What is Force? - A General Definition

[rbj]

Raquel Welsh: "Would you like to pet my kitty?"

Johnny Carson: "Sure, if you move the cat."

...

well, i screwed up. first it was supposed to be Zsa Zsa Gabor not Raquel Welsh (Sophia Loren, etc. i get all of those '60s sex-bombs mixed up). second, it's a false urban legend:

http://www.snopes.com/radiotv/tv/zsazsa.htm

see a video clip where this is discussed (Johnny and Jane Fonda):

http://www.snopes.com/radiotv/video/zsazsav.rm

still worth a giggle.

 

[pmb_phy]

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.

At this point I believe that the OP should clarify what he is asking. Is he seeking a definition of force or the mechnism of interacting bodies which produces accelerations and for which there is a non-zero force on the body.

Jammer addresses Newton's second law in his book Concepts of Force. On page 124 Jammer writes

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 ~ \Delta(mv).
...
Force, for Newton, was a concept given a priori, intuitively and ultimately in analogy to human musclular force.

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.

Pete

 

[Andrew Mason]

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.

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.

AM

 

[pmb_phy]

How modern?

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 as

\frac{dp}{dt} = q[E + vxB]

where p = \gamma m_0[/tex]. This form remained to this day. I doubt that you could find and article or a upper level undergrad textbook published after 1970 that would indicate otherwise.<br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Feynman was quite clear that F=ma was more than a definition as the concept of force is based on empirical fact. </div> </div> </blockquote><img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f615.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":confused:" title="Confused :confused:" data-smilie="5"data-shortname=":confused:" /> clear in what sense? Where did you get that opinion from? What Feynman actually wrote was (as posted above).<br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> 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 <i>always</i> true; but it is not. </div> </div> </blockquote>If you looked at the context of that that statement made by Feynmen then you&#039;ll see that he means that F = dp/dt<br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> 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. </div> </div> </blockquote>In the cases you give, the equation of motion will be<br /> <br /> dp/dt = -kx<br /> dp/dt = mg<br /> dp/dt = kq^2/r^2<br /> <br /> It has been emphsized in almost all my posts on this that in non-relativistic cases and when the mass is not a function of time then F = ma is an <i>equality</i>, but not a <i>definition</i>.<br /> <br /> Pete

 

[Gokul43201]

what is force anyway?
and i want the most general defenition.

A force is that thing, which when acting individually on a single (massive) particle, causes it to accelerate.

 

[robphy]

When I introduce "force" to my class, I say:

a "force" is a push or a pull on an object due to another object,
which can be added [and scalar multiplied] like a vector

later,
\sum \vec F_i \equiv \vec F_{net} \stackrel{\mbox{Newton\ II}}{=} \frac{d\vec p}{dt}

 

[Andrew Mason]

clear in what sense? Where did you get that opinion from? What Feynman actually wrote was (as posted above).

Feynman, Lectures, vol 1, ch 12, p. 12-3:

"In the same way, we cannot just call f=ma a definition, deduce everything purely mathematically, and make mechanics a mathematical theory, when mechanics is a description of nature. By establishing suitable postulates it is always possible to make a system of mathematics, just as Euclid did, but we canot make a mathematics of the world, because sooner or later we have to find out whether the axioms are valid for the object of nature. "​

AM

 

[pmb_phy]

When I introduce "force" to my class, I say:

a "force" is a push or a pull on an object due to another object,
which can be added [and scalar multiplied] like a vector

later,
\sum \vec F_i \equiv \vec F_{net} \stackrel{\mbox{Newton\ II}}{=} \frac{d\vec p}{dt}

The reason I refer to F_net as simply F is due to things like the electric field E at a point P due to charges in its vicinity. Those charges produce a (net) force on a test particle placed at P. Normally we say that the force F at P is given by F = qE. I don't recall anyone writing F_net = qE. I also keep with many texts such with Goldstein when I write F = dp/dt. But that is my personal preference. If one merely observers the test particle and what it is doing then what one measures is dp/dt of the particle.

Pete

 

[robphy]

The reason I refer to F_net as simply F is due to things like the electric field E at a point P due to charges in its vicinity. Those charges produce a (net) force on a test particle placed at P. Normally we say that the force F at P is given by F = qE. I don't recall anyone writing F_net = qE. I also keep with many texts such with Goldstein when I write F = dp/dt. But that is my personal preference. If one merely observers the test particle and what it is doing then what one measures is dp/dt of the particle.

Pete

I would say F_electric = qE since it is but one of the many forces that can appear in "the vector sum of the forces".

 

[pmb_phy]

I would say F_electric = qE since it is but one of the many forces that can appear in "the vector sum of the forces".

In that case, to be consistent, why not write F_electric = qE_net?

Also, in analytical mechanics one is given the Lagrangian and unless one knows the reason for the potential then one derives the (canonical) force from which it is impossible to determine if there are more than one sources.

Better yet let me ask you these two questions: (1) Under what circumstances would you call F a net sum when this force is derived from a Lagrangian that I give you? (2) under what conditions do you use the term E_net rather than E?

Pete

 

[TuviaDaCat]

im wondering about wether force must be defined using time...
after all, i can measure a force, without watching a body acclerate in a system which one force far greater all other forces...

 

[robphy]

In that case, to be consistent, why not write F_electric = qE_net?

E is the value of the vector field at a point. Implicitly, it is the vector sum of those E-fields from other objects that contribute to it. You could write "net", if you wish. If I really want to emphasize things, I use a lot of "decorations" and write:
F_{electric on q} = qE_{[net] at q's location}

I think the point of emphasizing "net" in F_net is that it is the net-force that is related to the acceleration of the particle, and not that each force somehow contributes an acceleration to the particle. This should remind someone that forces need to be added vectorially first... then one can use Newton-II.

In addition, many problems say "one applies a force F"... but that is not necessarily the net force.

Also, in analytical mechanics one is given the Lagrangian and unless one knows the reason for the potential then one derives the (canonical) force from which it is impossible to determine if there are more than one sources.

Better yet let me ask you this question: Under what circumstances would you call F a net sum when this force is derived from a Lagrangian that I give you?

Pete

Let me think more about this.
But let me say this much...
the point of "net" is that forces superpose like vectors... in particular, the forces from various external objects. Similarly, if you have numerous potentials, then the potentials are additive [and so the derived forces are additive as vectors]. Certainly, if there is just one external object (or potential), then the sum is trivial.

 

[pmb_phy]

But let me say this much...
the point of "net" is that forces superpose like vectors... in particular, the forces from various external objects. Similarly, if you have numerous potentials, then the potentials are additive [and so the derived forces are additive as vectors]. Certainly, if there is just one external object (or potential), then the sum is trivial.

I fully understand this view and wouldn't argue against it. I don't use it myself. But I have my reasons, some of which I posted here.

Pete

ps - I have scanned in the Am. J. Phys. article Force and the inertial frame by Robert W. Brehme and can e-mail it to those who are interested. The topic of the paper is identical to the topic of this thread. This link may work

www.geocities.com/physics_world/gr/bondi_1957.pdf

 

[Andrew Mason]

Just a further comment on Feynman, Vol1, Ch. 12 of Lectures. Feynman maintains that force as a physical concept has a meaning that exists independently of F=ma or F=dp/dt. He says that if it were merely a definition (he uses the example of 'gorce', which has no physical meaning) it would have no use.

AM

 

[robphy]

Just a further comment on Feynman, Vol1, Ch. 12 of Lectures. Feynman maintains that force as a physical concept has a meaning that exists independently of F=ma or F=dp/dt. He says that if it were merely a definition (he uses the example of 'gorce', which has no physical meaning) it would have no use.

AM

My post #36 is consistent with this.
In fact, as a prelude to Newton's Law of Motion F=dp/dt (F=ma to the algebra-based class), I discuss what could be called "Aristotle's Law of Motion" F=mv. (Of course, Aristotle does not have a correct law of inertia.)

 

[pmb_phy]

Andrew Mason
Just a further comment on Feynman, Vol1, Ch. 12 of Lectures. Feynman maintains that force as a physical concept has a meaning that exists independently of F=ma or F=dp/dt. He says that if it were merely a definition (he uses the example of 'gorce', which has no physical meaning) it would have no use.

As it is obvious in that chapter, Feynman took F = ma (actually dp/dt) as a law of nature. As I mentioned earlier it is more common nowadays to take F = dp/dt as a definition of F. Otherwise you run into circular logic. That Feyman held F to be F = dp/dt is evident on page 15-9 where he writes

To see the consequences of Einstein's modification of m we start with Newton's law is the rate of change of momentum, or

F = d(mv)/dt

...

Force now has as much of a meaning as tourque does since tourqe is a defined quantity. I.e. in the case of force it is used to simplify laws, such as the Lorentz force law dp/dt = q[E + vB]. Same idea holds for things like momentum too.

My post #36 is consistent with this.
In fact, as a prelude to Newton's Law of Motion F=dp/dt (F=ma to the algebra-based class), I discuss what could be called "Aristotle's Law of Motion" F=mv. (Of course, Aristotle does not have a correct law of inertia.)

Note: F = ma was never written by Newton in his Principia. F = ma comes from Euler, wyhich, of course, is not true in all cases (I.e. for relativistic particles moving in a field)

Pete

 

[Andrew Mason]

As it is obvious in that chapter, Feynman took F = ma (actually dp/dt) as a law of nature. As I mentioned earlier it is more common nowadays to take F = dp/dt as a definition of F. Otherwise you run into circular logic.

I understand what you are saying, but I don't agree that force must be 'defined' in order to avoid circular logic. You cannot question the validity of a definition. But you can question the validity of Newton's second law. You can do experiments to see if it is true.

If we were to measure the acceleration of a given mass with a given force applied to it and then measure the acceleration with double the force applied and found the acceleration to be something other than double, we would have to question the validity of F=ma.

AM

 

[robphy]

I understand what you are saying, but I don't agree that force must be 'defined' in order to avoid circular logic. You cannot question the validity of a definition. But you can question the validity of Newton's second law. You can do experiments to see if it is true.

If we were to measure the acceleration of a given mass with a given force applied to it and then measure the acceleration with double the force applied and found the acceleration to be something other than double, we would have to question the validity of F=ma.

AM

...or ask if we are working in an inertial frame.

 

[robphy]

Note: F = ma was never written by Newton in his Principia. F = ma comes from Euler, wyhich, of course, is not true in all cases (I.e. for relativistic particles moving in a field)

Pete

Yes, I am aware... but that's why I put that in parenthesis... for the algebra-based (i.e. non-calculus) students that I may teach.

 

[pmb_phy]

Yes, I am aware... but that's why I put that in parenthesis... for the algebra-based (i.e. non-calculus) students that I may teach.

Ok. At this point I think anything else I have to contribute would be mere semantics since all that needed to be said was said.

Pete

 

[Farsight]

what is force anyway?
and i want the most general defenition.

How about "Energy transfer"?

 

[Swapnil]

what is force anyway?
and i want the most general defenition.

Why don't we just leave force as an undefined term like a point or a plane? We can't define everthing, we got to stop somewhere right?

 

[pmb_phy]

Why don't we just leave force as an undefined term like a point or a plane? We can't define everthing, we got to stop somewhere right?

That would lead different people to separate definitions and some laws of physics would then simply be wrong and calculations would not match nature. It is of the utmost concern that the equations of motions at least be right.

ma = q(E + vxB)

would not describe nature where as

dp/dt = q(E + vxB)

would. It is very important to know what must be postulated and what must be defined. Otherwise its not clear how we should measure things. I.e. how do I measure force if I never define it or give a relation for it?

Pete

 

[pmb_phy]

How about "Energy transfer"?

Loosley (very loosely) speaking, a force need not be present for a transfer of energy to take place. The term "energy transfer" has no real meaning other than it is useful in calculations and in equations of conservation. "Energy" refers to a number associated with a system but does not have a location. People use it as if it does but that is a matter of convenience. For example: If a particle is moving at constant velocity in an inertial frame then where is the kinetic energy located? "inside" the particle? A foot behind it? Where? When scientist refer to the transfer of energy they typically mean that the phenomena to which they are associating energy is moving. E.g. an EM wave moves through space and there is a certain amount of energy associated with the EM wave but its not quite right to say that the energy is "in" the field, only that there is energy "associated" with the field.

Worms ... big can ... wide open!

Pete

 

[robphy]

That would lead different people to separate definitions and some laws of physics would then simply be wrong and calculations would not match nature. It is of the utmost concern that the equations of motions at least be right.

ma = q(E + vxB)

would not describe nature where as

dp/dt = q(E + vxB)

would. It is very important to know what must be postulated and what must be defined. Otherwise its not clear how we should measure things. I.e. how do I measure force if I never define it or give a relation for it?

Pete

Of course,
dp/dt = q(E + vxB)
only applies if there were no other unbalanced forces, and if this were in an inertial frame. The correct term on the left-hand should be F_Lorentz, which, if you want, is another name for the right-hand side. That is to say, it is a definition of the Lorentz force.

The equal sign in
dp/dt = q(E + vxB)
is really more complicated
dp/dt = F_net = F_Lorentz = q(E + vxB)
where
the left-most equal sign is Newton's Second Law [in an inertial frame]
the second equal sign says that there are no other forces in this particular problem
and
the right-most equals sign is a definition (or re-expression) of the Lorentz force.

Not all equal signs mean the same thing, physically. Some are laws, some are definitions, some are true for the specific situation under consideration.

This could also be taken as a comment on pmb_phy 's #23 and an elaboration of my post #36. (To me, force is defined first, before it is used in Newton's Laws.)

 

[pmb_phy]

Of course,
dp/dt = q(E + vxB)
only applies if there were no other unbalanced forces, and if this were in an inertial frame.

Those kinds of things are normally taken for granted unless otherwise explicitly stated. Otherwise its just a waste of space ... and paper ... and trees! Save the trees

The correct term on the left-hand should be F_Lorentz,

I've never seen anyone do that in every piece of literature that I've read. Have you?

The equal sign in
dp/dt = q(E + vxB)
is really more complicated

Actually it is quite uncomplicated and quite precise. It states that the time rate of change of momentum of the particle equals the right side.

Not all equal signs mean the same thing, physically. Some are laws, some are definitions, some are true for the specific situation under consideration.

I use an equal sign here only because the sign for definition, i.e. three horizontal lines, is not on my keyboard.

To me, force is defined first, ..

Me too.

Rob - Do you know of any upper classman texts which use the notation that you've given above? If so then please provide reference. Thanks dude.

Pete

 

[robphy]

Those kinds of things are normally taken for granted unless otherwise explicitly stated. Otherwise its just a waste of space ... and paper ... and trees! Save the trees

It seems the topic of this thread asks about the definition of force. IMHO, it's best adddressed by logically laying out the issues, even if verbose. For this topic, nothing should be taken for granted. More trees might be wasted if we end up talking in circles because an assumption has gone unnoticed.

I've never seen anyone do that in every piece of literature that I've read. Have you?

There is a trend in introductory physics to clearly label forces... their nature, their source, and their target. Have a look at some new introductory books [where the authors are trying to be careful to define a notion of force]. I strongly advocate first naming forces with a decorated letter before getting bogged down in the details of the nature of the force.

Actually it is quite uncomplicated and quite precise. It states that the time rate of change of momentum of the particle equals the right side.

...sure... when it's the only force (for instance).

As I stated in parenthesis, "To me, force is defined first, before it is used in Newton's Laws", I'm trying to clarify the logical relationships implicit in your concise statement [which is fine for a reader that understands the implicit logic... but again, the topic of this thread needs clarity].

I use an equal sign here only because the sign for definition, i.e. three horizontal lines, is not on my keyboard.

Sure... but the logic must be made clear for this thread.

Rob - Do you know of any upper classman texts which use the notation that you've given above? If so then please provide reference. Thanks dude.

Pete

Nope... probably because everyone hopefully understands what is going on. However, the layout of the equations... stressing the logical chains of reasoning... are inspired by "Equation Poems" (Am.J.Phy., May 1996, Volume 64, Issue 5, pp. 532-538) http://link.aip.org/link/?AJPIAS/64/532/1 .

 

[pmb_phy]

It seems the topic of this thread asks about the definition of force. IMHO, it's best adddressed by logically laying out the issues, even if verbose. For this topic, nothing should be taken for granted.

And for that reason I remained silent and in agreement when the "sum of forces" mentioned many times above popped up. I see no need to repeat that which was heavily stressed above ... unless you're concerned with those readers who are only reading the later and current posts. In that case I see your point.

There is a trend in introductory physics to clearly label forces... their nature, their source, and their target. Have a look at some new introductory books [where the authors are trying to be careful to define a notion of force]

Already done. But there is such a thing as beating a dead horse. Previous posters early in this thread beat that horse to an early death.

Have you read my post on the idea of what it means for a force to be a sum of forces? If so then you may gleen from it why I leave "net" out of the notation.

Thanks

Pete

 

[baryon]

Why do't we imagine force as influence? That way, instead of talking about a gravitational force we could talk about gravitational influence. It seems like it would make more sense since the velocity of photons is slightly altered in the presence of massive objects over the brief period that the photons are near the massive object. It's almost as if the path of light is influenced by the presence of massive objects.:zzz:
Whats more, the shape of the Earth is distorted by the gravity of the sun and even the moon. The moon nearly flies away from the Earth with every revolution, but is pulled back into orbit by the earth. So the moon is influenced by the Earth and the Earth is influenced by both the sun and the moon. The effects of the moon's influence can be observed in the tides.
Would it be possible to define all forces this way? The strong force, for example, is the force that holds nuclei together. Perhaps the protons in the nucleus are influenced by this strong "force." In fact, string theory require a gravitational force and predicts a massive partiicle known as the graviton. The formulas used are often dismissed by many physicists as descriptions of the strong force.

 

[Farsight]

There's quite a big difference between a "force₁" like gravity and the "force₂" imparted by say a spring. It's as if we need two different words here. I like impulse myself, but that's force₂ times time.

Oh and just to muddy the waters, we also have the sort of force₃ that you can join. Or you can force₄ somebody to do something they don't want to do. And of course, may the force₅ go with you. Any more for any more?

http://www.answers.com/topic/force

And are we talking about force₂?