Frame of reference. Doubt I've got my head round it completely, but with the given *The total momentum in the CoM frame is always zero, by definition* we never end up in a situation where momentum is lost.
You may try to get Heiwa to stop babbling about WTC Towers. Good luck. Nobody else has been able to do so.
Not even now, after he's been explicitly warned.
Unfortunately, he has demonstrated a long history of being both incompetent and rude.
___
To the topic at hand:
Here's the real deal regarding Conservation of Momentum & Conservation of Energy.
(My apologies to those here who obviously already understand.)
Conservation of momentum is a demonstrated law of the universe. It is NEVER violated. Ever. From subatomic particles, to photons, to Brownian motion, colliding billiard balls, to falling portions of buildings, to colliding galaxies.
If you want the superficial explanation, go to a freshman level physics textbook.
If you want the deeper reason, you've got to go to the amazing theorems of Emmy Noether. The deep reason is that every symmetry in the universe CREATES a conservation law. It REQUIRES one.
The fact that the laws of the universe are uniform (i.e., "symmetrical") under spacial displacement (i.e., no matter where you are) creates the law of conservation of momentum.
Conservation of energy is (just slightly) different. It is an "empirical observation" that most physicists believe to be a law, as well.
Conservation of energy results from time (instead of spatial) symmetry. To the best of current observation, the laws of the universe appear to be constant throughout observable time, as evidenced by images of stars and galaxies millions & billions of light years away. Which automatically translates into millions & billions of years ago.
The debate appears to be "does all observable time necessarily equate to all time?" That's one for the physicists. (Perhaps of the next century.)
Nonetheless, we pragmatically accept that conservation of energy is also a law that nobody has ever seen violated. Under unimaginably intense scrutiny.
That's where you stand.
TOTAL Energy IS conserved. But it is easily transformed from one form (e.g., kinetic) into others (e.g., potential, heat, electrical, deformation, noise, chemical, etc.). Or into WORK.
The KINETIC portion alone is NOT conserved. Part of the kinetic energy goes to heating & deforming the objects.
BTW, another fundamental difference:
Energy is a scalar. As mentioned, energy gets transformed very easily from one form to others. Tallying up the different forms of energy is quite easy. Measuring the major forms of energy is also easy (if you have the right instrumentation), but there are some forms (the noise, the total heat generated, the total deformations in a collision) that can be a bear to measure.
Momentum is a vector. Unlike energy, there is nothing else for it to be transformed into, ergo it is always, always conserved. But you have to "add it up" like vectors (considering both magnitude & direction), not like scalars (that have only magnitude).
Some of you might ask "What happens to the momentum of a ball rolling across the ground that comes to rest? It had momentum (= m*v) when I threw it, and now its momentum is zero, because v=0."
The answer is, of course, that it's momentum was transferred to the earth, and (ever so slightly) slowed down or speeded up the rotation of the earth (depending on whether you threw it east or west).
Don't confuse or commingle momentum & energy. If a collision produces more heat, then there IS less energy available to deform parts. But there is NOT less momentum transferred because of energy transformation or energy losses.
Heiwa's conclusion that an inelastic collision between a 1 kg, 10 m/s object and a 1kg, 0 m/s object produces a 2 kg, 7.07 m/s object (in order to maintain CoE) gets an "F" grade in freshman physics. It is simply wrong.
Momentum IS conserved. The end result is that you have a 2 kg, 5 m/s object.
And some of the initial energy is transferred into heat, some into noise, and some into permanent deformation of the components.
Yeah, Emmy Noether may be (IMHO) the single most important physicist that nobody's ever heard about. (Except for almost all the rest of them, of course.)
Her theories are a watershed, revolutionary turning point in our fundamental understanding of the universe. The concepts are beautiful, elegant and incredibly far reaching.
It may well be that the SINGLE, MOST IMPORTANT, and most fundamental determinant of everything (all particles and all forces in the universe) may well be "symmetry". Her concepts lead directly to the modern physics of "gauge theory", in which a variety of local and global symmetries produce all 4 forces (electromagnetic, strong nuclear, weak nuclear & gravity), plus their carriers, plus a set of conservation laws: conservation of charge, conservation of spin, etc.
And, as above, conservation of momentum & of energy.
You may try to get Heiwa to stop babbling about WTC Towers. Good luck. Nobody else has been able to do so.
Not even now, after he's been explicitly warned.
Unfortunately, he has demonstrated a long history of being both incompetent and rude.
___
...
Heiwa's conclusion that an inelastic collision between a 1 kg, 10 m/s object and a 1kg, 0 m/s object produces a 2 kg, 7.07 m/s object (in order to maintain CoE) gets an "F" grade in freshman physics. It is simply wrong.
Momentum IS conserved. The end result is that you have a 2 kg, 5 m/s object.
Hm, that was an elastic collision where objects continued at different angles (difference 90°) after collision, where CoM and CE are perfectly conserved. Please, use vectors and you'll understand. Very politely as usual with best greetings - Heiwa.
Heiwa wrote:PS to Moderator OWE - pls do not remove my posts.
Only those that fit appropriate criteria are removed. In cases where there happens to be something of value buried in string of spam posts, sorry, goes with the territory.
The issue you seem to be trying to raise is that, in the real world, energy changes form (dissipation of KE) and is transferred between objects which are necessarily not isolated from the system in some ideal way, therefore it appears that momentum is not conserved. Is that the gist of it?
For analytic or computational purposes, a system is defined so as to isolate the elements of interest. Factors arising through interaction with agents outside the system must, of course, receive proper accounting in order to get correct or useful results. These factors may be introduced as constraints, external forces, virtual potentials, accelerated frames, etc., depending on what is most expedient, so long as it is correct.
When the system includes coupling to a body of enormously greater mass than any element of the system, this is dealt with by applying a constraint that some portion of the system is fixed to maintain constant distance wrt the big body, which defines a useful stationary frame of reference. The CoM of the earth is not stationary, but a reference frame wrt ground level can be considered so for many localized systems.
Proper system definition is important in any mechanical problem and, likewise, understanding of the fundamental principles essential. The principles of conservation in classical mechanics are sound, doesn't prevent misapplication! In an earlier post, I showed that all the initial KE was lost in one frame of reference and half in another. That's not the same as saying twice the energy was dissipated. The delta KE is the same in both cases. This is an expression of symmetry, as tfk said, or invariance under translation of frame which is linear in time. Inertial frames must give the same result.
I knew Saunders Mac Lane who attended the lectures of http://en.wikipedia.org/wiki/Emmy_Noether" onclick="window.open(this.href);return false
one year in Gootingen. On several occasions he spoke of her; the Wikipeida page is quite accurate AFAIK.
Heiwa wrote:PS to Moderator OWE - pls do not remove my posts.
Only those that fit appropriate criteria are removed. In cases where there happens to be something of value buried in string of spam posts, sorry, goes with the territory.
The issue you seem to be trying to raise is that, in the real world, energy changes form (dissipation of KE) and is transferred between objects which are necessarily not isolated from the system in some ideal way, therefore it appears that momentum is not conserved. Is that the gist of it?
For analytic or computational purposes, a system is defined so as to isolate the elements of interest. Factors arising through interaction with agents outside the system must, of course, receive proper accounting in order to get correct or useful results. These factors may be introduced as constraints, external forces, virtual potentials, accelerated frames, etc., depending on what is most expedient, so long as it is correct.
When the system includes coupling to a body of enormously greater mass than any element of the system, this is dealt with by applying a constraint that some portion of the system is fixed to maintain constant distance wrt the big body, which defines a useful stationary frame of reference. The CoM of the earth is not stationary, but a reference frame wrt ground level can be considered so for many localized systems.
Proper system definition is important in any mechanical problem and, likewise, understanding of the fundamental principles essential. The principles of conservation in classical mechanics are sound, doesn't prevent misapplication! In an earlier post, I showed that all the initial KE was lost in one frame of reference and half in another. That's not the same as saying twice the energy was dissipated. The delta KE is the same in both cases. This is an expression of symmetry, as tfk said, or invariance under translation of frame which is linear in time. Inertial frames must give the same result.
I fully agree! But as the 'system' includes the earth with quite big mass, the momentum 'disappears' there. In my structural damage anaysis approach just looking at energy applied and dissipated that problem is removed.
PS. OT? Apparently, anything other than "dustification, vaporizing of giant steel beams, and heating everything up to pyroclastic temperatures" is off-topic in this forum.
OneWhiteEye wrote:PS. OT? Apparently, anything other than "dustification, vaporizing of giant steel beams, and heating everything up to pyroclastic temperatures" is off-topic in this forum.
OneWhiteEye wrote:PS. OT? Apparently, anything other than "dustification, vaporizing of giant steel beams, and heating everything up to pyroclastic temperatures" is off-topic in this forum.
Incidentally, my post wasn't off-topic if you consider that it contained an ambiguous example of symmetry / broken symmetry, the reference to which is another example of symmetry / broken symmetry, and I'll spare you the infinite recursion.
Finally followed the Emmy Noether link. Astonishing. I thought this was somebody making the circuit now. I must have had some really sexist professors; most of what I was taught rests on this foundation and I never heard her name, to my recollection. Of course, I may have been sleeping one off the day she came up.
Very interesting in relation to this thread, though doesn't say much: Dissipation
Noether's Theorem (above) wrote:Noether's theorem does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.
OneWhiteEye wrote:Finally followed the Emmy Noether link. Astonishing. I thought this was somebody making the circuit now. I must have had some really sexist professors; most of what I was taught rests on this foundation and I never heard her name, to my recollection.
Nor mine. Not even by most mathematicians, who certainly taught her abstract algebra stuff. Somewhat to my (now) astonishment, not even by Ogla Taussky-Todd. So never knew who Noetherian rings were named for until I becaqme friends with Saunders Mac Lane.
It is quite easy to make a 1-D ‘crush model’ to simulate an inelastic collision between two similar structures of different size; just consider a classical system of material points with unit mass constrained to move without friction along a straight line. The material points are linked by springs forming a chain. How this chain behaves under input from a momentum, i.e. one point mass is given a small initial velocity, can be established.
Each material point (except the end ones) are constrained by two springs (potentials) and adding up all potential yields a Lagrangian L that in turn provides the Euler-Lagrange equation of motion of the chain. The chain is initially in equilibrium – all masses are at rest. Giving an impulse to one mass point will start the propagation of an elastic wave in the chain. We can add damping to the chain so that the wave will slowly diminish with time. We can also add gravitation to the chain – each mass point is subject to acceleration g producing forces compressing the chain (when it is fixed at one end).The springs can be adjusted for gravity so each spring compresses equally in a vertical gravity field (the chain is vertical and the mass points are on top of each other).
Imagine such a vertical chain consisting of 97 yellow mass points (part A) and 13 green mass points (part C). Part A is connected to ground at one end. The inelastic collision between parts A and C of the chain (it looks like WTC 1! being struck by its top part) is then simulated by giving the A mass point adjacent to the C mass point a downward impuls as described above. The elastic wave will then develop in both parts A and C. Evidently both parts of the chain compresses/decompresses until damping stops the motions of the material points (the initial momentum has disappeared!) after a certain time.
Evidently all 110 springs in the chain behave differently during the collision and it is quite easy to establish what spring will be most loaded (compressed) in the collision, i.e. be broken first! Guess or calculate which one it will be!
