So try to read some of the "Principia..." to get glimpse of Newton's reasoning. Just first ten pages... You can do it! You'll then see that the core idea behind his dynamics is a momentum conservation. Idea of force is secondary to momentum: F = dp/dt. And the amount of movement (momentum) is a product of mass and velocity.prosteve037 said:It just seems more reasonable to me that he'd notice that (for example) force ∝ mass, or force ∝ acceleration, instead of force ∝ product of mass and acceleration.
xts said:You may try to read "Principia..." just to see yourself the kind of argumentation Newton used.
There are several English translations available on-line - I recommend (as the easiest to read) - American translation from mid 19th century: http://rack1.ul.cs.cmu.edu/is/Newton/
You may want to skip all the introduction, and start from page 84 - there are corollaries to the principles - explained and illustrated geometrically.
You're right... Google then for full text, or use the link (it surely works) posted by Harrylin: http://gravitee.tripod.com/ (cancel when asked for login) - it contains most important parts of the text.Jadaav said:The site mentioned above does not work for me please. Any idea ? I really want to read the Principia...
xts said:So try to read some of the "Principia..." to get glimpse of Newton's reasoning. Just first ten pages... You can do it! You'll then see that the core idea behind his dynamics is a momentum conservation. Idea of force is secondary to momentum: F = dp/dt. And the amount of movement (momentum) is a product of mass and velocity.
xts said:For my understanding of Newton's work, concept of momentum is derived from the concept of centre of mass (momentum it is its derivative over time) and galilean relativity applied to centre of mass. Two-arm levers, scales, etc. devices, leading to concept of centre of mass, were well known even long before Galileo.
Newton made lots of experiments with colliding penduli (different masses, elastic, semi-elastic and inelastic collisions). So he had direct experimental confirmation of momentum conservation (he knew that the angle pendulum reaches is proportional to the velocity at the lowest point if the angle is small). He could easily compare masses and find their proportions and could measure the angles pendulum reaches.
Yes, that is what I was trying to tell you long time ago already...prosteve037 said:So in short, he used proportioning techniques to deduce the formula?
xts said:Yes, that is what I was trying to tell you long time ago already...
xts said:I rather believe that most of his ideas come from astronomical observations, especially Kepler laws. Pendulum experiments and common experience thought experiments (as well as Galileo's experiments) might help him to extend F~a into F~ma.
Newton did not measure momentum. He measured only proportions between momenta. Even further - not between momenta directly, but proportion between masses (easy with balance or combining several identical weights together) and proportions between velocities - these are in turn proportional to max angle of pendulum (in an approximation of small angles - Newton knew this relation). Measuring angles was pretty simple.
Make two Newtonian penduli (a ball is hung on two cords mounted in two points of the ceiling, to ensure it travels in a plane) - one of some mass, the second of three times bigger mass.prosteve037 said:So if he measured proportions between masses and proportions between velocities, where does momentum come into play?
xts said:Make two Newtonian penduli (a ball is hung on two cords mounted in two points of the ceiling, to ensure it travels in a plane) - one of some mass, the second of three times bigger mass.
Now deflect the heavier one by some angle (small enough to use sin(x)=x approx) from equilibrium, and lighter one by three times bigger angle. Release both of them simultaneously.
See that after collision they bounce to a maximum angles having the proportion 1:3, although (as the collision was not perfectly ellastic) the angles are smaller than original.
Conclusion: momentum of some body is equal to momentum of another body traveling 3 times slower but weighting 3 times more
From the perspective of our discussion 1800 is just yesterday - those were pretty modern times. Newtonian mechanics got reformulated to algebraic form in early 18th century. Whewell wrote his works after analytical mechanics by Lagrange and Hamilton.prosteve037 said:even at that time (around the 1800s I believe)
I believe - yes. Actually, in Whewell's times the other value measuring amount of motion was also used: kinetic energy, having even stranger property: it is preserved in ellastic collisions and in gravitational interactions, but it gots lost in inellastic collisions.Was mv just defined as the "quantity of motion" of an object because it was the only similar characteristic between two objects in an experiment involving collisions?
He found that such defined 'quantity of motion' is always preserved in isolated systems, so it may be very useful to formulate laws of motion.But on what grounds does Newton stand in making such a definition?
Yes and no. He knew that maximum velocity of the pendulum is proportional to maximum deflection angle (for a given pendulum length). But he didn't care about expressing the velocity in our modern terms (m/s or inches per second). It is yet another case, where Newton, in his euclidean approach, was focused on proportions, but not on the actual numeric values. So (you did it wrong!) he could go one step further: <br /> \theta_M/\theta_m = m/M\quad\Longrightarrow\quad<br /> v_M/v_m=m/M but he never did the next step: v_M/v_m=m/M\quad\Longrightarrow\quad Mv_M=mv_m - because for him it made no sense to multiply ounces by something else than pure number. It was also a reason why Newton never mentioned any numerical values of velocity: he could define it as a 'change of position (in time)', but he had no unit to measure it. He could measure the angle, but not the velocity: it was not only technical problem, but he lacked units of measure. He could measure angles (in degrees), but he had no unit for velocity. The idea of 'metre per second' (or rather feet per second) came 50 years later.Newton took the thetas and did some math to replace them with the appropriate final velocities
I agree with your sentiment here, but not your dates. Have you tried reading physics texts written in the early 1800s? Physics then was quite different from the classical physics of today. Physics was rewritten from the ground up twice during the 19th century, first by Hamilton (born 1805) and then again by Gibbs and Heaviside in the latter part of the century. The modern notation of Newton's second law, \vec F = m\vec a, dates to the late 19th century.xts said:I don't know Whewell's books (ok, I'll try to read some...), but,
From the perspective of our discussion 1800 is just yesterday - those were pretty modern times. Newtonian mechanics got reformulated to algebraic form in early 18th century. Whewell wrote his works after analytical mechanics by Lagrange and Hamilton.
if you read the original Latin formulation of the second lawprosteve037 said:I was under the impression that Newton deduced
\textit{F}\propto{m}
\rightarrow \textit{F = k}_{1}\textit{m}
where in SI Units they would be in the form
\textit{F = ma}...
how did he resolve that \textit{k}_{1} is dependent on acceleration and/or that \textit{k}_{2} is dependent on mass?
prosteve037 said:I was under the impression that, by experiment, Newton deduced
\textit{F}\propto{m} \rightarrow \textit{F = k}_{1}\textit{m}
(where \textit{k}_{1} is some constant)
and
\textit{F}\propto{a} \rightarrow \textit{F = k}_{2}\textit{a}
(where \textit{k}_{2} is some constant)
and then found that either/both
\textit{k}_{1}\propto{a} \rightarrow \textit{k}_{1}\textit{ = c}_{1}\textit{a}
(where \textit{c}_{1} is some constant)
and/or
\textit{k}_{2}\propto{m} \rightarrow \textit{k}_{2}\textit{ = c}_{2}\textit{m}
(where \textit{c}_{2} is some constant)
thus creating
\textit{F = c}_{1}\textit{ma}
and/or
\textit{F = c}_{2}\textit{ma}
where in SI Units they would be in the form
\textit{F = ma}
However, I've read in some other forums how Newton actually meant
\textit{F}\propto{ma} \rightarrow \textit{F = kma}
Which is the case? Did he use the first method or did he simply state the second?
If he did use the first method, how did he resolve that \textit{k}_{1} is dependent on acceleration and/or that \textit{k}_{2} is dependent on mass?
logics said:if you read the original Latin formulation of the second law
Lex II: "mutationem motus proportionalem esse vi motrici impressae": "change of motion is proportional to applied force",
you'll see that all interpretations are not true: Newton deduced only the obvious principle that the effect is proportional to the cause,
In Newton's words, zoobyshoe," hypotheses fingis": you are imagining things. What Newton says is clear: you are fantasising about "what he dropped", "when he dropped" and even "why he dropped". You reverse the historical facts : somebody applied, later, "momentum" to what Newton referred to as quantity of motion [measure of the same arising from velocity and quantity of matter]. And that "almost" gives you the power of deciding what suits you when it suits you. [and you cite "wiki" (!) as your authority]zoobyshoe said:... you're short changing Newton ...
But all your effort is not necessary if you read, carefully, what I said: for Newton everything was simple because he considered [as it is right] "motus" as one concept. "motion, speed, velocity, momentum" are redundant distinctions as there cannot be speed without direction nor velocity without mass, do you realize that? and cannot be matter without quantity : "pears" must be "quantity of pears", moreover there was no reason, then, to take mass into account.He defines momentum "quantity of motion"... Thereafter almost every time he uses the word "motion" it is short for "quantity of motion"... for convenience. From wiki: "According to modern ideas this is understood, in modern terms, as an equivalent of:..."
The big problems arose later, when Leibniz' theory was verified and it was accepted that E = v².logics said:\textit{v, [p, E]}\propto{F}
Mass was not considered, as gravity was the only known force at the time, and its effect is not influenced by mass.
I don't have to hypothesize about his shortening of the term, because I can read:logics said:in Newton's words "zoobyshoe, hypotheses fingis": you are imagining things. What Newton says is clear: you are fantasising about "what he dropped", "when he dropped" and even "why he dropped". You reverse the historical facts : somebody called, later, "momentum" what Newton referred to as motion and matter. And that "almost" gives you the power of deciding what suits you when it suits you. [and you cite "wiki" (!) as your authority]
[bold added]
It was even better for him, fabulous, because he naively thought that both Energy and velocity/momentum are proportional to force: Fg → Ek→ v,p
zoobyshoe said:He specifically defines momentum (calling it "quantity of motion) in defintion II. It's completely clear he understands it is the product of the mass and velocity.
xts said:I believe - yes. Actually, in Whewell's times the other value measuring amount of motion was also used: kinetic energy, having even stranger property: it is preserved in ellastic collisions and in gravitational interactions, but it gots lost in inellastic collisions.
He found that such defined 'quantity of motion' is always preserved in isolated systems, so it may be very useful to formulate laws of motion.
Yes and no. He knew that maximum velocity of the pendulum is proportional to maximum deflection angle (for a given pendulum length). But he didn't care about expressing the velocity in our modern terms (m/s or inches per second). It is yet another case, where Newton, in his euclidean approach, was focused on proportions, but not on the actual numeric values. So (you did it wrong!) he could go one step further: <br /> \theta_M/\theta_m = m/M\quad\Longrightarrow\quad<br /> v_M/v_m=m/M but he never did the next step: v_M/v_m=m/M\quad\Longrightarrow\quad Mv_M=mv_m - because for him it made no sense to multiply ounces by something else than pure number. It was also a reason why Newton never mentioned any numerical values of velocity: he could define it as a 'change of position (in time)', but he had no unit to measure it. He could measure the angle, but not the velocity: it was not only technical problem, but he lacked units of measure. He could measure angles (in degrees), but he had no unit for velocity. The idea of 'metre per second' (or rather feet per second) came 50 years later.
I've greatly enjoyed all of xts' posts in this thread and wouldn't want to think there was any conflict.prosteve037 said:Anywho, it seems that we have a conflicting argument here in terms of zoobyshoe's post and xts'. From what I can see, (and please correct me if I'm wrong) while xts says that Newton had no clear-cut mathematical definition for momentum (\textit{mv}) zoobyshoe is saying that Newton knew full well that momentum had to be \textit{mv} (Hence why I ask zoobyshoe about his view on how Newton came to see it this way).
Definition II
The quantity of motion is the measure of the same arising from the velocity and quantity of matter conjunctly.
The motion of the whole is the sum of all of the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple.
I would add that Galileo worked everything out geometrically, as well.xts said:At Newton's times proportionality was perfectly known and understood - it was used even more frequently than nowadays. Just contrary - those times the numerical values, measurement units, etc. were rather neglected. It was the effect of geometrical representation. As in Euclid "Elements" - the line segment represent the value, and twice longer section represent twice bigger value, but no one cares to say that 1 inch on the drawing represents 1 pound of mass. You may make the same Euclidean construction in different scale, and all conclusions will be the same.
Such approach is really difficult to understand for modern people, who learn on numbers, rather than on Euclodean constructions.
Newton was one of the very last scientists using such geometrical representations (but it was common till his times, Copernicus did the same). It was 18th century when numerical approach (started by Rene Descartes even a bit earlier than Newton worked) finally won popularity.
As far as I can see Newton worked everything out in terms of conservation of momentum, and there's no indication so far in my reading that kinetic energy will be brought into it.So because the concept of momentum was considered long before energy, can we just disregard any connection between the formulation of mv and the concept of kinetic energy?
"Citation needed."PatrickPowers said:I have read that Newton worked out his mathematics using algebra, analytic geometry, and calculus, then translated it all to the then-more-familiar geometry so it could be understood and accepted.
D H said:"Citation needed."
Newton is talking about himself in the third person here? What's this quote from? A letter? A publication of the Royal Society?PatrickPowers said:By the help of the new Analysis Mr. Newton found out most of the Prepositions in his Principia Philosophiae: but because the Ancients for making things certain admitted nothing into Geometry before it was demonstrated synthetically, he demonstrated the Propositions synthetically, that the System of the Heavens might be founded upon good Geometry. And this makes it now difficult for unskilful men to see the Analysis by which these propositions were found out.
--- Sir Isaac Newton, 1715
zoobyshoe said:Newton is talking about himself in the third person here? What's this quote from? A letter? A publication of the Royal Society?
Any way you could just link me to these two letters?PatrickPowers said:Third person, yes. A letter. You can easily find this and all of his letters online. He also wrote that algebra was for "bunglers."