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velocity requires some delicate experimentation, because the apparent friction 1s |
much reduced ïf the lower surface vibrates very fast. When the experiment is done |
at very hiph speed, care must be taken that the obJjects do not vibrate relative |
to one another, since apparent decreases of the friction at hipgh speed are often |
due to vibrations. At any rate, this friction law is another of those semiempirical |
laws that are not thoroughly understood, and in view of all the work that has |
been done it is surprising that more understanding of this phenomenon has not |
come about. At the present time, in fact, it is impossible even to estimate the |
coeflicient of friction between two substances. |
lt was pointed out above that attempts to measure by sliding pure substances |
such as copper on copper will lead to spurious results, because the surfaces in |
contact are not pure copper, but are mixtures of oxides and other impurities. lf |
we try to get absolutely pure copper, iŸ we clean and polish the surfaces, outgas |
the materials in a vacuum, and take every conceivable precaution, we sfill do |
not get . Eor If we tilt the apparatus even to a vertical position, the slider will |
not fall of —the two pieces of copper stick togetherl The coeficient , which is |
ordinarily less than unity for reasonably hard surfaces, becomes several times |
unity! The reason for this unexpected behavior is that when the atoms in contact |
are all of the same kind, there is no way for the atoms to “know” that they are in |
diferent pieces of copper. When there are other atoms, in the oxides and greases |
and more complicated thin surface layers of contaminants in between, the atoms |
“know” when they are not on the same part. When we consider that it is Íorces |
between atoms that hold the copper together as a solid, it should become clear |
that it is impossible to get the right coefficient of friction for pure metals. |
The same phenomenon can be observed In a simple home-made experiment |
with a fat glass plate and a glass tumbler. If the tumbler is placed on the plate |
and pulled along with a loop of string, it slides fairly well and one can feel the |
--- Trang 238 --- |
coefficient of friction; it is a little irregular, but it is a coefficient. If we now wet |
the glass plate and the bottom of the tumbler and pull again, we fnd that it |
binds, and if we look closely we shall ñnd scratches, because the water is able |
to lift the grease and the other contaminants of the surface, and then we really |
have a glass-to-glass contact; this contact is so good that it holds tight and resists |
separation so much that the gÌass 1s torn apart; that is, it makes scratches. |
12-3 Molecular forces |
We shall next discuss the characteristics of molecular forces. These are Íorces |
between the atoms, and are the ultimate origin of friction. Molecular forces have |
never been satisfactorily explained on a basis of classical physies; it takes quantum |
mechanics to understand them fully. Empirically, however, the force between |
atoms is illustrated schematically in Eig. 12-2, where the force ' between two |
atoms is plotted as a function of the distance r between them. “There are diferent |
cases: in the water molecule, for example, the negative charges sit more on the |
oxygen, and the mean positions of the negative charges and of the positive charges |
are not at the same point; consequently, another molecule nearby feels a relatively |
large force, which is called a dipole-dipole force. However, for many systems the |
charges are very much better balanced, in particular for oxygen gas, which 1s |
perfectly symmetrical. In this case, although the minus charges and the plus |
charges are dispersed over the molecule, the distribution is such that the center |
of the minus charges and the center of the plus charges coincide. A molecule |
where the centers do not coincide is called a polar molecule, and charge times |
the separation between centers is called the dipole moment. A nonpolar molecule |
F REPULSION |
ATTRACTION |
Fig. 12-2. The force between two atoms as a function of their distance |
of separation. |
--- Trang 239 --- |
1s one in which the centers of the charges coincide. Eor all nonpolar molecules, in |
which all the electrical forces are neutralized, it nevertheless turns out that the |
force at very large distances is an attraction and varies inversely as the seventh |
power of the distance, or ` = k/r7, where k is a constant that depends on the |
molecules. Why this is we shall learn only when we learn quantum mechanics. |
'When there are dipoles the forces are greater. When atoms or molecules get too |
close they repel with a very large repulsion; that is what keeps us from falling |
through the foorl |
These molecular forces can be demonstrated in a fairly direct way: one of |
these is the friction experiment with a sliding glass tumbler; another is to take |
two very carefully ground and lapped surfaces which are very accurately Ẩat, |
so that the surfaces can be brought very close together. An example of such |
surfaces is the Johansson blocks that are used in machine shops as standards for |
making accurate length measurements. If one such block is slid over another very |
carefully and the upper one ïs lifted, the other one will adhere and also be lifted |
by the molecular forces, exemplifying the direct attraction bebween the atoms on |
one block for the atoms on the other block. |
Nevertheless these molecular forces of attraction are still not fundamental in |
the sense that gravitation is fundamental; they are due to the vastly complex |
interactions of a]l the electrons and nuclei in one molecule with all the electrons |
and nuclei in another. Any simple-looking formula we get represents a summation |
of complications, so we still have not got the fundamental phenomena. |
Since the molecular forces attract at large distances and repel at short distances, |
as shown In EFig. 12-2, we can make up solids in which all the atoms are held |
together by their attractions and held apart by the repulsion that sets in when |
they are too close together. At a certain distance ở (where the graph in Fig. 12-2 |
crosses the axis) the forces are zero, which means that they are all balanced, so |
that the molecules stay that distance apart from one another. If the molecules are |
pushed closer together than the distance đ they all show a repulsion, represented |
by the portion of the graph above the r-axis. To push the molecules only slightly |
closer together requires a great force, because the molecular repulsion rapidly |
becomes very great at distances less than ở. If the molecules are pulled slightly |
apart there is a slight attraction, which increases as the separation increases. If |
they are pulled sufficiently hard, they will separate permanently——the bond 1s |
broken. |
Tf the molecules are pushed only a øer small distance closer, or pulled only |
a 0erU small distance farther than đ, the corresponding distance along the curve |
--- Trang 240 --- |
of Eig. 12-2 is also very small, and can then be approximated by a straight line. |
'Therefore, in many circumstaneces, if the displacement is not too great the ƒorce |
¡s proportional to the đisplacemenf. Thĩs principle 1s known as Hooke”s law, or |
the law of elasticity, which says that the force in a body which tries to restore the |
body to its original condition when ït is distorted is proportional to the distortion. |
This law, of course, holds true only if the distortion is relatively small; when 1$ |
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