5. What is a force?

            Physical science basically consists of predicting the behavior of basic particles as a function of time. In order to do this a group of particles is identified and labeled the “system”. Another group of particles which act upon the “system” is identified as the “environment”. The environment acts upon the system for a period of time and the time phased response of the system is determined.

            The manner that the environment acts upon the system can be illustrated with a system consisting of a single basic particle acted upon by a series of “head-on” impacts by basic particles making up the environment. Let each collision produce a momentum change of  where m is the system particle mass and  is its change of velocity. Let each impact be in the same direction, let the impacts occur at equal time intervals , and let all velocities be parallel (of the system and environment particles). The system particle velocity will increase in equal amounts in equal times. The smoothed curve of this response will have a slope of , or for infinitely decreasing velocity and time increments the slope will be . This is called the “acceleration” of the particle. The time rate of momentum change of the particle is , or its mass times its acceleration “a” and, thus, is ma. The system imparts an equal and opposite momentum back to the environment (because of the conservation of linear momentum). The time rate of momentum change is thus, . Since the mass is constant this can be written as  which is the time rate of momentum change and this is named “force”, F. We thus have .

            The equation  is one of the three Newton laws of motion. Another law is that for any force there is always an equal and opposite reaction. This law follows simply from the fact that the resulting mass times acceleration (produced by a force) is which also is the time rate of momentum change and this, of course, is the definition of force. The last law of Newton is that a particle not acted upon by any force continues with its same motion indefinitely. This follows from the postulates of the theory (changes can only occur as the result of a collision).

            These results can be generalized to a system with any number of particles with the provision that the acceleration considered is the acceleration of the center of mass of the system of particles.