Why F = m * a? vs Why not F = m + a?

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Discussion Overview

The discussion centers around the formulation of Newton's second law of motion, specifically questioning why the relationship is expressed as F = m * a instead of an alternative formulation like F = m + a. The scope includes conceptual reasoning and mathematical justification.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the validity of F = m + a, suggesting that adding mass and acceleration is inappropriate due to differing units, akin to adding apples and oranges.
  • Another participant proposes a hypothetical formulation F = C_1mz + C_2a, indicating that while it is mathematically possible to create such expressions, they must adhere to specific unit requirements for constants C_1 and C_2.
  • A later reply emphasizes that the validity of the formula F = m * a is ultimately supported by experimental evidence rather than purely mathematical reasoning.
  • One participant references Newton's original Latin text to provide historical context to the formulation of the law, although this does not directly address the question posed.

Areas of Agreement / Disagreement

Participants express disagreement regarding the formulation of the law, with some supporting the traditional F = m * a and others exploring alternative expressions. No consensus is reached on the validity of F = m + a.

Contextual Notes

Participants highlight the importance of unit consistency in physical equations and the reliance on experimental evidence to validate theoretical formulations. The discussion does not resolve the implications of the proposed alternative formulations.

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Why F = m * a?

Why not F = m + a?
 
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Adding acceleration and mass is just like adding apples and oranges, it can't be done.

Look at the units involved and combine them in a manner which makes sense.
 
Of course, it would be (mathematically) possible to have something like [itex]F= C_1mz+ C_2a[/itex] where [itex]C_1[/itex] and [itex]C_2[/itex] are constants with the correct units ([itex]C_1[/itex] would have to have units of "Newtons per kg" or "meters per second squared" and [itex]C_2[/itex] has units of "Newtons-seconds square per meter" or "kilograms".

But the only good Physics explanation as to why a specific formula is true is "that is what the experimental evidence shows".
 
From: http://en.wikipedia.org/wiki/Newton's_laws_of_motion

"Newton's original Latin reads:
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
This was translated quite closely in Motte's 1729 translation as:
Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd."
 

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