First Formulation of Second Law as F=ma ?

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    F=ma Law Second law
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Discussion Overview

The discussion revolves around the historical formulation of Newton's Second Law of Motion, specifically the transition to the modern expression "F=ma." Participants explore who first articulated this formulation and reference various historical figures, including Descartes and Euler, while also discussing the contributions of Galileo.

Discussion Character

  • Historical
  • Debate/contested

Main Points Raised

  • One participant questions whether Descartes was the first to express Newton's Second Law in the form "F=ma."
  • Another participant asserts that Descartes died when Newton was young and suggests that Newton's first law is attributed to Descartes, referencing Harris Benson.
  • A different participant mentions that Benson's work highlights Galileo's role in formulating the first law, quoting his work "Two New Sciences."
  • Some participants discuss the evolution of the second law, noting that Newton's formulation is an extension of earlier principles, particularly regarding motion without external influences.
  • One participant expresses skepticism about the historical accuracy of the "modern formulation," suggesting it may be simplified for educational purposes.
  • Another participant claims that Euler was the one who first put the law into the modern form, citing Max Jammer's work.
  • A later reply confirms Euler's contribution, referencing his work "Mechanica" from 1736.

Areas of Agreement / Disagreement

Participants do not reach a consensus on who first formulated "F=ma," with multiple competing views regarding the contributions of Descartes, Galileo, and Euler. The discussion remains unresolved regarding the historical attribution of the formulation.

Contextual Notes

Participants express uncertainty about the historical timeline and the evolution of the laws of motion, highlighting the dependence on interpretations of earlier works and the context in which they were written.

j_wendt
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First Formulation of Second Law as "F=ma"?

Newton expressed his Second Law of Motion as
The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
.Who was the first to put it into the modern form F=ma? Was it Descartes?
 
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Descartes died when Newton was 7... In fact, according to Harris Benson, Newton's first law is due to Descartes!
 
quasar987 said:
Descartes died when Newton was 7... In fact, according to Harris Benson, Newton's first law is due to Descartes!

1650,exactly.Born in 1596.Newton was born on Christmas Day 1642,according to the Julian Calendar,7th of January 1643 according to the Gregorian one.

I never heard of this Harris Benson,but maybe he should have asked Galileo Galilei as well.I believe it's his law.

Daniel.
 
Benson is the author of 3 non-calculus based physics book. They are generally a very good introduction to the subject imo.

Don't worry, he also mentions Galileo's leading role in the formulation of the first law by quoting "Two new sciences":

"A body stays in motion at constant speed on an horizontal plane without friction."

However, the second law as we know it is more recognizable in the extension of this principle to all bodies, and not just those moving on an horizontal plane without friction. :smile: On this topic, Descartes wrote:

"A body which is not under an exterior influence moves in a straight line at regular speed."

... And then Newton really just replaced the vague expresion "under an exterior influence" by the somewhat less vague "force". :smile:
 
quasar987 said:
However,the second law as we know it is more recognizable in the extension of this principle to all bodies, and not just those moving on an horizontal plane without friction. :smile: On this topic, Descartes wrote:
"A body which is not under an exterior influence moves in a straight line at regular speed."
... And then Newton really just replaced the vague expresion "under an exterior influence" by the somewhat less vague "force". :smile:

Does that make any sense to you??I think u probably meant the first law. :wink: The second speaks about the variation of momentum under nonnull resulting exterior forces.

Daniel.
 
I don't know about its history, but I have the impression that the "modern formulation" that you mention is, instead, the watered-down version tailored for non-calculus courses, where the mass is almost always assumed constant.
 
j_wendt said:
Newton expressed his Second Law of Motion as .Who was the first to put it into the modern form F=ma? Was it Descartes?
I believe it was Euler. Max Jammer calls F=ma "Euler's forumation" in his book Concepts of Mass in Contemporary Physics and Philosophy.

Pete
 
Thanks for the reference, Pete. The book is online at Amazon; I may have to spend the $10 D/L it. The first few pages look interesting.

The index is also at Amazon, but it doesn't seem to mention Euler.

John
 
It indeed Euler[/URL] , Mechanica, 1736.
 
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