Forces

Back to the main page/Back
to the previous page

The Jedi had access to "The Force" and it carried them through all sorts of predicaments. What is a force? Where do forces come from, and where do they go? You push on a door, and the force you exert opens it. How many forces are there? How different is the force of Sammy Sosa's bat on a baseball from Tiger Woods' driver on a golf ball? A familiar and puzzling force is that of gravity as it pulls things to Earth. Chemical forces seem to hold molecules together. Is the force of the wind a special kind of force (as gravity seems to be)?

Here's a seemingly simple problem: I sit on a table and the table supports
my weight. How does it do this? Clearly, the table pushes up on me by just as
much as I (with the help of gravity) push down, and we come to a state of
equilibrium. Now I lay my book on the table beside me. The book pushes down and
the table pushes up and the book, like me, is at rest on the table. Question:
How does the table know just how hard to push on me and how hard to push on the
book? It's reasonable to expect the table to push harder on me (i.e. exert a
larger force), but how does it know *how much* harder? Think about it -
we'll find the answer soon enough.

The first two

Getting back to our list of forces, it seems that it can get quite long: What
forces make a car go, or an electric train? It would seem that the force to keep
an electric train moving should be electrical and a car's forces should derive
from the gasoline it its tank. How different are these? It begins to look as if
the list is an enormous one, but it turns out that the list is not very long at all.
There are, in fact only four forces we have to deal with. One we've mentioned,
gravity. We need to understand more about the gravitational force, but for now
we just want to establish our list. The next force is the electrical, or more
properly the electromagnetic force. It's much stronger than the gravitational
force, as you can easily show: Run a rubber comb through your hair and move it
close to a small piece of paper lying on the table. When the comb passed through
your hair some electrons from your hair were transferred to the comb, so it had
a net negative charge. This relatively small amount of charge, when put near the
piece of paper, provides a force strong enough to lift the paper right off the
table, in spite of the fact that the whole earth, through its gravitational
influence, is trying to keep it down! Later on we'll calculate how much the
difference between the two forces are, but for now it suffices to say that the
difference is enormous. Now, as far as our every day experience is concerned,
we've exhausted the list - there's only two! Well, there's really four, but the
other two, which I'll talk about later, are only noticeable on an atomic scale.
Wait a minute - what about the Sosa's baseball and Tiger Woods' golf ball? These
forces are electrical. Take a close-up look at a bat hitting a ball: the two
objects come so close to each other that the atoms in the bat interact with the
ones in the ball. Atoms are tiny positively charged things (nuclei) surrounded
by a swarm of negatively charged electrons. Well, that's a crude description of
an atom, but it serves our purpose here. It's an experimentally verified and
well known fact that like electrical charges mutually repel each other, and
opposite charges attract. As the ball and the bat come together, the first each
sees is the electrons of the other. (The electrons are, after all, on the
outside of their atoms). The electrons repel each other and the ball heads for
the bleachers. I'm ready to admit that no one uses this electrical interaction
to actually *calculate* the effect of bat on ball - there are way too many
electrons involved - but the *fundamental process* is electrical. As for
the other forces mentioned above, and in fact *all* the other forces we
encounter on a macroscopic scale aside from gravitational ones, they too are electrical. For example, the
intermolecular forces that are released when gasoline is combusted by our car
engines are there due to the electrical make-up of the atoms that comprise the
molecules of the fuel.

The other two

There are two more forces. One is fairly easy to figure - at least it's easy to see that it should exist. The model of the atom mentioned the previous paragraph is the one everyone learns about in school: A nucleus made of protons and neutrons surrounded by rings of electrons. We also learn that the electrons carry negative charges and the protons have an equal positive charge. As the electrons move in their orbits they spread themselves out as much as possible because they mutually repel each other. How about the protons? They're all positively charged and they are really close together. Why don't they fly apart? Answer: They must be trying to, and since they don't it must be that something (a force!) is holding them together. Rule gravity out - it's much too weak. It must be another, very strong force. We call it, well ..., the "strong" force (or, more formally, the "strong interaction"). How strong is this force? It must hold the nucleus together against the electrical repulsion of the protons. Check out the periodic table of the elements. There are about 100 elements. That means 100 protons pushing each other apart. The strong force is able to withstand the force of 100 protons, but not more, otherwise we would have more elements. Conclusion: the strong force is (roughly) 100 times that of the electrical force.

The other force is called the "weak" force (or weak interaction). This force is involved in the process whereby a neutron decays into a proton and in so doing ejects an electron and a neutrino in a process called beta decay. (Actually, its an antineutrino and the process can also start with a proton and eject a positron, but here we just want to establish the list). The force that is involved in these processes is the weak interaction. It is weak indeed, but not so weak as gravity.

The four forces differ greatly in strength and range. Of the
two we experience every day, the electromagnetic force is by far the greater. As
an example, two protons are electrically repelled and gravitationally attracted.
The electrical repulsion is over one million trillion trillion times greater
than the gravitational attraction. That's
10,000,000,000,000,000,000,000,000,000,000,000,000 greater or (as a demonstration
of why we like to use "scientific notation") 10^{37} times
greater. If the two protons could get next to each other the attractive force
would overcome the electrical force by about 100 times, but this force doesn't
extend for distances much beyond the diameter of a proton (electromagnetic and
gravitational forces extend to infinity). The weak force is much greater than
gravity, but tiny compared with the other two, and extends over an even shorter
range than the strong interaction.

Dealing with forces

Aside from the strikingly short list of fundamental forces, on
a more mundane level we deal with forces every day. Gravity is fundamental and
familiar, as is electricity (or electromagnetism), but often not as a
force. Forces like those between bats and balls are called mechanical
forces and its more practical to deal with them as the kind of forces Newton
described rather than as the electromagnetic interactions they fundamentally
are. Nuclear forces are not things we deal with very often, so we won't consider
them now. A good working
definition of a mechanical force is a push or a pull. This definition also
illustrates an important characteristic of forces, and one we will have occasion
to use: If a force is a push or a pull, how do you quantify it? You can describe
how hard you push, but that's not enough. You also need to tell the *direction*
of the push. I can ask you to push on something with a force of 10 N, but if I
don't specify a particular direction you may not provide the desired results.
Both magnitude (how hard you push) and direction are required to completely
define a force. (Try to push on something without involving a direction). In the
business of science we call things requiring magnitude and direction
"vectors". By the way, the unit 'N' for our 10 N force is called a
Newton in honor of Sir Isaac Newton. It's the metric counterpart of the English
pound. To convert between the two, 1 N = .2248 lb, or in the other direction 1
lb = 2.448 N (or roughly two and a half Newtons per pound). Although pounds may be more
comfortable for you, its time to bite the bullet and go metric. Only the United
States hasn't already made the move to measuring things in metric units. Maybe after you take this course,
graduate and make it to congress you will have seen the light and so push (no
pun intended) us along to metric sanity.

Categories of Phenomena

When Newton published his laws of motion in 1687 he brought a
means of predicting, to any (at least in principle) degree of accuracy, the
motions of planets in their orbits about the sun as well as the flight of a
cannon ball over the surface of the earth. Using his laws the world could be
considered as a fine clock, which when wound up in a known way would tick away
predictably and flawlessly into the distant future. Given a few pieces of
critical information about how a physical
system started out, Newton's equations
accurately predicted the future of the system from that time forward. If the
system became complicated by virtue of the number of its parts, the equations
would become cumbersome but solvable: Even the mutual interactions (via gravity)
of all the planets and all their moons are determined by (simultaneously)
solving a single set of equations (Newton's famous universal law of gravitation
F_{g} = Gmm'/r^{2}). But what if the number of interacting
particles becomes enormous, as in the case of the air molecules in a room? Here
the number becomes very large, on the order of Avogadro's number (6.022 x 10^{23}).
In principle you might suppose that the picture doesn't change fundamentally,
even though the number of simultaneous equations becomes so large that there is
no hope of ever solving them, even with the help of the most powerful computers.

On the other hand, there is hardly any motivation to find out how molecules in a gas move in such fine detail. We want to know how the gas behaves as a whole, and very precise information about its behavior can be obtained statistically using methods introduced by Boltzmann. The question now arises: Which approach, the Newtonian regime of a clock-like world or the statistical methods of Boltzmann are more fundamental? The question becomes more puzzling in the quantum mechanical world where even the most elementary interactions of a single particle (e.g. an electron) yield better to a statistical interpretation than to a precisely deterministic one. The matter is still under question.