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Forces
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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") 1037 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 Fg = Gmm'/r2). 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 1023). 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.