What Do F=ma and the Definitions of Force and Mass Really Mean?

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    F=ma Means
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Discussion Overview

The discussion revolves around the definitions and implications of the equation F=ma, specifically focusing on the meanings of force (F) and mass (m) within classical physics. Participants explore theoretical, philosophical, and practical aspects of these concepts, questioning their foundational meanings and relationships.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that F=ma is a mathematical representation of force experienced by an accelerating object, emphasizing its empirical basis.
  • Others suggest that the definitions of F and m are not trivial and have been subjects of extensive philosophical and scientific inquiry, referencing historical texts and ongoing debates in physics.
  • One participant proposes that mass can be seen as an additive property, suggesting that it is intrinsic to objects rather than merely a correlation with force.
  • Another viewpoint posits that the relationship between force and mass may not be straightforward, questioning the implications of defining force in terms of mass and acceleration.
  • Several participants highlight the distinction between inertial mass and gravitational mass, particularly in the context of General Relativity.
  • Some contributions emphasize practical understandings of F=ma, suggesting that the equation's utility lies in its ability to predict motion based on observed forces.
  • There are challenges to the clarity of terms like "shove twice as hard," indicating that the definitions of force and mass may not be universally agreed upon.
  • One participant mentions that in consistent unit systems, F=ma defines force while mass is defined through other means, such as standard references.
  • A claim is made that mass can be interpreted as the total energy content of an object, linking it to broader physical principles.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus on the definitions and implications of force and mass. Some agree on the empirical validity of F=ma, while others challenge its foundational meanings and the relationships between the quantities involved.

Contextual Notes

The discussion touches on unresolved philosophical questions and the dependence of definitions on context, as well as the historical evolution of these concepts in physics.

  • #31
cocosisi said:
1. masses are something intrinsic to objects, and additive
...
... It really gets me confused.

I think it will be much easier if you understand the definition of "inertial mass" to be "resistance to acceleration".

By the way; there has been no definitive proof as to the origin (source) of inertial mass; IOW, proof of the source of this "resisitance to acceleration" has not been shown definitively to be intrinsic to the matter itself.
In fact there is plenty of speculation that it is actually EXtrinsic, and could arise in a Machian sort of way from the totality of the rest of the matter in the universe. It has also been postulated that this "inertial resistance" comes from the Quantum vacuum field in the surrounding vacuum, which is also quite EXtrinsic to the material particle itself.

IOW, the origin of inertial mass is still an open question in physics.

Creator :smile:
 
Last edited:
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  • #32
cocosisi said:
F=ma
How do we define m and F? If their definition both come from this equation, then the equation doesn't really mean anything...

But their definitions do not come from this equation. The equation simply expresses how they are related through a.

Physics, and virtually every other field of science, ultimately rests upon a small set of basic concepts that are taken as virtually self-evident (similar to axioms in mathematics). Time is taken as one of those concepts, distance the second, and mass (or force—take your pick) the third. In other words, every other quantity in classical mechanics is defined via a set of rules that, ultimately, involves some combination of time, distance, and mass (or force). But these three "fundamental indefinables" are defined only "operationally"—that is, via procedures for their measurement.
 

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