# Basic Concepts: Force

This is the first post I'm doing for the "Basic Concepts" series. When I asked for suggestions, I got a good long list of stuff, and it's hard to know quite where to start. I'm going to start with "Force," because physics as we know it more or less started with Isaac Newton, and Newton is best known for his work on forces. In fact, as-you-know-Bob, the SI unit of force is the "Newton," in ol' Isaac's honor.

(I should note that this particular discussion is adapted from a lecture that I give in the introductory mechanics class, so there's also a "path of least resistance" argument for starting with "Force.")

"Force" is one of those words that gets used both in everyday speech and in physics, but in this case, the technical meaning isn't all that far removed from the everyday meaning. When you think of forces in an everyday sense, you think of things that you do to try to change the behavior of objects (or people)-- pushing them, pulling them, hitting them, threatening to hit them, etc. The basic idea carries over-- forces are things that change the motion of objects.

To put it a little more formally, and give the broadest possible definition (I'll get more specific below):

Force is the quantification of an interaction between two objects.

If you have two objects that interact with one another in some way, you describe the size and effect of that interaction in terms of a force. Force, in turn, is related to the motion of the object via Newton's Laws of Motion, of which there are three, because three is the magic number:

1. An object at rest tends to remain at rest, and an object in motion tends to remain in motion in a straight line at constant speed, unless acted on by a force.
2. The net force on an object is equal to the time rate of change of the momentum, or Fnet = dp/dt (which is equal to mass times acceleration for reasonable-size objects at speeds much lower than the speed of light).
3. If one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude to the first force, and in the opposite direction.

These can be summarized as "1) Inertia, 2) F = ma, 3) Action-Reaction," and anybody who has ever taken physics has seen them. They can be understood a little better by thinking in terms of force as the quantification of interaction. The first law is just the codification of common sense: objects don't change their motion unless some interaction causes them to do so. If you see a change in the motion of some object, you can deduce that there must've been an interaction to cause that change, and indeed that's how we detected all the forces we know (about which more later).

The second law is just the quantification of the first law: it tells you how big a force you need to get a given change in motion. The units of force are defined in terms of the second law: a one-newton force is the result of an interaction that causes a one-kilogram object to accelerate at one meter per second.

The third law tells you that interactions always go both ways. If particle A interacts with particle B, particle A is also affected by that interaction. This is why I specify that force is the interaction between two objects-- there may be more than two objects in a system (nine eight planets orbiting the Sun, say), but in terms of forces, you think about them two at a time. The interaction between the Earth and the Sun produces a force on the Earth and a force on the Sun. The interaction between the Earth and Jupiter produces a force on Jupiter, and a second force on the Earth, and so on. You determine the motion by adding up the forces due to all possible pairs, and then applying the second law.

So, if forces are interactions, what sort of interactions are allowed? Modern physics says that there are only four types of interactions possible between fundamental particles (though there's a sort of cottage industry in looking for a fifth). Every particle interaction you see is due to one of these four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force.

The most obvious and inescapable of the forces we see in daily life is gravity. The graviational interaction says that all objects with mass experience a force that pulls them toward every other object with mass. The gravitational force in incredibly weak, on the scale of fundamental forces, but is really obvious in everyday life because the mass of the Earth is gigantic. Every person reading this is being pulled toward the center of the Earth with a force that is rather substantial-- 9.8 newtons per kilogram of your mass (assuming you're near the surface of the Earth, anyway-- if you're reading this from orbit, the force will be somewhat smaller). You're also attracted to the monitor of your computer, with a force that's smaller by something like ten orders of magnitude, by virtue of the fact that both you and it are objects with mass. This force is totally insignificant compared to the other forces you experience, but it's there all the same.

The next most obvious force is electromagnetism, which involves forces between charged particles. When your clothes stick to you on a dry winter day, that's electromagnetism. Odds are, it's also holding something to your refrigerator right now. But more than that, electromagnetism is resposible for your ability to operate a computer-- the atoms making up your body are held together by electromagnetic forces, as are the atoms making up the computer itself. Pretty much any everyday force you can think of (other than gravity) is ultimately due to electromagnetic forces between the component atoms of the interacting objects.

The other two are less obvious, but no less important. The strong nuclear force binds quarks together into protons and neutrons, and hold protons and neutrons together in the nuclei of atoms. It is, as the name implies, an extremely strong force-- 137-ish times stronger than electromagnetism, and better than 30 orders of magnitude stronger than gravity. It's also an extremely short-range force-- protons and neutrons separated by more than 10-15 m (the radius of the nucleus of an atom, more or less) don't feel the strong force at all. So it's not something that you're likely to experience directly any time soon.

The final fundamental force is the weak nuclear force, which is somewhere between gravity and electromagnetism in strength. It's even less obvious than the strong nuclear force, and really only turns up indirectly through certain types of radioactive decay. Which is not to say that it's not important-- the weak force plays a crucial role in determining the abundances of heavy elements (basically anything other than hydrogen), and since you're mostly made of heavy elements, that's pretty darn important, whether you realize it or not.

How are these interactions transmitted from one particle to another? All of these forces act between particles that are separated by some distance of empty space. So, how is that possible?

In the classical picture, this is just one of those things. Physicists generally speak of these forces in terms of "fields" which fill all of space, which is pretty much just a way of saying "the interaction extends through empty space, don't ask me why." You can deal with most everyday phenomena involving gravity and electromagnetism by working with continuous fields, and not really worrying about the mechanism by which the forces are transmitted from one particle to another. I may try to talk more about "fields" in a later Basic Concepts post.

When you start to think about forces between particles at the level where quantum mechanics becomes important, a couple of weird things happen, which cause this "field" business to break down. In order to make an accurate description of the interaction between quantum particles, it's necessary to think in more detail about how the forces are transmitted, and the concept of "exchange bosons" or "force carriers" has to be introduced. In this picture, any interaction between fundamental particles-- two electrons repelling each other, for example-- has to be mediated by the exchange of a particle. At the most fundamental level, we understand the repulsion between two electrons as being due to the exchange of a photon: One electron emits a photon, the other absorbs it, and the recoil due to the emission and absorption is responsible for pushing the two apart.

All of the fundamental forces are, in principle, understood in these terms, and each force has its own exchange bosons. Particles interact through the electromagnetic force by exchaging photons, which are basically little bundles of light. The weak force operates through the emission and absorption of three different particles, the W+, W-, and Z-- which one is passed between the particles depends on the charge of the particles involved. It may seem extravagent to have three different exchange bosons for the weak force, but that's nothing compared to the strong force: the strong force operates by the exchange of "gluons," which come in eight varieties.

Photons, W, and Z particles have all been directly detected (photons in experiments with lasers and atoms, the W and Z bosons in accelerator experiments). Gluons can't really be seen by themselves, but their existence is strongly implied by a variety of accelerator experiments.

In the exchange picture, gravity would be carried by a particle called a "graviton." Nobody has yet constructed a successful theory of "quantum gravity" yet, though. That is, nobody has a theory that matches up with reality and describes the gravitational interaction between particles in terms of the exchange of gravitons, let alone detected a graviton (there's some question about whether it's even possible to detect a single graviton). Our current working theory of gravity-- Einstein's General Theory of Relativity-- describes the force in geometric terms, as resulting from the curvature of space and time, which are continuous. This doesn't really play nice with the other theories, and that situation makes lots of people unhappy. It's generally believed that there ought to be a quantum theory of gravity that works like the quantum theory of the other forces, but writing one down turns out to be ridiculously difficult, and attempts to do so have required all sorts of bizarre contortions.

And that's pretty much everything I can think of to say about the concept of "Force" as it occurs in physics. Any questions?

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Forces might well be quantifiable (the viability of mathematical physics depends on that being the case), but it makes no sense at all to say forces are quantifications.

So my questions is, "What is a force?"

By bob koepp (not verified) on 16 Jan 2007 #permalink

Wakalixes make it go!

[this is good]

*applause*

I think I just learned me some physics, which is more than I can say for two miserable years in high school and another in college.

this is very nice post, i learned something. i hope energy and angular momentum are on the list, too.

So when I push someone, which force is doing the pushing at the quantum level? Are the atoms in my hand electromagnetically repelling his chest atoms?

By Jonathan Weed (not verified) on 16 Jan 2007 #permalink

Good post, I think I'm going to like these. As a non-scientist who loves science (especially physics) I sometimes spend too much time trying to wrap my head around "cool" ideas like "entanglement" and forget the basics. A refresher course always helps.

Thanks for this. I think I'll be learning a lot from these "basics" posts.

I'll go along with Jonathan in comment #5 in asking for a better explanation of how EMF and gravity translate to the everyday forces of mechanics.

Also, I think you'll need to do another "basics" post on why "three is the magic number." ;-)

So when I push someone, which force is doing the pushing at the quantum level? Are the atoms in my hand electromagnetically repelling his chest atoms?

I'd say that it's elecromagnetic repulsion between the atoms making up your hand and the stoms making up the other person's chest. Other than gravity pulling you down toward the center of the Earth, nearly all the everyday forces you experience involve contact between two objects, and that's going to involve electromagnetic forces between atoms.

"Field" is next, I think (though it might be a few days), followed by "energy."

The net force on an object is equal to the time rate of change of the momentum, or Fnet = dp/dt (which is equal to mass times acceleration for reasonable-size objects at speeds much lower than the speed of light).

I could see some people confused by this statement and the nomenclature, although your later description makes it quite clear.

(Net force is time rate of change of momentum)
I could see some people confused by this statement and the nomenclature, although your later description makes it quite clear.

I had just finished writing lecture notes for discussing forces in the context of Special Relativity, where you really have to use the dp/dt definition, which is why that was a little more formal.

I wasn't just trying to be cute (or obnoxious) when I asked, "What is a force?" The closest thing in Chad's post to a characterization or definition is "forces are things that change the motion of objects." Perhaps it would help to consider what would be missing from a "force free physics" of the sort imagined by various theorists over the centuries.

By bob koepp (not verified) on 16 Jan 2007 #permalink

Force is a subject where if I think about it in terms of air hockey demonstrations of Newton's laws in high school, I feel I understand it, yet if I think about it enough, I feel left out of some cosmic understanding. It's easy to see how those hockey pucks just knock one another out of the way and transfer momentum in the process, whether one sees that as the whole puck doing it, as surface electrons in one repelling surface electrons in the other, or exchange photons taking the momentum from one puck to the other. But why?

As you note, everything in life apart from the mostly stable nuclear forces giving us building blocks and the essentially constant effect of gravity is the EM force. That's what we're used to. So we're used to things with charged particles in them banging around with other things that have charged particles, even if balanced by other charged particles in them to be electrically neutral overall. We're used to material holding up other material through EM forces in the materials or being too heavy to be held up. We're not used to seeing a whole lot of neutrinos or even high energy photons pass right through us. We think we're solid when we not really. So we see ourselves banging around with other solid objects, when they're not solid either. It's just the EM force makes it seem that way. Why? Why aren't there more objects that just pass right through us?

Nature doesn't "like" too much charge piling up in one place, unlike how it "feels" about black holes for gravity or an iron nucleus for the strong force. Then there are particles that can be oblivious to all that. Why? What's the difference between charge and mass. To me, they're just numbers and participants in different reasons for why things are the way they are, but there must be some real difference, right? Maybe there's an answer to that in physics beyond the college physics I took, but I've felt lost trying to see it. I understand everything written here, but there's something more. I know I don't understand that.

This is good stuff. I'm going to pick up on one "style" point -

[Newton's] first law is just the codification of common sense: objects don't change their motion unless some interaction causes them to do so

Whatever this is, it's not common sense. Common sense says that objects will eventually come to rest unless something's acting on them, because common sense is learned in a world where friction and air resistance are ubiquitous.

A most excellent post!

"... which is pretty much just a way of saying 'the interaction extends through empty space, don't ask me why.'"

LOL!

Jonathon: Yes, electromagnetism is covering most of the bases here -- both repulsion between the surface atoms of your skins, and the energy conversions done by your muscles. Gravity can get a bit in, though, because you're solid enough to transmit its force through your body, say by leaning into the shove. That solidity is based on not only EM forces but also a bit of quantum wierdness (exclusion) which makes your atoms act mostly like discrete objects rather than clouds of particles.

By David Harmon (not verified) on 16 Jan 2007 #permalink

Of the things that physicists deal with, space and time seem like the ones best tied down, and these give velocity and acceleration. Acceleration is what relates force to mass, and so force and mass are equally mysterious objects.

The best books I've seen on the subject are those by Max Jammer, which are available now used for about \$5 on Amazon. In my own opinion, we cannot understand force or mass until they are put into the same geometrical language that velocity and acceleration live in. Which means that they have to be written in terms of probabilities.

DavidD says:

What's the difference between charge and mass. To me, they're just numbers and participants in different reasons for why things are the way they are,

Actually, that's pretty much exactly what they are. One thing Chad didn't discuss (maybe he's saving it for later and I'm going to steal his thunder - ha ha!) was "generalized charge" - that is, the idea that every force not only has its own type of field (or exchange boson in the quantum world), but each force also has its own type of "charge" that quantifies how much a given object is going interact with that force.

The charge associated with the electromagnetic force is simply electric charge (and yes, it can be confusing when "charge" is used both in the general sense and in the electric sense). The larger in magnitude an object's electric charge is, the more it's going to be affected by the electromagnetic force (and the more it's going to affect other electrically-charged particles - Newton's third law says that affecting and being affected by are equal). Similarly, mass is the charge of the gravitational force - the larger an object's mass, the more it's affected by gravity and the larger its own gravitational field will be. The fact that electric charge can be both positive and negative while mass is never negative (as far as we know) actually tells theorists interesting things about the differences between the photon and the graviton, even though we've never observed a graviton in the lab.

The strong and weak nuclear forces have charges as well. They're called "color charge" and "weak charge" respectively. Color charge in particular is more mathematically complicated than mass or electric charge. Mass has one polarity (positive), electric charge has two (positive or negative), but color charge has six different polarities (red, blue, green, antired, antiblue, antigreen), which is why there have to be so many different types of gluons to send messages between particles with various different combinationas of color charges. Color charge has nothing to do with actual colors in the normal sense - it's just particle physicists being goofy (see also: "electroweak flavour", "strangeness", "quark", "glueball", "selectron", "wino", and many others).

Note that each force ignores the charges of the other forces. It doesn't matter how much mass a particle has - if it has an electric charge equal to that of one electron (-e), then its electromagnetic force will be exactly equal to that of one electron.

To wander a bit further afield, there's one final wrinkle with mass. To be completely technical, there are two types of mass: "gravitational mass", which is the charge of the gravitational force (how hard gravity pulls on it); and "inertial mass", which is the "m" in "F = ma" (how hard you have to push to get something to move). The observation that these two types of mass are exactly the same is a variant of Einstein's Equivalence Principle and all of General Relativity depends on this equivalence.

@Daniel Barlow:

@DavidD:
Hopefully Chad will consider your questions in composing the posts on energy and fields. Energy considerations look large in the explanation for why gravity fields and electromagnetic fields can act differently. And part of the issues you are wondering about also stem from some very advanced stuff, so you are indeed asking tough (and good!) questions there. It helps to realize, at least from a phenomenological standpoint, gravity and EM (well, really we should say electrodynamics, but let's not put Descarte before the horse) are indeed different because gravitational interaction depends on whether the two things interacting have mass but electromagnetic interaction depends on not only whether the two objects have a charge but also what TYPE of charge.

@agm: forgive me if I got the wrong end of the stick here, but I thought the goal here was to explain this stuff, not just to prove your intellectual superiority. Please explain how "don't change their motion" and "eventually come to rest" are the same thing.

Whatever this is, it's not common sense. Common sense says that objects will eventually come to rest unless something's acting on them, because common sense is learned in a world where friction and air resistance are ubiquitous.

Actually, I don't agree with this. People do recognize that objects in motion tend to remain in motion; at least, they do here in the Northeast where everybody has seen a few icy winters. Getting people to understand the first law is mostly a matter of getting them to explicitly recognize that friction and air resistance are themselves forces, which I don't find that hard to sell.

I wish all this talk about "force" would stop. Instead of getting rid of it by using Hamilton's formalism instead of Newton's, we drag it into quantum mechanics where it is clearly out of place. (The classical limit of quantum mechanics is Hamilton's formalism, which is based on the principle of least action and has no need of the dubious concept of force.)
What is quantum mechanics sans embroidery? A mathematical formalism that allows us to calculate the probabilities of possible measurement outcomes on the basis of actual outcomes. In quantum mechanics we say that two objects interact if the probabilities of outcomes of measurements performed on one object depend on the actual outcomes of measurements performed on the other object. Unfortunately

"Physicists are, at bottom, a naive breed, forever trying to come to terms with the 'world out there' by methods which, however imaginative and refined, involve in essence the same element of contact as a well-placed kick." (B.S. DeWitt and R.N. Graham)

Please explain how "don't change their motion" and "eventually come to rest" are the same thing.

In empty space an object that is not changing velocity or direction is at rest. In that in order to change speed/velocity or direction a force must be applied.

It is important to realize the difference between velocity and acceleration( which is a change in velocity or direction) this is not always obvious.

I don't frequent this blog too often. Is there always this much woo floating around in the commentariat?

I wish all this talk about "force" would stop.

Different models on the same subject are useful, since what is easy in one may be difficult in another.

No one would think of using only one software language for this very reason.

the SI unit of force is the "Newton,"
...
9.8 newtons per kilogram

Now I'm going to go anal and nitpicky, but the rather common US misuse of the SI system bugs me a lot. It is very standardized, and some of the rules are made to remove ambiguousness in text use, and among symbols and prefixes. (So Mars probes doesn't crash unnecessarily, for example. :-) The SI system, or measurements in general, would btw make good basic physics articles.

An SI measurement consists of a value and a unit, with space between. All units are spelled lowercase, i.e. "meter", "newton". Units derived from persons have uppercase symbols, i.e "m", "N".

The value contains the plural and the unit should reject the article (makes software formatting simpler, btw). The above now becomes "the SI unit of force is "newton", ... 9.8 newton per kilogram".

Also, prefixes are often misused. All prefixes larger than 1 are uppercase, all smaller are lowercase. There is one exception, due to a base unit exception. For historical reasons, the unit for mass is kilogram, not gram. Since this unit must be spelled "kilogram (kg)", the "kilo (k)" prefix is lowercase.

So it is "1 kN" or "2 GN", or "3 mN" or "4 uN". Really anal, but OTOH to see '5 GG' and '6kn' is enough to make a grown man cry. :-)

Experimentally, I suspect that we ONLY assert that a force is present when we see the acceleration of a mass.

We don't "see" a force, anymore than we feel a temperature.

That's why the definition of "field" is trickier than "force." Nobody detects a field as such. It is inferred from the forces that are themselves inferred from accelerations of masses. Maxwell did not start with fields in a vacuum. He theorized with space packed by vortices, and other things before abstracting everything away except fields. Fortunately, Heaviside simplified Maxwell's math to the 4 equations seen on many a T-shirt today. They can further be compressed to one, by going to 4-dimensional space-time, but that's another blog thread.

Or am I oversimplifying?

One of the fundamental properties of force is that it is directional, so I think you should find some way of including that in your definition.

For me, the most subtle of Newton's Laws is the 3rd. I think a lot of physics newbies get very confused about reaction forces, and the subject could do with being clarified with a few simple examples of the horse-and-cart variety.

We can also define subtraction A-B as the difference vector between the tip of B to the tip of A, when the tails are put on the same point.

Given two vectors A and B, their cross product AÃB is a vector C

More precisely a pseudovector, because it doesn't behave as a proper vector under rotations. The difference is important in physics. ( http://en.wikipedia.org/wiki/Cross_product , http://en.wikipedia.org/wiki/Pseudo-vector )

A 1 kilogram object experiences a force of 9.8 newtons straight down - 9.8n down is a vector quantity.

Now I'm going to nitpick considering that this is a math blog. On the other hand we discussed ambiguousness of symbols in the last basic post (i vs j for imaginary unit). And here we have a rare and basic case of an unambiguous symbolization in form of SI units - which can be important if we don't want Mars probes to crash unnecessarily. (Nudge, nudge.)

Besides, it is one of my most beloved pet peeves.

An SI measurement consists of a value and a unit, with space between. All units are spelled lowercase, i.e. "meter", "newton". Units derived from persons have uppercase symbols, i.e. "m", "N".

The value contains the plural and the unit should reject the article (makes software formatting simpler, btw). The above now becomes "a force of 9.8 newton straight down - 9.8 N down".

Also, prefixes are often misused. All prefixes larger than 1 are uppercase, all smaller are lowercase. There is one exception, due to a base unit exception. For historical reasons, the unit for mass is kilogram, not gram. Since this unit must be spelled "kilogram (kg)", the "kilo (k)" prefix is lowercase.

So it is "1 kN" or "2 GN", or "3 mN" or "4 uN". Really anal, but to see '5 GG' and '6kn' could be enough to make some grown men cry. Uh, but not me, btw. :-)