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3 lubricant films that can be as thin as a few molecules. It is em- ployed to measure how such lubricant films affect the sliding friction associated with relative motion of the mica surfaces. In the 1990s it was established that friction did not correlate directly with the strength of the adhesive bond itself. Instead, it is associated with adhesive "irreversibility," or how surfaces behave differently while being stuck together compared to being unstuck. There are a few minor mechanisms that act so as to increase the friction. One is a plowing mechanism, when a hard surface slides against a soft one, and plows out a series of grooves. A second one, with very rough surfaces, consists of a component of the motion perpendicular to the interface. (This is the rough- ness effect, which at one time was thought to be the main component of friction.) Third, there is elastic hysteresis, as result of the fact that there is elastic compression and then relaxation of the material near the contacting interface, and not all the energy is recoverable. Fourth, there is an electrostatic attraction between the surfaces, but this is only significant when electri- cally insulating materials are used. Friction coefficient values Values of the friction coefficient are required in analyzing many problems in mechanics, in order to estimate the frictional forces at interfaces and to compute their consequences. Figure 3 shows typical friction coefficient values, plotted as a function of the state of cleanliness or of lubrication of the surfaces. As will be seen, friction coefficients range from about 1.5 to about .07 depending on the sliding conditions. Unlubricated metals give higher friction than nonmetals, but well-lubricated metals give less. In consequence, when sliding mechanisms giving low friction are desired, metals are used when a lubricant is available, but nonmetals are preferred when the surfaces must operate in an unlubricated condition. It should be emphasized that the friction coefficient values shown in Fig. 3 are typical ones, and that in any specific case friction values differing by as much as 30% are quite likely to be found. Indeed, it is not yet possible, even for an expert in the friction field, to be able to estimate the friction coefficient in any given case to within 10% or better. A number of sliding systems are exceptional, in that they give friction values that are rather different from those shown in Fig. 3, and much use is made of their exceptional friction properties. Elastomeric materials like rubber give friction values that are about twice as great as those of other nonmetals, and this explains the use of rubber in shoe soles and heels, in automobile tires, and in other cases in which good traction is required. Solids that give exceptionally low friction, about half the values for other nonmetals, include graphite, Teflon, and ice. Teflon and graphite are used in low-friction coatings, while the low friction of ice is made use of in skating and skiing. Per- haps the lowest friction values are found in mammalian joints (like the human knee joint), where it has been found that fric- tion coefficient values are generally as low as .02. It is not clear how such a low value is achieved. Two special cases of low friction should be mentioned. One involves the use of rolling rather than sliding action. This generally produces much lower friction than is possible during sliding. For example, ball bearings generally give friction coef- ficients in the range .002 to .005. The other involves fluid-lubri- cated sliding systems at high sliding speeds, in which hydro- dynamic effect allows separation of the surfaces by a full fluid film. Here friction coefficient values of .001 – .003 are common. Frictional oscillations It was noted above that the laws of friction are not perfectly obeyed. This generally means that if one of the variables (for example, load or apparent area) is varied by a factor of 10, the friction coefficient is changed by less than 10%. Only one of these departures from constancy has practical significance, namely, if the friction goes down when the sliding speed goes Friction (continued) + ward ' s science + ward ' s science Fig. 3: Typical friction coefficient values.