Nuanced Interpretation of Potential Energy, Mass, and Kinetic Energy in Classical Mechanics:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

04-10-2024

Abstract

This paper delves into the intricate relationships among potential energy (PE), mass, and kinetic energy (KE) within classical mechanics, advocating for a more nuanced understanding of these fundamental concepts. It highlights how changes in potential energy significantly influence mass and the generation of kinetic energy. The direct proportionality between force and acceleration (a ∝ F) and the inverse relationship between acceleration and mass (a ∝ 1/m) illustrate that increasing acceleration necessitates a decrease in effective mass, emphasizing the dynamic interplay of these variables. Furthermore, the generation of kinetic energy stems from changes in potential energy, underscoring that KE is not a "free lunch," but rather a consequence of energy transformations. The paper suggests that without accounting for these changes, the classical mechanics framework remains incomplete. By recognizing the interconnectedness of PE, mass, and KE, this interpretation provides deeper insights into the principles governing motion and energy transformations within physical systems.

Presentation

In classical mechanics, the relationships among potential energy (PE), mass, and kinetic energy (KE) are often interpreted too simplistically. A more nuanced understanding reveals that changes in potential energy inevitably influence mass and the generation of kinetic energy.

While force (F) and acceleration (a) are directly proportional (a ∝ F), mass (m) is inversely proportional to acceleration (a ∝ 1/m). This means that as acceleration increases due to an applied force, the effective mass may decrease to maintain equilibrium in this relationship. This inverse relationship underscores that alterations in potential energy significantly impact mass.

Moreover, the generation of kinetic energy cannot be considered a "free lunch." Kinetic energy is fundamentally derived from the change in potential energy, represented by the equation KE = ΔPE = (PE in motion) − (PE at rest). This indicates that the kinetic energy produced during motion is a direct consequence of changes in potential energy. Thus, the mass of the object cannot remain constant; it must adapt to reflect these energy transformations.

Importantly, when considering only the relationship between force and acceleration (a ∝ F), without accounting for changes in potential energy, the overall understanding remains incomplete. The mass (m), which in classical mechanics can represent potential energy, must also change when potential energy varies. Therefore, ΔPE should be viewed as influencing a mass that differs from the invariant mass, effectively representing an effective mass.

Conclusion

Recognizing the interconnectedness of potential energy, mass, and kinetic energy provides a more comprehensive view of classical mechanics. This nuanced interpretation enriches our understanding of how energy transformations influence the properties of mass and motion within physical systems. Acknowledging these relationships not only clarifies existing theories but also opens avenues for future research and practical applications in the field of physics.

References:

[1] Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.org (MDPI). https://doi.org/10.20944/preprints202409.1190.v2