 kg barrel is 5 times as great as the intensity of the reciprocal energy force applied by the 100 kg. astronaut, and the reciprocal inertial resistance of the astronaut is only 1/5th that of the barrel. The combination of these reciprocal factors is the reason for the different reciprocal accelerations of each body. Thus, such accelerations depend upon the ratio of the masses involved, vis. 5:1.
Newton’s first and second laws describe the state and motion of a body and an applied energy related force, but they do not completely describe the relationship between the source of the energy related force and the motions which it creates. Newton’s third law, which he deduced completely by himself, describes or implies these missing relationships: the reciprocal and equivalent motions, actions, and reactions of the forces, masses and accelerations involved.