High School Why do we take k=1 in the derivation of F=k*ma?

[Dale]

But I'm just stating what is, I think, the conventional way of teaching it.

I am not sure it is the conventional way, but I agree with you on the validity of this approach. And since most people think of physics in terms of SI units I think this is the best view.

 

[e-pie]

I think this is the best view.

Maybe but what is physics without units? What is physics without some particular case?

To quote Feynman on this in my own words: I need a formula for Euclidean space. Mathematicians will first derive the base case say for n=1,2,3 and further generalize it into n. But Physics don't always require particular cases, Physicists need the formula for n=3. Physics is an exact science whereas mathematics to some extent is not(as it always gives generalized versions of everything).

Mass of a bar is 1 or n does not make any sense if no unit is given. Atleast it is true for Physics.

 

[Dale]

Maybe but what is physics without units?

This is a weird response. Did I suggest doing physics without units?

 

[e-pie]

Let's clear up on what each other is suggesting. I rushed a bit.

You go first.

 

[Dale]

Let's clear up on what each other is suggesting. I rushed a bit.

You go first.

Newton’s 2nd law is a definition in SI units. It cannot be tested using SI units.

 

[e-pie]

Newton’s 2nd law is a definition in SI units. It cannot be tested using SI units.

Please explain further. Maybe I am getting a wrong interpretation.

Are you suggesting the F=kma approach where k=1 because F, m and a are unit value?

 

[Dale]

Please explain further. Maybe I am getting a wrong interpretation.

Are you suggesting the F=kma approach where k=1 because F, m and a are unit value?

Since 1 N = 1 kg m/s^2 by definition it is logically impossible to ever find $f\ne ma$ in SI units.

 

[e-pie]

Since 1 N = 1 kg m/s^2 by definition it is logically impossible to ever find $f\ne ma$ in SI units.

True. But SI units did not exist when Newton wrote the laws around 1687. Even CGS was proposed by Gauss in 1830s. So historically a logical deduction of the statement using a particular set of units is not the option rather a more philosophical or experimental discussion is viable.

 

[Dale]

But SI units did not exist when Newton wrote the laws

I never said otherwise.

a more philosophical or experimental discussion is viable

Only if the discussion uses units where it isn’t a tautology. Such systems of units are possible in principle, but I don’t believe any are extant.

 

[e-pie]

Only if the discussion uses units where it isn’t a tautology. Such systems of units are possible in principle, but I don’t believe any are extant.

Fair point.

 

[gmax137]

I just don't understand the idea that Newton 1 & 2 are "definitions." Newton says, acceleration is proportional to force. This revises what had been believed for the preceding 2000 years, that velocity is proportional to force. They (Aristotle) may not have stated it that way, but that is the essence of the belief. And it is a reasonable belief, based on observation of things like books sliding across tables - they come to rest if you stop pushing on them. Reasonable but untrue in the end. See for instance
http://theoreticalminimum.com/courses/classical-mechanics/2011/fall/lecture-2

Until Newton, people seeing "a body in constant motion" looked for the motive force: the little angel wings propelling the chariot of the sun across the sky.

In my mind, Newton 1 and 2 aren't definitions, it is a pure description of how the world works in other words physics.

 

[Dale]

I just don't understand the idea that Newton 1 & 2 are "definitions."

Well, then how would you quantitatively define “force” without referencing Newton’s 2nd law?

Newton’s first law can be seen as a definition of an inertial frame and the second law as a definition of force. If you don’t use Newton’s laws to define them then you need to find another definition.

 

[ZapperZ]

I just don't understand the idea that Newton 1 & 2 are "definitions." Newton says, acceleration is proportional to force. This revises what had been believed for the preceding 2000 years, that velocity is proportional to force. They (Aristotle) may not have stated it that way, but that is the essence of the belief. And it is a reasonable belief, based on observation of things like books sliding across tables - they come to rest if you stop pushing on them. Reasonable but untrue in the end. See for instance
http://theoreticalminimum.com/courses/classical-mechanics/2011/fall/lecture-2

Until Newton, people seeing "a body in constant motion" looked for the motive force: the little angel wings propelling the chariot of the sun across the sky.

In my mind, Newton 1 and 2 aren't definitions, it is a pure description of how the world works in other words physics.

Imagine you don't know what "force" is. I decide to call a quantity "force" as the product of m and a. There's nothing that allowed me to derive that relationship. It wasn't written in the stars, or came about due to some logical series of thought. It came out of an "assignment" that I'm calling a quantity to be known as "force" and assigning how it is quantifiable.

That, by definition, is a definition!

Zz.

 

[e-pie]

I decide to call a quantity "force" as the product of m and a.

Assuming you are using same abstraction for mass and acceleration, how would you know without a logical series of thought that F=ma and not ma^2?

The point is:historically speaking, the level of rigor we use in today's science was not common around 1680s.The habit of clearly stating the axioms, proving the theorems, deriving equations with explicit meaning, defining each term independently was introduced during 1800s. So Newton may be, never tried or was aware that his laws lacked in some areas, so to avoid further confusion he never did.
But, in Newton's defense physical laws are a kind of approximation of natural behavior. We may never be 100% true. And in that sense the first two laws are what Newton had intended to use as precursor for the third law which really is a law.
While laws at formative stage try to define causes of some particular physical phenomenon, they are much later generalised. And from all the laws what we get are characteristics of a physical interaction-force.This is insufficient information to define something. Let me use an analogy,
You may see from a large distance away that something standing upright, two hands, two legs.. barely visible is walking. Suppose these are the only piece of information you can gather and you name the animal(supposedly it is) Human. Then based on these characteristics would human be accurately defined. No! The definition we can make is not wrong but not "fully" accurate also. That is we need a separate law/a comparison of all other animals/unique features of the human animal to define it. This studying I think is really analysing the situation by logically eliminating wrong options/choices.

Disclaimer. I am not a Physicist. I may be wrong.

Thanks.

More here

http://www.feynmanlectures.caltech.edu/I_12.html

 

[ZapperZ]

Assuming you are using same abstraction for mass and acceleration, how would you know without a logical series of thought that F=ma and not ma^2?

I don’t. I happen to call it force. I could easily can it ugamungo.

Zz.

 

[e-pie]

Thanks. I edited my previos post 44. Please see it.
I get your point.

 

[Dale]

Assuming you are using same abstraction for mass and acceleration, how would you know without a logical series of thought that F=ma and not ma^2?

By definition. You don’t need to have a logical series of thought. Definitions are true by definition.

So Newton may be, never tried or was aware that his laws lacked in some areas, so to avoid further confusion he never did.

It is not an indication of anything lacking to say that they are definitions. Good definitions are essential to a good theory!

in Newton's defense

There is no need to defend Newton here. He is absolutely not being attacked, nor his theory.

 

[Herman Trivilino]

delete

 

[e-pie]

Definitions are true by definition.

This can go in cycles forever.

To arrive at a definition, one must experiment/observe, rationally think and analyze... This is a logical series of thought.

And what unique property makes definitions true, you cannot define "definition" by using itself.
Eg. Bird cannot be defined using "bird", we need to use nouns like mammals, extended breast bone etc. to define it.

It is not an indication of anything lacking to say that they are definitions. Good definitions are essential to a good theory!

Newton never did directly define what a Force is. We are interpreting the implied from the laws.

A note. Since the OP's question has been answered, he has long left and this discussion is bound to end on a philosophical note, I say we call it a day.

 

[Herman Trivilino]

There is no experiment you can do test $F=ma$.

Soon after vacuum pumps became reliable enough to produce vacuums, in the late 1800's, researchers were able to accelerate particles to fast enough speeds to not only test it, but to discover that it's not a valid relationship. But for slower speeds $F=ma$ is very much a good-enough approximation.

 

[Herman Trivilino]

Since 1 N = 1 kg m/s^2 by definition it is logically impossible to ever find $f\ne ma$ in SI units.

Huhh?! We currently define the Newton as a kilogram meter per second squared and know that $F \neq ma$. Are you conflating the definition of the Newton with the definition of force?

 

[Dale]

Huhh?! We currently define the Newton as a kilogram meter per second squared and know that $F \neq ma$. Are you conflating the definition of the Newton with the definition of force?

What? I don’t know what you are saying.

 

[Herman Trivilino]

What? I don’t know what you are saying.

$F=ma$ is an approximation, valid only in the limit of slow speeds. The Newton is defined by BIPM to be a kilogram times a meter per second squared.

 

[e-pie]

Good definitions are essential to a good theory!

Since there are 7 most fundamental quantities that cannot be defined, according to you all of Physics is then wrong, because we talk about time, length yet no one can define it.

Newton himself said that we must stop asking "what" and start asking "how".

A lot of "what" s will eventually continue till eternity and nothing productive will come out from a philosophical discussion.

 

[e-pie]

$F=ma$ is an approximation, valid only in the limit of slow speeds. The Newton is defined by BIPM to be a kilogram times a meter per second squared.

We all know this and the discussion has traveled past scientific facts.

 

[Herman Trivilino]

Since there are 7 most fundamental quantities that cannot be defined, according to you all of Physics is then wrong, because we talk about time, length yet no one can define it.

The seven base units are indeed defined. What makes them base units is that they are not derived. But they are very carefully defined. The definitions undergo changes to keep up with the demands of science, technology, and engineering.

 

[Dale]

To arrive at a definition, one must experiment/observe, rationally think and analyze... This is a logical series of thought.

No, to arrive at a definition one need only write the definition down. Observations, experiments, and rational thought then can be used to determine if the definition is useful or not.

Newton never did directly define what a Force is.

Yes, this is a modern view of his theory.

you cannot define "definition" by using itself.

So what? Why should that be at all relevant.

You are just getting silly now. Have you seriously never done a proof in geometry or logic where at some point in the proof you used “by definition” as a justification? If you seriously have not then you should practice doing a few proofs, e.g. prove that a square is a rhombus and a rectangle.

 

[e-pie]

The seven base units are indeed defined. What makes them base units is that they are not derived. But they are very carefully defined. The definitions undergo changes to keep up with the demands of science, technology, and engineering.

If you mean that second is defined in this way

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

then strictly speaking that is not definition. That is standardizing.

 

[Dale]

$F=ma$ is an approximation, valid only in the limit of slow speeds.

Oh, I see what you are saying. I missed that at first.

Yes, Newtonian physics is not valid in all domains, but F=ma is valid wherever Newtonian physics is. In relativistic physics the concept of force needs to be redefined.

 

[Dale]

Since there are 7 most fundamental quantities that cannot be defined,

They most certainly can be defined. See chapter 2 of the BIPM brochure on the SI. It clearly identifies the descriptions as definitions of the SI units.

https://www.bipm.org/en/publications/si-brochure/section2-1.html#section2-1-1