How did Newton come about with F=ma?

  • Context: Undergrad 
  • Thread starter Thread starter yasar1967
  • Start date Start date
  • Tags Tags
    F=ma Newton
Click For Summary

Discussion Overview

The discussion centers on the origins of Newton's formulation of the relationship between force, mass, and acceleration, specifically questioning why he did not express it in the form F=kma and how he arrived at his conclusions. Participants explore theoretical and historical aspects of Newton's work, including references to Galileo's experiments and the development of units in different measurement systems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Historical
  • Technical explanation

Main Points Raised

  • Some participants question why Newton did not write the equation as F=kma, suggesting he may have reasoned from Galileo's experiments that a=F/m.
  • Others note that in certain systems of units, such as the metric system, the constant of proportionality can be set to one, making F=ma a valid expression.
  • It is mentioned that Newton did not use the same physical concepts of force and motion that are understood today, and he primarily employed geometric arguments rather than algebraic expressions.
  • Some participants argue that Newton's definitions of motion and force differ from modern interpretations, with references to his definitions of quantity of motion and impressed force.
  • A later reply asserts that Newton conducted significant experiments in mechanics and optics, countering the claim that he was solely a theoretical physicist.
  • Discussion includes the implications of unit definitions in the metric system and how they relate to the formulation of physical laws.
  • There is a mention of the speed of light and its significance in the metric system, with some participants discussing its numerical representation and relation to other physical constants.

Areas of Agreement / Disagreement

Participants express differing views on Newton's experimental practices, the formulation of his laws, and the implications of unit systems. There is no consensus on how Newton arrived at his conclusions or the significance of the constant of proportionality in his equations.

Contextual Notes

Some limitations in the discussion include the lack of access to Newton's original texts, the ambiguity in the definitions of force and motion, and the historical context of Newton's work compared to modern physics.

yasar1967
Messages
73
Reaction score
0
If he's thought Force must be proportional to the mass and acceleration why didn't he write down the equation in:
F=kma

form , how did he cancel out the k constant?

or did he come to the solution with Galileo's fallen objects experiments and reasoned :

a=F/m (a equals to g here of course)

examining the results and seeing that as m stays constant F must be changing so that g always the same??

As far as I know Newton is not an experiment-man, he's more of a theoretical-physicist.
 
Physics news on Phys.org
You can always choose a system of force, mass and acceleration units in which k equals 1.
 
In typical English units, one does have to use F=kma. Newton did not say F=ma. That statement is true in the metric system, but work on the metric system started in the late 18th century, 100 years after Newton published his Principia Mathematica. The metric system was explicitly formulated so as to make the constant of proportionality equal to one.
 
yasar1967 said:
If he's thought Force must be proportional to the mass and acceleration why didn't he write down the equation in:
F=kma
<snip>
As far as I know Newton is not an experiment-man, he's more of a theoretical-physicist.

I don't have a copy of the Principia with me (it's available online, IIRC), but Newton didn't have the same physical concepts of force and motion that we have today. As a point of fact, Newton never wrote "F = ma". He generally used geometry and geometrical arguments.

Newton made several definitions:

I) The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.

II) The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.

III) The Innate force of matter (vis insita) is the power of resisting, by which every body, as much as in it lies,endeavors to perservere in its present state, whether it be of rest, or of moving uniformly forward in a straight line.

IV) An impressed force (vis impressa) is an action exerted on a body, in order to change it's state, either of rest, or of moving uniformly forward in a straight line.

V) A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center.

It's important to note that definition II and III are now taken to refer to momentum, while IV would translate to F = dp/dt. Also, there is a distinction between the origins of various forces. AFAIK, Newton did not use the d/dt notation, either.

Now, if you ask the question "How did Newton come up with these defintions?", the answer is simply that he was a scientist of the first rank. Or that he came up with correct definitions while his competitors came up with useless defintions.
 
thank you
 
yasar1967 said:
If he's thought Force must be proportional to the mass and acceleration why didn't he write down the equation in:
F=kma

form , how did he cancel out the k constant?

or did he come to the solution with Galileo's fallen objects experiments and reasoned :

a=F/m (a equals to g here of course)

examining the results and seeing that as m stays constant F must be changing so that g always the same??

As far as I know Newton is not an experiment-man, he's more of a theoretical-physicist.

Newton's second law states the following:

II. The "rate of change of motion,"i.e., the rate of change of momentum" is proportional to the impressed force and occurs in the direction of the applied force.
Mathematical Physics, by Donald H.Menzel

I see nothing in there that states that F=ma

If you use mass pounds in the US customary system (also known as imperial) then the proportionality constant is not m. Of of course if you use slugs then it is m.

Anyway, I presume in the metric system that the unit of mass was chosen to eliminate the constant of proportionality.
 
You should probably read Newton's Principia to develop an insight into his method, although I think he was more about presenting results than he was about how he reached them.
 
John Creighto said:
Anyway, I presume in the metric system that the unit of mass was chosen to eliminate the constant of proportionality.

In the metric (SI) system, the unit of force (the Newton) is defined as the force that causes a 1-kg object to accelerate at 1 m/s^2.
 
jtbell said:
In the metric (SI) system, the unit of force (the Newton) is defined as the force that causes a 1-kg object to accelerate at 1 m/s^2.

That's a good point. You can pick any unit of mass and then define the force to get rid of the constant or you can define any unit of Force and then choose then define the definition of the mass to get rid of the constant.

It is interesting to think that given a certain set of units what other units can we derive from them. What to take as fundamental besides the speed of light?
 
  • #10
I think it is pretty amazing that the speed of light is 3*10^8 m/s, within many decimal places. One of the, if not the most fundamental quantities is just about an integer in metric. I suppose of all the quantities, chances are that one will be that way, but the fact it is the speed of light for metric is pretty cool.
 
  • #11
That's not an accident- because the speed of light and the definition of 'second' as a duration of time are related, c_0 was defined to be a nice even number, leaving the second to be some wacky number of electromagnetic oscillations. NIST has some documents online discussing precisely this point.
 
  • #12
Actually, the 3*10^8 figure is an approximation - just so students aren't frustrated using 2.99792458*10^8 every time something involving the speed of light needs to be calculated.
 
Last edited:
  • #13
D H said:
The metric system was explicitly formulated so as to make the constant of proportionality equal to one.
[citation needed][/color]

:smile:
 
  • #14
neutrino said:
Actually, the 3*10^8 figure is an approximation - just so students aren't frustrated using 2.99792458*10^8 every time something involving the speed of light needs to be calculated.

OOps- my bad. You are right of course. The nice simple number resulting from the definition of c_0 is the permeability of free space: 4*pi*10^-7.
 
  • #15
yasar1967 said:
As far as I know Newton is not an experiment-man, he's more of a theoretical-physicist.

This isn't true. Newton actually carried out many important experiments in mechanics and optics. Some of these were amazingly precise given the available equipment. Their results were fundamental to his final synthesis.
 
  • #16
neutrino said:
[citation needed][/color]

:smile:

Dimensional analysis.
 
  • #17
Andy Resnick said:
I don't have a copy of the Principia with me (it's available online, IIRC), but Newton didn't have the same physical concepts of force and motion that we have today. As a point of fact, Newton never wrote "F = ma". He generally used geometry and geometrical arguments.
Newton's Laws of Motion in their original form, translated into English from the original Latin, are http://members.tripod.com/~gravitee/axioms.htm#Law I". (press cancel if a password window comes up).

AM
 
Last edited by a moderator:
  • #18
yasar1967 said:
If he's thought Force must be proportional to the mass and acceleration why didn't he write down the equation in:
F=kma

form , how did he cancel out the k constant?

or did he come to the solution with Galileo's fallen objects experiments and reasoned :

a=F/m (a equals to g here of course)

examining the results and seeing that as m stays constant F must be changing so that g always the same??

As far as I know Newton is not an experiment-man, he's more of a theoretical-physicist.

I think you're half-right to say the equation could have been F=kma. However, since the every object of mass m has a different characteristic eg. density, surface area, perhaps Newoton believed that k is already considered within m and thus decided to remove k as a redundant property?
 
  • #19
well,to know exacly how he came to this formula(and surely many other equations and quantities) u have to read the original textbooks written by the past scientist if available,
to get a half of what u want,the problem of today science is that no One knows how much effort is taken to get these information(i.e. did u know that scientist worked 50 years to prove that the Pythagorean theory :in a triangle: is not correct in every case and finaly it led to solid geometry!)
and about your question Columb has done a similar experiment about electrical forces,i think some experiment are done in this case.
 
Last edited:

Similar threads

Graduate Uncovering the Origins of F = ma: Newton's Experiment and Measurements
  • · Replies 9 ·
Replies
9
Views
2K
High School F=ma -- How did Newton find this?
  • · Replies 27 ·
Replies
27
Views
8K
High School F=ma -- True or an Illusion....
  • · Replies 19 ·
Replies
19
Views
3K
Graduate Which way did Newton find F = ma?
  • · Replies 73 ·
3
Replies
73
Views
23K
Undergrad Newton’s Laws and Euler’s laws
  • · Replies 17 ·
Replies
17
Views
6K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
Undergrad Change of coordinates in a potential energy field
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Calculating your weight in an elevator
  • · Replies 24 ·
Replies
24
Views
3K
High School Relationship between mass and acceleration
  • · Replies 9 ·
Replies
9
Views
3K
High School How did Newton come up w/ 1st law? Why does friction exist?
  • · Replies 21 ·
Replies
21
Views
3K