Unsolved Problem in Classical Mechanics (Bulletin of Pure and Applied Sciences – Physics, 2020)
The critical analysis of the foundations of classical mechanics is proposed.  Methodological basis of the analysis is the unity of formal logic and rational  dialectics. The main results of the analysis of concepts “force”, “work” and “work of  force” are the following statements: (1) the standard concept “work of force”  contradicts to dialectics (practice) and formal logic because the concept “force” is a  general abstract concept. The concept “force of interaction of material objects” is a  general concrete concept because this concept expresses the property (feature, sign,  quality) of the interaction of material objects. But the property does not perform the  work because the property is not a material object. Work is performed by a  controllable (operated) material object. Consequently, the standard mathematical  definition of work is an incorrect relationship; (2) the concept “force of interaction of  material objects” can only be defined in a genetic way: one should measure the force  of interaction with the help of a dynamometer. The dynamometer reading represents  the value of the measured quantity (force). If the measured quantity (force) is a  variable quantity, then a change of this quantity (force) is called the movement of  this quantity (force). But if the force is a constant quantity, then the movement of the  force does not exist. Consequently, the standard mathematical definition of work is  an incorrect relationship; (3) the position of the force in the coordinate system cannot  be determined because a force is not a material object, and the quantity of the force  does not have the dimension (measure) “meter”. This signifies that: (a) a force does  not exist in the material coordinate system; (b) a force does not exist on the material  path; the path length (distance) for force does not exist. Consequently, force cannot  move over a distance that has the dimension “meter”. This signifies that the  standard mathematical definition of work is an incorrect relationship; (4) in point of  view of dialectics; work and energy are nonidentity concepts. Work is the activity of  man, a robot, a controllable machine created by man. Work represents a rational,  reasonable, well-directed, purposeful, purposive activity which manifested in the  informational and material change of reality. This activity is the impossible if  intellectual, informational, energy, and material resources do not exist. Thus, the  standard mathematical definition of the work of force is a formal-logical, dialectical  (practical), and physical errors.