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Physics Question - ma = mg
SiliconWizard:
--- Quote from: TimFox on June 23, 2021, 09:59:36 pm ---You have merely re-stated Newton's Third Law.
--- End quote ---
Yes, it all comes from Newton's laws. Nothing special. It's just that the notion of weight is something that is actually not all that intuitive.
--- Quote from: TimFox on June 23, 2021, 09:59:36 pm ---However, if you drop the mass, and it falls freely with nothing resisting it until it hits your foot, it accelerates according to Newton's Second Law, where the accelerating force equals the weight (defined above) and the mass is the mass. The velocity when it hits your foot is left as an exercise for the reader.
--- End quote ---
I'm not sure what an "accelerating force" is. There is force, and there is acceleration.
And actually, in freefall, the weight has absolutely no effect. Acceleration is the gravity (if you simplify things of course and suppose there are no friction forces due to air - hence why true experiments must be done in vacuum), and it doesn't depend on mass whatsoever. In turn, the speed doesn't depend on mass either. That's something not really intuitive and that many people, even educated ones, have a hard time with.
TimFox:
An accelerating force is that in Newton's First Law, usually stated now as "an object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net external force". In the original, "Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare". See "Newton's Principia for the Common Reader" by S Chandrasekhar, available at https://oiipdf.com/newtons-principia-for-the-common-reader
The Second Law gives the result of such an external force, usually stated now as "F = m a," where a is the resulting acceleration from that force. Actually, Newton's original statement translates as "F = dP/dt", where P is now called the "momentum" (original "quantity of motion"), and this version works better in Special Relativity. A discussion of this in https://blogs.bu.edu/ggarber/archive/bua-py-25/newtons-second-axiom/ clarifies this:
"Lex II: Mutationem motus proportionalem esse vi motrici impressae,
et fieri secundum lineam rectam qua vis illa imprimitur.
In translation (by Andrew Motte) this becomes:
LAW II.
The alteration of motion is ever proportional to the motive force impressed;
and is made in the direction of the right line in which that force is impressed.
Newton then goes on to clarify:
If any force generates a motion, a double force will generate double the
motion, a triple force triple the motion, whether that force be impressed
altogether and at once, or gradually and successively. And this motion
(being always directed the same way with the generating force), if the body
moved before, is added to or subducted from the former motion, according
as they directly conspire with or are directly contrary to each other ; or
obliquely joined, when they are oblique, so as to produce a new motion
compounded from the determination of both."
I believe that Newton assumed that the inertial mass and the gravitational mass are equal, and this became a cornerstone of Einstein's theory.
Once again, I suggest considering the Atwood Machine, where gravitational acceleration and inertial masses form an interesting demonstration.
RJSV:
Sorry TIM, I disagree with the use of the term 'MOTION': That's too loose, why not try use the direct terms, Changes in position= velocity (or called speed or rate) and if accelerating/decelerating then you have another 'rate', of change, that of velocity change.
To drive a point home I would ask: "...So then, what are the units of this 'MOTION' thingy that you mentioned ?"
Are you going to reply: "...Why.. it's feet per second
..of course...".
But that's called VELOCITY.!!! Don't misunderstand, this is a friendly, and voluntary activity,JUST BUSINESS
and so I gotta speak out. The sarcasm is only all in fun. (Refer to Nominal animal previous post)
I'm going to re-name VELOCITY: How about 'Wiggles'? ... Or BANNANAs per sector!
Wordsaladwordsalad. (thanks for your patience)
TimFox:
In terms of Newton's work: "quantity of motion" is what is now called "momentum". Terminology changes through the centuries. In non-relativistic mechanics, P = m v , where the vectors P and v are, respectively, the momentum and the velocity, while the scalar m is the mass. In Principia, if I remember correctly, Newton defined the mass as the product of the volume and density, but modern usage defines the density as the mass divided by the volume. There are a lot of circular definitions in the history of science.
Nominal Animal:
--- Quote from: T3sl4co1l on June 25, 2021, 03:36:40 pm ---What, you don't use bananas for angle too!? 0/10 disappointed.
--- End quote ---
Next time it comes up, I swear I'll say "it's two bananas short of ninety degrees". Let the mayhem commence.
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