# First Formulation of Second Law as F=ma ?

1. Dec 24, 2004

### j_wendt

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

Newton expressed his Second Law of Motion as
.Who was the first to put it into the modern form F=ma? Was it Descartes?

2. Dec 24, 2004

### quasar987

Descartes died when Newton was 7... In fact, according to Harris Benson, Newton's first law is due to Descartes!

3. Dec 24, 2004

### dextercioby

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.

4. Dec 24, 2004

### quasar987

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. 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".

5. Dec 24, 2004

### dextercioby

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

Daniel.

6. Dec 24, 2004

### ahrkron

Staff Emeritus
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.

7. Dec 26, 2004

### pmb_phy

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

8. Dec 27, 2004

### j_wendt

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

9. Dec 29, 2004

### j_wendt

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

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