Calculation of Effective mass and Gravitating mass: Extension to Classical mechanics

Calculation file attached: Here

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

This expression F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, reflects an extended classical mechanics approach where the total force F is associated with both the matter mass Mᴍ and the effective mass Mᵉᶠᶠ. Here, the effective mass Mᵉᶠᶠ is introduced as an additional term that modifies the system's dynamics in motion. The effective acceleration aᵉᶠᶠ represents the combined effect of traditional acceleration and the influence of effective mass.

F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, Mᵉᶠᶠ generated when F acting in motion (v)

• F is the total force applied to the object, measured in Newtons N.
• Mᴍ is the matter mass of the object, representing its traditional inertial mass, measured in kilograms (kg).
• Mᵉᶠᶠ is the effective mass, which arises due to the interaction of the object with the applied force during motion, measured in kilograms (kg).
• aᵉᶠᶠ is the effective acceleration experienced by the object, which accounts for both the matter mass and the effective mass in the system, measured in meters per second squared (m/s²).
Calculation in attached file.

#EffectiveMass #GravitatingMass #EffectiveMassCalculation #GravitatingMassCalculation

Dominance of Effective Mass vs. Matter Mass: Determining Positive or Negative Effective Acceleration

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

Whether the effective acceleration (aᵉᶠᶠ) is negative or positive depends on which factor dominates the system—effective mass (Mᵉᶠᶠ) or matter mass (Mᴍ)—in both scenarios of motion or gravitational potential difference.

#EffectiveAcceleration #MassDominance #GravitationalPotential

Effective Mass and the Inverse-Square Law of Gravity: Implications for Gravitational Acceleration

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

In scenarios involving the inverse-square law of gravity and the concept of effective mass, these factors collectively influence an object's motion.

According to the inverse-square law of gravity, as an object moves away from the Earth's surface, the gravitational force it experiences decreases with the square of the distance. In this context, the concept of 'effective mass' becomes crucial. Effective mass introduces an 'effective acceleration' (aᵉᶠᶠ) by effectively changing the object's resistance to gravitational force.

The reduction in gravitational influence due to effective mass occurs because this mass type is not static; it is generated as the object moves or elevates. As the object ascends, the 'effective mass' modifies the overall gravitational pull, enabling the object to accelerate more easily, even as it moves farther from Earth.

In the context of 'effective mass', the inverse-square law also applies. As an object moves away from the Earth's surface, the gravitational force decreases with distance, and 'effective mass' changes the object's resistance to this force. 'effective mass', which is generated through the object's elevation and motion, modifies the gravitational pull on the object, allowing it to accelerate differently depending on whether it is moving closer to or farther from Earth.

#EffectiveMass #effectiveacceleration #GravitationalAcceleration # InverseSquareLaw

Effective Mass and Acceleration: Invariance in Classical Mechanics and Newton's Second Law

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

This expression a ∝1/Mᴍ, describes that acceleration a is inversely proportional to the matter mass Mᴍ when a force F is acting on the object. In classical mechanics, the matter mass Mᴍ is considered invariant, meaning it does not change. 

Given an object with a constant or invariant mass, when a fixed force is applied, the acceleration experienced by the object varies inversely with its mass. Consequently, for the same applied force, the object's apparent mass—referred to as its 'effective mass'—affects its acceleration:  

This perception is influenced by the object's interaction with the applied force. A lighter object (with a smaller effective mass) will experience greater acceleration, while a heavier object (with a larger effective mass) will experience lesser acceleration. The invariant mass remains constant. Thus, the concept of 'effective mass' is crucial, as it represents the apparent mass of the object in interaction with mechanical forces in motion or gravitational forces in a gravitational potential. This phenomenon is further detailed in the following discussion:

Enhancing Newton's Second Law of Motion:

Newton's second law of motion asserts that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. When 'effective mass' is considered, this law incorporates an additional concept: 'effective acceleration.'

The effective mass modifies the system's dynamics by changing the system's resistance to acceleration. For a given applied force, an object with effective mass will experience greater or lesser accelerations compared to an object with regular mass. This can be understood as a form of mechanical advantage, where varying forces are required to achieve specific levels of acceleration. Essentially, the system's resistance to acceleration is optimized, which enhances the dynamics of motion.

#ClassicalEffectiveMass #EffectiveMass

Classical Mechanics and Negative Effective Mass: Foundations for 'Extended Classical Mechanics'

27-08-2024

A comprehensive approach for the research paper 'Extended Classical Mechanics: Negative Effective Mass and Acceleration Boost in Motion and Gravitational Dynamics' by Soumendra Nath Thakur involves establishing 'effective mass' within the framework of classical mechanics and integrating the concept of 'negative effective mass' using insights from the research by Chernin et al in Dark Energy and the Coma Cluster of Galaxies. This combined approach will provide a robust foundation for exploring acceleration dynamics and gravitational effects.

#effectivemass #ExtendedClassicalMechanics