Newtons first law

How did newton come up with the f=ma equation? Expetimentation, mathematical deduction or did he just define force that way?

Why don't you ask him? He might have AMA on Reddit someday.

"A newton (N) is the international unit of measure for force"

If I had to guess he just defined it...

Welp, "Some concept is described by those elements whose change also directly affects the change in the magnitude of the concept itself." is what a high me wrote apparently.

Not trying to be smug or anything, I just hope I'm right because I was breaking my head with physics equations and why they are what they are until not too far away from now... after this "realization" I sort of just let go and accepted it.

Which are the most reddit scientists?
Actual scientists I mean not black science man etc.

That's his second law.

Shit, is this master Yoda behind the keyboard?

He defined all three terms, by fiat, early in the Principia. Which is what a good textbook should do. His definitions came to be accepted to because they produce results which seem to apply usefully in the real world.

The only ambiguity was that he had to assume inertial mass (which is what's in F=mA) was the same as gravitational mass (F=GmM/R^2) because this makes all objects fall with the same acceleration. The equality couldn't be justified except that "it works" until Einstein.

My professor said that no matter how you try you will never derive Newton's equations, you can think them as given by god.

Maybe that's how he really got them.

Maybe they're underivable because they're what the physics is built upon? It can't be a magical circle, right? It has to begin somewhere. idek

Newton thought that if nothing interacts with an object, its velocity should remain static (that is if you're moving at 10 m/s and nothing interacts with you you would forever go at 10 m/s). So if something does interact with you your velocity should change. You would be affected by a 'force'. Originally that's how he wrote his equation F = m * (dv)/(dt).

and this turned out to be correct when you test it in space where there is no air resistance, did he get lucky? or maybe he tested it in some vacuum

>did he get lucky? or maybe he tested it in some vacuum
Neither. You don't need a perfect vacuum to recognize how objects behave as you approach more vacuum-like conditions.

It's really just the definition and how we describe force. No experimentation needed.

I imagine the whole situation backward from yours. He gets hit in the head with an apple, it hits so hard he thinks someone clobbered him. When he looks and sees that it's only a small apple, he wonders how it felt so heavy when it hit him even though it's lite. Then he thinks about how speed affected the apparent "weight" of the apple, which wasn't contained in the apple itself but just a result of how fast it was moving.

He discovered the relationship between mass an acceleration was usable to determine the amount of force imparted. There were no units for this new formula, as he was the first to discover it, which is why the “F” is given the unit “Newtons”. In simple terms, he just defined force that way.

He deduced it from the behavior of rolling spheres

Ignore all the brainlets in this thread. Newton figured that out through EXPERIMENTATION. He actually made things collide (rocks, etc), thought about the results a lot, and was able to see the pattern. Look it up.

His laws cannot be deduced mathematically from anywhere, they are obtained directly from reality. That's his whole deal, what separated him from people like Descartes, who insisted on deducing everything, thinking that experiments are not necessary to understand reality.

No you retard. Mass, force and acceleration are concepts that have been around for thousands of years. He didn't redefine those concepts, he found how they are related, something nobody had been able to do before, and what enabled humanity to have all the technology we have today.

he derived the equations purely by dropping large metal spheres from pisas leaning tower

Unit of Force = N
Unit of Mass = kg
Unit of Acceleration = (m)/(s^2)
N = (kgm)/(s^2)

Simple unit analysis makes it eaay in retrospect, but I don't know how we would have determined it deductively,

He found a good definition for force you massive faggot learn how to read properly

He was a genius.

It's impossible to find out exactly what his thought process was, but mainly it was due to Kepler's law that he saw how his constant are in same time translated to derivatives of position.

Ever heard of a lever?

It's pretty crazy that something that appears kind of dumb can have such massive results on our knowledge of reality. What if someone walked by and saw him doing his experiments? They'd think "What the fuck is that guy doing lol". It doesn't seem like something that would help you peer deep into the nature of reality, in fact you'd probably look crazy if you claimed it would

But indeed it does and it's obvious now. Are there any other simple experiments that haven't been done which will give deep insights into reality, or are they all done now and we have to instead move towards LHC style experiments?

this board is not for you

an apple fell on his head

It's a postulate, introduced by reasoning about the phenomena in reality.
But in fact, he did not write
[math] \mathbf{F} = m\mathbf{a} [/math],
neither,
[math] \mathbf{F} = \frac{d\mathbf{p}}{dt} [/math],
but he did write something like "the rate of change in the momentum of a body is proportional to the force applied on it". In a mathematical notation, this proposition is translated as the second equation above. The first one is a particular case of the second, assuming the body's mass is constant at any given time.

This should be kind of obvious, but if there were an obvious basic experiment that hadn’t been conducted that would benefit our knowledge, somebody would have conducted it. You can’t acknowledge a gap’s solution as obvious and just leave it be.