/sci/ - Science & Math

>The equation could be interpreted as the faster something is moving, the more energy is required to move it more?
No

>>4250818
How so? Does the speed of an object modify the amount of force needed to move it at all?

>>4250812

a = acceleration, not speed

Yes, force is proportional to acceleration according to the equation.

My teachers were always very adamant that you add the E symbol that means "sum of" when talking about newtons second law, but whatever.

I interpret the law as an ultimate cause/effect law that basically makes everything in the universe predicable, if you could assimilate all the data. Pretty neat stuff.

Assuming the same friction, force, mass, and acceleration, they would move exactly the same.

Bodies accelerate because there are force/s acting on them. Be careful, because acceleration is the change of velocity but it doesn't mean the value of speed is changed (see uniform circular motion).

Forces may only depend on position and/or time and/or velocity), F=F(x,v,t) but never depend on acceleration. Newton's equation only stablishes a relationship between forces and accelerations. It's a differential equation that can be solved in very few cases. You can play around and obtain results from it, like the conservation of mechanical energy

>>4250840
But then how does the speed of light come into play? What about mass moving just a hair under the speed of light? Increasing its speed would use the same amount of energy as accelerating an object at rest?

Bodies accelerate because there are force/s acting on them. Be careful, because acceleration is the change of velocity but it doesn't ALWAYS mean the value of speed is changed (see uniform circular motion).

Forces may only depend on position and/or time and/or velocity), F=F(x,v,t) but never depend on acceleration. Newton's equation only stablishes a relationship between forces and accelerations. It's a differential equation that can be solved in very few cases. You can play around and obtain results from it, like the conservation of mechanical energy

>reading into Newtonian mechanics too much
ISHYGDDT

It all breaks down at the quantum level anyway. It's not precise, merely a statistical approximation.

You don't understand what you're talking about.

>If the same amount of force is applied to both, wouldn't one accelerate more then the other?
I'm guessing by accelerate you mean total speed gained? You're thinking about this all wrong. An acceleration is a rate of change. If you apply a certain force to an object of a certain mass you can't tell how much velocity it will gain unless you specify the length of time or the distance over which the force is applied.

Works is the Force applied summed over the path it is applied along. If you apply a force to an object moving really fast and an object moving really slow for the same amount of time they each gain the same amount of velocity. The faster object will gain a lot more energy though. If you apply the same force over the same distance then they will gain the same amount of energy but the slower one will gain a lot more velocity.

>>4250847
Assuming the same friction, yes.

>>4250847

Newtonian physics don't apply to objects moving near the speed of light. The laws are not generalized, they only work in the macro world.

>>4250853
But then why is it impossible to exceed the speed of light?

>>4250831
> E symbol
Upper case sigma

>>4250812
>The equation could be interpreted as the faster something is moving, the more energy is required to move it more

Nope

\thread

>>4250812
>I'd really like input from people who actively study this stuff, not just people who've taken a year of undergrad physics.
In a year of undergrad physics I studied vastly more complex problems than Newton's Second Law. The people who are actively studying this probably think Newton is the guy who turns figs into cookies.

>>4250812
No. You are completely wrong.

\thread

>>4250859
I see. What laws govern particles? And shouldn't Newtonian mechanics be emergent from them?

STOP! OK!
didn't read whole thread, but my questions are:
1)how F=ma is derived (I mean from what)
2)how momentum p=mv is derived?
Or these are just axioms (don't know how it is called in physics)

>>4250875
I'm pretty sure both come directly from experiment.

>>4250864
I lol'd heartily.

>>4250864
Because as the speed of something increases, the mass decreases. If you were to obtain parity with light speed you would be massless as this is the speed where light, a massless entity travels at. Therefore if you did travel that fast, you would cease to exist at that speed. And since you cannot destroy matter, that speed is unreachable for objects with mass. Its like an asymtote on a function depicting speed and mass.

>>4250875

Proposed and confirmed by experiments.

Still, the second law can be derived from 'higher' principles like the one of least action. Nature seems to look for paths that make energy spending minimum, and the analysis of that confirms the laws of motion, which is pretty cool.

Do you see a "v" anywhere in F=ma? No, so it is velocity independent. It doesn't matter how fast you're moving (assuming non-relativistic speeds), it always takes the same amount of force to produce the same amount of acceleration.

I think you have a lack of understanding as to what acceleration actually means. If you drop a bowling ball from some height, it will start off with zero velocity. After the first second, it will be moving at about 10 meters per second. After two seconds, it will be moving at about 20 m/s, etc. The fact that the velocity changes over time means that the ball is accelerating. Acceleration is the rate change of velocity over time.

>>4250875
>>4250875
we've never actually proven they are we just assume its so and make guesses this is also how we came up with evolution theres not really any evidence we just assume and do tests and then make the results fit.

>>4250892
can you elaborate on that higher principles, because that's what I'm interested in?

>>4250894
no, mass increases. you could not reach light speed because your mass would have to be infinite and would therefore require infinite energy

>>4250894
Ahhhhh. So mass changes with speed. This is what I was looking for. So to modify my question:

You are an observer looking at two objects moving at different speeds. At the same speed they have the same mass. If you apply the same amount of force to both, then one would end up moving faster then the other? So, if time is movement, then it would appear one is moving faster in time?

>>4250882
>>4250875
>>4250891
>>4250892
LMFAO.

Fundamentally they are derived from symmetry laws and calculus of variations. It its pretty complicated shit (compared to the shit you know). Pretty much all physics can be derived from that shit.

All physics equations you have/will ever see are derived from that shit.

>>4250909
No, assuming the same friction

>>4250909

>>4250913
>It its pretty complicated shit (compared to the shit you know).

LOL. It is taught in Classical Mechanics 2; it is not complicated shit at all. You're a pretentious douchebag and you don't understand physics. It's not wrong to say that F=ma and p=mv are axioms determined from observation, historically they were. The principle of least action isn't any more valid than Newton's formulation of mechanics, it is just a different axiom from which to formulate classical mechanics.

ITT: People are implying that neutrinos didnt already break light speed

>>4250931
Actually, least action principles can be extended to QM and GR, but Newtons laws completely fail at those levels. Working in terms of energy is more fundamental.

You're correct though, that at the Newtonian scales the Lagrangian and Hamiltonian formulations are completely equivalent to Newton's laws.

>>4250931
>The principle of least action isn't any more valid than Newton's formulation of mechanic

Nope. The principle of least action IS A FUCKING FUNDAMENTAL OF THE UNIVERSE (Everything we know).

It can be used to derive Classical Mech (Newtonian, Lagragian, Hamiltionian), Relativity (Special, General), Quantum Mech, QFT, QED, QCD, etc. It is a universal law that always fucking applies. There is no known physics that exists independent of the least action principle.

Newtonian Mech is shit that only works for a narrow range of physical systems. Least action APPLIED TO FUCKING EVERYTHING.

I'd hate to be your students bro.

>>4250931
>taught classical mech 2
>doesn't know that the least action principle applies to all fucking physics

You must go to a really shitty university. Some state school?

>>4250931
>The principle of least action isn't any more valid than Newton's formulation of mechanics

>>4250931
>thinks the least action principle only works for classical mechanics

>>4250971
We get it, samefag.

Man you people are fucking lame.

Guys Guys Guys, I just saw something

So,
F = m*a
Right?

But
a^2+b^2=c^2 -> a=sqrt(c^2-b^2)

Therefore:
F = m*sqrt(c^2-b^2)

>>4250990
Welcome to /sci/

>>4250931
>The principle of least action isn't any more valid than Newton's formulation of mechanics, it is just a different axiom from which to formulate classical mechanics.
10/10 best new physics troll

sage because babby OP can't read a physics textbook or understand arithmetic

>>4250995
Oh my god... My entire life has been a lie!