F = maby YellowTaxi Tags: None 

#1
Nov1909, 06:29 PM

P: 196

Does this equation F= ma (Newton's famous second law of motion) actually tell us anything?
When I was studying physics at college I realised that every time we used this equation, a couple of lines of algebra later it seemed we'd always divide throughout by the object's own mass and find out it's equation of motion. Amazing Or is it? Weren't we really just adding the all the acceleration vectors together to find out the object's path ? (Not amazing) If so, then that F = ma law isn't adding any new information whatsoever to the laws of motion, and the whole thing of Newton's 2nd law is an illusion. Aren't Galileo's principle of inertia (1st law), and the conservation of momentum (3rd law) all that we really need to do physics ? 



#2
Nov1909, 11:48 PM

P: 87

well first off, F=MA is probably one of the most integrated parts of physics..... EVER. you can derive so many things from it, Momentum is actually derived from F=MA using calculus, so technically you would need F=MA to get your momentum equations. And the reason why you would divide through by the mass was to probably isolate A because once you have A you can derive the formula for its velocity and then the formula for its position all in terms of time
Sincerely, FC 



#3
Nov2009, 02:59 AM

P: 288

@OP 



#4
Nov2009, 04:07 AM

Sci Advisor
HW Helper
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P: 26,167

F = ma(erm … technically, it's F = d(mv)/dt ) Take the Lorentz force as an example … the equation of motion is mx'' = q(E + x' x B) … there is no necessity give the RHS a name, but it's convenient to call it "force". So F = ma is really only a statement of the general physical principle that acceleration (and not higher derivatives of position) is determined by various inputs, and is proportional to inertial mass. Ultimately, it's a consequence of Emmy Noether's famous theorem, that every symmetry has its conservation principle. How do you get "field" forces (like the Lorentz force) out of conservation of momentum? For nonfield physics, I think you can get F = m dv/dt from conservation of momentum and Newton's third law by considering the whole universe, and dividing it into two parts, whose action and reaction are equal and opposite. 



#5
Nov2009, 08:44 AM

P: 87

[QUOTE=sganesh88;2450997]I don't think so. Momentum can be defined independently of F=ma.[QUOTE]
Im sorry to burst your bubble but i just recently went through how Newton himself derived it using F=ma, of course using calculus, in my physics class. Im not trying to argue just saying where i got it from. Sincerely, FoxCommander 



#6
Nov2009, 08:53 AM

P: 288





#7
Nov2009, 10:18 AM

P: 87

Im not trying to argue. seriously, im just telling you how it was done 


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