Apparent Weight in the Context of Extended Classical Mechanics:

Apparent weight (Wᵃᵖᵖ) is the perceived lightness or heaviness of an object, shaped by the interplay between its matter mass and effective mass within the surrounding environment. In regions with strong gravitational potential energy but minimal or no external gravitational force, the object’s effective mass can reduce its apparent weight or even make it seem weightless. This happens because the gravitational environment alters how the object’s mass interacts with external forces, potentially making the object appear lighter due to the negative value of apparent mass or as though it’s being pushed upward due to the effect of negative effective mass. Thus, apparent weight reflects not only the force of gravity but the combined effects of the object’s matter mass, its effective mass influenced by apparent mass, the surrounding gravitational field, and any other external forces acting on it.

The apparent weight can also be influenced by the object’s motion. When moving upward, the object can feel heavier due to the opposing force needed to overcome gravity. In contrast, when in free fall, the object experiences weightlessness, as the forces acting on it, including gravity, are effectively in balance, and there is no contact force to give the sensation of weight.

The apparent weight (Wᵃᵖᵖ) can be expressed dynamically as:

 Wᵃᵖᵖ = Mᵉᶠᶠ⋅gₑₓₜ

Where gₑₓₜ is the weak external gravitational acceleration, and (Mᵉᶠᶠ) is the effective mass, which includes a negative component due to the negative apparent mass (Mᵃᵖᵖ):

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

Where Mᵉᶠᶠ includes both matter mass and apparent mass contributions.

Classical Mechanical interpretation of apparent weight:

However, the interpretation of apparent weight within the framework of extended classical mechanics introduces a redefined and expanded perspective. Here, apparent weight is not merely the perceived weight of an object, as described in classical mechanics, but a dynamic property shaped by the interaction between matter mass and effective mass, influenced by negative apparent mass. 

This interpretation diverges from the classical view, which attributes apparent weight solely to the imbalance between gravitational force and contact force. For instance, in classical mechanics, an object submerged in water has an apparent weight equal to its actual gravitational force minus the buoyant force exerted by the fluid. 

In contrast, extended classical mechanics redefines apparent weight as a dynamic property shaped by the gravitational environment and external forces that influence an object's effective mass. This framework introduces a more nuanced understanding of apparent weight under varied conditions—such as strong gravitational potentials or near-weightless states—by accounting for the combined effects of matter mass (Mᴍ) and negative apparent mass (Mᵃᵖᵖ). Unlike classical mechanics, which attributes apparent weight merely to the subtraction of contact force from gravitational force, extended classical mechanics emphasizes the role of effective mass (Mᵉᶠᶠ), providing a richer explanation for weight dynamics beyond classical interpretations.

Soumendra Nath Thakur
ORCiD:0000-0003-1871-7803
November 26, 2024 

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