Definition of Work: Unsolved Problem in Classical Mechanics

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.

Keywords: general physics, classical mechanics, Newtonian mechanics, mathematical methods in physics, formalisms in classical mechanics, education, philosophy of science, history of science.

PACS: 01.40.Fk, 01.40.-d, 01.55.+b, 01.65.+g, 01.70.+w, 01.90.+g, 02.90.+p, 04.25.Nx, 45.05.+x, 45.20.- d, 45.20.D-