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107. That the molecules of solids cling together with forces of great magnitude is proved by some of the simplest facts of nature; for solids not only do not expand indefinitely like gases, but it often requires enormous forces to pull their molecules apart. Thus, a rod of cast steel 1 centimeter in diameter may be loaded with a weight of 7.8 tons before it will be pulled in two.

The following are the weights in kilograms necessary to break drawn wires of different materials, 1 square millimeter in cross section, the so-called relative tenacities of the wires.

Lead, 2.6

Silver, 37

Platinum, 43
Copper, 51

Iron, 77

Steel, 91

108. Elasticity. We can obtain additional information about the molecular forces existing in different




substances by studying what happens when the weights applied are not large enough to break the wires.


FIG. 92. Elasticity of a steel wire

Thus, let a long steel wire (for example, No. 26 piano wire) be suspended from a hook in the ceiling, and let the

*This chapter should be preceded by a laboratory experiment in which Hooke's law is discovered by the pupil for certain kinds of deformation easily measured in the laboratory. See, for example, Experiment 13 of the authors' Manual.

lower end be wrapped tightly about one end of a meter stick, as in Fig. 92. Let a fulcrum c be placed in a notch in the stick at a distance of about 5 cm. from the point of attachment to the wire, and let the other end of the stick be provided with a knitting needle, one end of which is opposite the vertical mirror scale S. Let enough weights be applied to the pan P to place the wire under slight tension; then let the reading of the pointer p on the scale S be taken. Let three or four kilogram weights be added successively to the pan and the corresponding positions of the pointer read. Then let the readings be taken again as the weights are successively removed. In this last operation the pointer will probably be found to come back exactly to its first position.

This characteristic which the steel has shown in this experiment, of returning to its original length when the stretching weights are removed, is an illustration of a property possessed to a greater or less extent by all solid bodies. It is called elasticity.

109. Limits of perfect elasticity. If a sufficiently large weight is applied to the end of the wire of Fig. 92, it will be found that the pointer does not return exactly to its original position when the weight is removed. We say, therefore, that steel is perfectly elastic only so long as the distorting forces are kept within certain limits, and that as soon as these limits are overstepped it no longer shows perfect elasticity. Different substances differ very greatly in the amount of distortion which they can sustain before they show this failure to return completely to the original shape.

110. Hooke's law. If we examine the stretches produced by the successive addition of kilogram weights in the experiment of § 108, Fig. 92, we shall find that these stretches are all equal, at least within the limits of observational error. Very carefully conducted experiments have shown that this law, namely, that the successive application of equal forces produces a succession of equal stretches, holds very exactly for all sorts of elastic displacements so long, and only so long, as the limits of perfect elasticity are not overstepped. This

law is known as Hooke's law, after the Englishman Robert Hooke (1635-1703). Another way of stating this law is the following: Within the limits of perfect elasticity elastic deformations of any sort, be they twists or bends or stretches, are directly proportional to the forces producing them. The common spring balance (Fig. 57) is an application of Hooke's law.

111. Cohesion and adhesion. The preceding experiments have brought out the fact that, in the solid condition at least, molecules of the same kind exert attractive forces upon one another. That molecules of unlike substances also exert mutually attractive forces is equally true, as is proved by the fact that glue sticks to wood with tremendous tenacity, mortar to bricks, nickel plating to iron, etc.

The forces which bind like kinds of molecules together are commonly called cohesive forces; those which bind together molecules of unlike kind are called adhesive forces. Thus, we say that mucilage sticks to wood because of adhesion, while wood itself holds together because of cohesion. Again, adhesion holds the chalk to the blackboard, while cohesion holds together the particles of the crayon.

112. Properties of solids depending on cohesion. Many of the physical properties in which solid substances differ from one another depend on differences in the cohesive forces existing between their molecules. Thus, we are accustomed to classify solids with relation to their hardness, brittleness, ductility, malleability, tenacity, elasticity, etc. The last two of these terms have been sufficiently explained in the preceding paragraphs; but since confusion sometimes arises from failure to understand the first four, the tests for these properties are here given.

We test the relative hardness of two bodies by seeing which will scratch the other. Thus, the diamond is the hardest of all substances, since it scratches all others and is scratched by none of them.

We test the relative brittleness of two substances by seeing which will break the more easily under a blow from a hammer. Thus, glass and ice are very brittle substances; lead and copper are not.

We test the relative ductility of two bodies by seeing which can be drawn into the thinner wire. Platinum is the most ductile of all substances. It has been drawn into wires only .00003 inch in diameter. Glass is also very ductile when sufficiently hot, as may be readily shown by heating it to softness in a Bunsen flame, when it may be drawn into threads which are so fine as to be almost invisible. We test the relative malleability of two substances by seeing which can be hammered into the thinner sheet. Gold, the most malleable of all substances, has been hammered into sheets 300000 inch in thickness.



1. Tell how you may, by use of Hooke's law and a 20-lb. weight, make the scale for a 32-lb. spring balance.

2. A broken piece of wrought iron or steel may be welded by heating the broken ends white hot and pounding them together. Gold foil is welded cold in the process of filling a tooth. Explain welding.

3. A piece of broken wood may be mended with glue. What does the glue do?

4. Why are springs made of steel rather than of copper?

5. If a given weight is required to break a given wire, how much force is required to break two such wires hanging side by side? to break one wire of twice the diameter ?


113. Proof of the existence of molecular forces in liquids. The facility with which liquids change their shape might lead us to suspect that the molecules of such substances exert almost no force upon one another, but a simple experiment I will show that this is far from true.

By means of sealing wax and string let a glass plate be suspended horizontally from one arm of a balance, as in Fig. 93. After equilibrium is obtained, let a surface of water be placed just beneath the plate and the beam pushed down until contact is made. It will be found necessary to add a considerable weight to the opposite pan in order to pull the plate away from the water. Since a layer of water will be found to cling to the glass, it is evident that the added force applied to the pan has been expended in pulling water molecules away from water molecules, not in pulling glass away from water. Similar experiments may be performed with all liquids. In the case of mercury the glass will not be found to be wet, showing that the cohesion of mercury is greater than the adhesion of glass and mercury.

FIG. 93. Illustrating cohesion of water

114. Shape assumed by a free liquid. Since, then, every molecule of a liquid is pulling on every other molecule, any body of liquid which is free to take its natural shape, that is, which is acted on only by its own cohesive forces, must draw itself together until it has the smallest possible surface com patible with its volume; for, since every molecule in the surface is drawn toward the interior by the attraction of the molecules within, it is clear that molecules must continually move toward the center of the mass until the whole has reached the most compact form possible. Now the geometrical figure which has the smallest area for a given volume is a sphere. We conclude, therefore, that if we could relieve a body of liquid from the action of gravity and other outside forces, it would at once take the form of a perfect sphere. This conclusion may be easily verified by the following experiment:

Let alcohol be added to water until a solution is obtained in which a drop of common lubricating oil will float at any depth. Then with a pipette insert a large globule of oil beneath the surface. The oil will be seen to float as a perfect sphere within the body of the liquid (Fig. 94). (Unless the drop is viewed from above, the vessel should have flat rather

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