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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
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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$