Total Energy of the System of Massive Bodies:

Soumendra Nath Thakur
0000-0003-1871-7803

13-05-2024

Definition: The term 'effective mass' (mᵉᶠᶠ) delineates the variability of inertial mass or rest mass and its influence on mass-energy equivalence. It denotes a purely energetic state, governed by kinetic energy, which correlates with kinetic energy (KE). Alterations in effective mass (mᵉᶠᶠ) do not represent actual shifts in mass, but rather perceived changes resulting from the kinetic energy within the system.

The total energy (Eᴛᴏᴛ) of a system of massive bodies is the sum of their potential energy (PE) and kinetic energy (KE), expressed as Eᴛᴏᴛ = PE + KE. In classical mechanics, potential energy arises from the gravitational interaction of the bodies and is given by PE = mgh, where m is the mass of the body, g is the acceleration due to gravity, and h is the height. Kinetic energy, on the other hand, stems from the bodies' motion and is defined as KE = 0.5 mv², where v is the velocity of the body. 

In classical mechanics, inertial mass remains invariant, and there is no conversion between inertial mass (m) and effective mass (mᵉᶠᶠ). Effective mass is purely an energetic state, influenced by kinetic energy, which aligns with KE. The relationship between force (F) and acceleration (a) (F ∝ a) is inversely proportional to mass (m), where a∝1/m. However, changes in effective mass (mᵉᶠᶠ) are not real changes in mass but apparent changes due to the kinetic energy of the system.

For example, when a person experiences a change in weight while ascending or descending in an elevator, their actual mass (m) remains constant, but they feel heavier or lighter due to changes in effective mass caused by the acceleration of the elevator. Similarly, when a person sitting in a moving vehicle experiences external forces due to acceleration or deceleration, their actual mass remains unchanged, but their effective mass varies due to the kinetic energy of the vehicle.

Therefore, effective mass is attributed to the gain or loss of kinetic energy of massive bodies, including persons, and this kinetic energy is equivalent to effective mass.

The discussion emphasizes the compatibility of classical mechanics with relativistic transformations, particularly concerning the relationship between mass and acceleration. By incorporating the effects of kinetic energy on the effective mass of an object, classical mechanics can extend its applicability to relativistic contexts.

Furthermore, considering the broader implications of force-mass dynamics in various contexts, such as accelerometers and piezoelectric materials, demonstrates the versatility of classical mechanics in describing object behaviour under different forces and conditions, including relativistic effects.

The acknowledgment of relativistic effects on effective mass underscores the importance of considering mass-energy equivalence principles in classical elucidations of dynamics. By recognizing the contribution of kinetic energy to the overall mass of an object, classical mechanics can provide a more comprehensive understanding of object behaviour at relativistic speeds.