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TuviaDaCat
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what is force anyway?
and i want the most general defenition.
and i want the most general defenition.
Hootenanny said:The most general definition of force is the rate of change of momentum;
[tex]\sum\vec{F} = \frac{d\vec{p}}{dt}[/tex]
In classical physics (where the mass of a body in motion is constant) this can be expressed in a more familiar form;
[tex]\sum\vec{F} = \frac{d\vec{p}}{dt} = \frac{d(m\vec{v})}{dt} = m\frac{d\vec{v}}{dt} = m\vec{a}[/tex]
However, there are certain circumstances in classical physics such as rocketry where the above expression fails (also when considering relativistic speeds). The original 'general' expression of Newton's second law, however holds in all cases.
[tex]\sum\vec{F} = \frac{d\vec{p}}{dt}[/tex]
No, it doesn't. Where did you get that idea from?Hootenanny said:The most general definition of force is the rate of change of momentum;
[tex]\sum\vec{F} = \frac{d\vec{p}}{dt}[/tex]
In classical physics (where the mass of a body in motion is constant) this can be expressed in a more familiar form;
[tex]\sum\vec{F} = \frac{d\vec{p}}{dt} = \frac{d(m\vec{v})}{dt} = m\frac{d\vec{v}}{dt} = m\vec{a}[/tex]
However, there are certain circumstances in classical physics such as rocketry where the above expression fail.
I think he meant F = mdv/dt fails if [itex]dm/dt \ne 0[/itex]. The correct expression is, of course: [tex]F = dp/dt = mdv/dt + vdm/dt = ma + vdm/dt[/tex]arildno said:No, it doesn't. Where did you get that idea from?
what is force anyway?
and i want the most general defenition
The (total) force on a particle equals the time rate of change of that particle's momentum.TuviaDaCat said:what is force anyway?
and i want the most general defenition.
If one assumes that F=dp/dt is a law of physics then then one is using circular logicic. However if one defines force as dp/dt the the circularity disappears. The error in login I mentioned is this - Newton's laws are said to hold only in an inertial frame, while an inertial frame is defined as any frame in which Newton's laws hold.In Eddington's words Every body continues in a state of rest or motion in sofar as it doesn't. A typical method today is to define the inertial frame in a way that has nothing to do with with Newton's first two laws, to define mass by Newton's third law, and to use the second as a definition of force.actionintegral said:This is a better question that you think! According to Bertrand Russell, the statement F=ma amounts to nothing more that a truism or circular definition.
That is a well known fact in both classical and relativistic mechanics. One need only turn to the Feynman Lectures to verify that fact. In volume I page 12-2, Feyman wrotearildo said:No, it doesn't. Where did you get that idea from?
Newton also gave one rule rule about the force: that the forces between interacting bodies are equal and opposite - action equals reaction. In fact, the law F = ma is not exactly true; if it were a definition we should have to say that that it is always true; but it is not
Ouch. In my humble opinion that's a bad habit.actionintegral said:Whenever I am thinking about non-relativistice force, I mentally replace the word "force" with "acceleration". Opposing forces are just accelerations that cancel out.
pmb_phy said:Ouch. In my humble opinion that's a bad habit.
Pete
actionintegral said:Ok - but why? What's the problem in setting m=1 everywhere? Or q=1? Or c=1? I'm not being a smart-aleck, I just don't like lugging around a lot of alphabetic luggage. If something is a constant, I set it =1 wherever possible and move on.
actionintegral said:Ok - but why? What's the problem in setting m=1 everywhere? Or q=1? Or c=1?
I'm not being a smart-aleck, I just don't like lugging around a lot of alphabetic luggage. If something is a constant, I set it =1 wherever possible and move on.
pmb_phy said:The (total) force on a particle equals the time rate of change of that particle's momentum.
If one assumes that F=dp/dt is a law of physics then then one is using circular logicic. However if one defines force as dp/dt the the circularity disappears. The error in login I mentioned is this - Newton's laws are said to hold only in an inertial frame, while an inertial frame is defined as any frame in which Newton's laws hold.In Eddington's words Every body continues in a state of rest or motion in sofar as it doesn't. A typical method today is to define the inertial frame in a way that has nothing to do with with Newton's first two laws, to define mass by Newton's third law, and to use the second as a definition of force.
For more on the details of this method please see
On force and the inertial frame, Robert W. Breheme, Am. J. Phys., 53(10, October 1985.
That is a well known fact in both classical and relativistic mechanics. One need only turn to the Feynman Lectures to verify that fact. In volume I page 12-2, Feyman wrote
Ouch. In my humble opinion that's a bad habit.
Pete
The essence of f=ma is that for a given force, acceleration varies inversely as the mass. This is not circular. A 1 kg falling brick with a string on a pulley pulls a cart along a horizontal surface. The cart accelerates half as fast if I double the cart's mass; three times as fast if I remove 2/3 of its mass. So for a given size of falling brick, ma = constant. If I change the mass of the falling weight, I change the constant. We call that 'constant' the "force".actionintegral said:This is a better question that you think! According to Bertrand Russell, the statement F=ma amounts to nothing more that a truism or circular definition.
Its possible to choose constants of nature such that c=1. One chooses a system of basic constants and when that is done then other quantities are then defined through those constants. You can choose the mass of a body to be 1 but if there are more than one particles then you have to allow for another particle having the value of two. Same with charge. If one thinks of force as being defined as F = dp/dt then and always remember that this is a definition rather than an equality then one is less likely to confuse F = ma with F = dp/dp. For example: you made the assertion that Opposing forces are just accelerations that cancel out. That is true if and only if you have the very special situation that the mass of each of the two particles are identical. In general what you said here is not true. If the masses are different then the accelerations will be different too.actionintegral said:Ok - but why? What's the problem in setting m=1 everywhere? Or q=1? Or c=1? I'm not being a smart-aleck, I just don't like lugging around a lot of alphabetic luggage. If something is a constant, I set it =1 wherever possible and move on.
Here he is defining a "material system" to be that definition such that his assertions are correct. In my extensive readings on the concepts of force and mass I've yet to see such a term used. He goes on to assumeA MATERIAL system (which consists of the SAME particles over time) is in the classical sense governed by two main laws:
This he states as a postulate of classical mechanics. However one simply does not need to define such a postulate since it can be reduced to a theorem. That theorem is stated as follows; If the total momentum of a system is conserved in all inertial frames of reference then it follows that the total mass of such a system is conserved. For a derivation of this theorem please see1. Conservation of MASS.
If Newton's second law follows from "1" then it is not a law but a theorem. aldrino makes the false statement that (, has two equivalent forms F=ma and F=dp/dt). This is a totally invalid statement in that it does not correspond to what is observed in nature. It totally fails for a relativistic particle moving under a force (and fails for non-constant mass systems). (Notice how he avoids mention of relativistic particles? How convenient for him!)2. A dynamical law known as Newton's 2.law that, due to 1.
I have to admit that I have no clue on what he means by this since the term is not defined in classical mechanics that I'm aware of and he does not define it here. He goes on to sayA GEOMETRICAL system does not contain the same particles over time, and is not governed by either 1 or either of the two forms of 2.
Newton's firtst two laws are valid under all circumstances and his third law fails when one gets into particles moving in fields such as the force between two charged particles. The reason being that the field has momentum.Don't apply laws on systems they are not valid for!
shows his misunderstanding of how forces is defined and what F = ma means. F = ma is not a definition. It is an equality under certain conditions. This equality fails under relativistic systems which aldrino fails to address.As for proof of my assertion that rocketry is, indeed, governed by F=ma, it suffices to say that a proper MATERIAL system is the rocket+fuel remaining+fuel ejected.
When stated as F = dp/dt it is assumed that one understands "F" as what you refer to as "sum of forces" aka "total force."TuviaDaCat said:the equations described above were all about the sum of forces on a body, not the force on one...
and I am pretty much sure that the 2 classical forces, gravity and electricity must have a common base...
You shouldn't assume that such a definition exists which is universally accepted. Actually I've never seen those terms defined and I've been studying physics for 20 years (one never stops studying physics. One merely stops going to school. ) .Hootenanny said:Could somebody point me in the direction of a formal definition of both a material and geometrical system, for I have not come across these terms before.
Thanks for the infopmb_phy said:That said, one could take "material system" as one consisting of "material". But that requires that I define "material." Of course one could use the term "material" to mean the same thing as "matter" except that "matter" is not a well-defined quantity. Einstein defined the term to include the EM field whereas many people nowadays understand the term as referring to systems which are entirely composed of particles which have non-zero proper mass.
I know, that is why I used it in my previous post as it is universally applicable. I didn't think that the definition using potential would be the 'most general' form so I omitted it, my mistake perhaps.pmb_phy said:Note: F=dp/dt is not something I created out of nothing. This is the definition of "force" as given in almost all textbooks on classical mechanics. E.g. Feynman, Marion & Thornton, Corben $ Stehle, and in Jammer's account of the defintion of force as defined by Newton in Jammer's text "Concepts of Force" (i.e. Newton used the term "force" to mean F = dp/dt). A.P. French's text Newtonian Mechanics (page 166 Eq. 6-1) also explains that F dt = dp is how F is found in Newton's Principia. Nowhere in the Principia does F = ma appear. See also page 315 on French.
Its of limited use. It requires that there exists a function U such that F = -grad U. This is not always the case. The force of friction does not hace such a function associated with it. Velocity dependant forces also cannot be expressed as -grad U. For example; the magnetic force on a charged particle F = qvxB cannot not be written as -grad U since a particle moving in such a field moves with constant potential energy. The Lorentz force is written asHootenanny said:I didn't think that the definition using potential would be the 'most general' form so I committed it, my mistake perhaps.
Speaking of units - From The Character of Physical Laws, Richard Feynmanactionintegral
Ok - but why? What's the problem in setting m=1 everywhere? Or q=1? Or c=1?
For those of you who want some proof that physicists are human, the proof is in the idiocy of all the different units which they use for measuring energy
pmb_phy said:... Lif****z ...
:rofl: :rofl: :rofl:rbj said:Raquel Welsh: "Would you like to pet my kitty?"
Johnny Carson: "Sure, if you move the cat."
...
Planets are bodies which are kept together by gravitational forces. If these forces didn't exist then planets wouldn't exist. The universe would simply consist of a gas of various particles.superweirdo said:Somebody earlier said that if there would be no force, planets would go through each other.
Precisely!However, if there are no forces, I believe planets would just vanish b/c there would nothing holding it together.
It is unclear whether it is meaningfull to say that an electron can "go through" another electron. We don't know the precise structure of electrons and as such we are unable to determine what would happen if one electron passes through another. Especially when "center of electron" is not a well defined quantity in QM.And I assume that electrons wouldn't go through each other, but when they would hit each other, what would happen?
You're now referring to "contact forces". Otherwise energy can be transferred to other particles through the field which they generate.Would they pass their kenetic energy to its collisioner. If yes, then wouldn't it take some kind of force to pass the energy from one to another? What kind of force is it anyways?
superweirdo said:Somebody earlier said that if there would be no force, planets would go through each other. However, if there are no forces, I believe planets would just vanish b/c there would nothing holding it together. And I assume that electrons wouldn't go through each other, but when they would hit each other, what would happen? Would they pass their kenetic energy to its collisioner. If yes, then wouldn't it take some kind of force to pass the energy from one to another? What kind of force is it anyways?
TuviaDaCat said:what is force anyway?
rbj said:Raquel Welsh: "Would you like to pet my kitty?"
Johnny Carson: "Sure, if you move the cat."
...
Hootenanny said::rofl: :rofl: :rofl:
At this point I believe that the OP should clarify what he is asking. Is he seeking a defintion of force or the mechnism of interacting bodies which produces accelerations and for which there is a non-zero force on the body.Mickey said:That's a question that physicists work on as part of the job description, I think.
It's a general case of questions like "what is gravity?" and "what is magnetism?" and so on. Looking for an answer to the question has given us many discoveries, namely that some forces are the same.
The greatest of Newton's contributions may be that he gave us such an interesting question.
Newton took the second law to refer to emperical facts. However the modern view is the second law is to be taken as a definition of force.The second law, likewise, has two possible interpretations: it may serve as a quantitative definition of force or as a generalization of emperical facts. In modern notation, according to Netwon, asserts F ~ [itex]\Delta[/itex](mv).
...
Force, for Newton, was a concept given a priori, intuitively and ultimately in analogy to human musclular force.
How modern? Feynman was quite clear that F=ma was more than a definition as the concept of force is based on empirical fact. Tension in a string; extension of a spring; stress/strain on a beam: F=-kx or F=mg or F = kq^2/r^2. These are real phenomena and more than definitions.pmb_phy said:Newton took the second law to refer to emperical facts. However the modern view is the second law is to be taken as a definition of force.
Nothing has really changed since Newton published his Principia. Nowadays physicists know that F = dp/dt isn't just a convinient for byt a neccesary form for the definition of force. The first relativistic instance I know of this was in an article written by Max Plank in which he stated that the Lorentz force equation can be written asAndrew Mason said:How modern?
clear in what sense? Where did you get that opinion from? What Feynman actually wrote was (as posted above).Feynman was quite clear that F=ma was more than a definition as the concept of force is based on empirical fact.
If you looked at the context of that that statement made by Feynmen then you'll see that he means that F = dp/dtNewton also gave one rule rule about the force: that the forces between interacting bodies are equal and opposite - action equals reaction. In fact, the law F = ma is not exactly true; if it were a definition we should have to say that that it is always true; but it is not.
In the cases you give, the equation of motion will beTension in a string; extension of a spring; stress/strain on a beam: F=-kx or F=mg or F = kq^2/r^2. These are real phenomena and more than definitions.
A force is that thing, which when acting individually on a single (massive) particle, causes it to accelerate.TuviaDaCat said:what is force anyway?
and i want the most general defenition.