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the center of the wheel. This is accomplished by making the arcs be of metals of different expansion coefficients, the inner
Unequal expansion of metals
metal, shown in black in the figure, having the smaller coeffi cient. The free ends of the arcs are then sufficiently pulled in by a rise in temperature to counteract the retarding effects.
FIG. 155. The thermostat
The principle is precisely the same as that which finds simple illustration in the compound bar shown in Fig. 153. This bar consists of two strips, one of brass and one of iron, riveted together. When the bar is placed edgewise in a Bunsen flame, so that both metals are heated equally, it will be found to bend in such a way that the more expansible metal, namely, the brass, is on the outside of the curve, as shown in Fig. 154. When it is cooled with snow or ice, it bends in the opposite direction.
The common thermostat (Fig. 155) is precisely such a bar, which is arranged so as to open the drafts by closing an electrical circuit at a when it is too cold, and to close the drafts by making contact at b when it is too warm.
QUESTIONS AND PROBLEMS
1. Why is the water at the bottom of a lake usually colder than that at the top? Why is the water at the bottom of very deep mountain lakes in some instances observed to be at 4° C. the whole year round, while that at the top varies from 0° C. to quite warm?
2. Give three reasons why mercury is a better liquid to use in thermometers than water.
3. Why is a thick tumbler more likely to break when hot water is poured into it than a thin one?
4. Pendulums are often compensated by using cylinders of mercury, as in Fig. 156. Explain.
5. The steel cable from which Brooklyn Bridge hangs is more than a mile long. By how many feet does a mile of its length vary between a winter day when the temperature is — 20° C. and a summer day when it is 30° C.?
6. If a surveyor's steel tape is exactly 100 ft. long at 20° C., how much too short would it be at 0° C.? 12
7. A certain glass flask is graduated to hold 1000 cc. at 15° C. How many cubic centimeters will the same flask hold at 40° C., the coefficient of cubical expansion of glass being .000025? /
8. The dial thermometer is a compound bar (Fig. 157) with iron on the outside and brass on the inside. A thread is wound about the central cylinder c. Explain the action.
9. Why may a glass stopper sometimes be loosened by pouring hot water on the neck of a bottle?
10. A metal rod 230 cm. long expanded 2.75 mm. in being raised from 0°C. to 100°C. Find its coefficient of linear expansion.
11. The changes in temperature to which long lines of steam pipes are subjected make it necessary to introduce "expansion joints." These joints consist of brass collars fitted tightly by means of packing over the separated ends of two adjacent lengths of pipe. If the pipe is of iron, and such a joint is inserted every 200 ft., and if the range of temperature which must be allowed for is from 30°C. to 125°C., what is the minimum play which must be allowed for at each expansion joint?
12. Show from equation 5, p. 140, that linear coefficient of expansion may be defined as increase in length per unit length per degree.
WORK AND HEAT ENERGY
172. Friction always results in wasted work. All of the experiments mentioned in Chapter VII were so arranged that friction could be neglected or eliminated. So long as this condition was fulfilled it was found that the result of universal experience could be stated thus: The work done by the acting force is equal to the sum of the kinetic and potential energies stored up.
But wherever friction is present this law is found to be inexact, for the work of the acting force is then always somewhat greater than the sum of the kinetic and potential energies stored up. If, for example, a block is pulled over the horizontal surface of a table, at the end of the motion no velocity has been imparted to the block, and hence no kinetic energy has been stored up. Further, the block has not been lifted nor put into a condition of elastic strain, and hence no potential energy has been communicated to it. We cannot in any way obtain from the block more work after the motion than we could have obtained before it was moved. It is clear, therefore, that all of the work which was done in moving the block against the friction of the table was wasted work. Experience shows that, in general, where work is done against friction it can never be regained. Before considering what becomes of this wasted work we shall consider some of the factors on which friction depends and some of the laws which are found by experiment to hold in cases in which friction occurs.
173. Coefficient of friction. It is found that if F represents the force parallel to a plane which is necessary to maintain uniform motion in a body which is pressed against the plane with a force F', then, for small
velocities, the ratio depends
F only on the nature of the surfaces in contact, and not at all on the area or on the velocity of the motion. The ratio is called the coefficient of friction for
FIG. 158. The ratio of F to F' is the coefficient of friction
the given materials. Thus (Fig. 158), if F is 300 g. and F' is 800 g., the coefficient of friction is 300 = .375. The coefficient of iron on iron is about .2; of oak on oak, about .4.
174. Rolling friction. The chief cause of sliding friction is the interlocking of minute projections. When a round solid rolls over a smooth surface, the frictional resistance is generally much less than when it slides; for example, the coefficient of friction of cast-iron wheels rolling on iron rails may be as low as .002, that is, of the sliding friction
FIG. 159. Friction in bearings
(1) Common bearing; (2) ball bearing
of iron on iron. This means that a pull of 1 pound will keep a 500pound car in motion. Sliding friction is not, however, entirely dispensed with in ordinary wheels, for although the rim of the wheel rolls on the track, the axle slides continuously at some point c (Fig. 159, (1)) upon the surface of the journal. Journals are frequently lined with brass or Babbitt metal, since this still further lowers the coefficient.
The great advantage of the ball bearing (Fig. 159, (2)) is that the sliding friction in the hub is almost completely replaced by rolling friction. The manner in which ball bearings are used in a bicycle
pedal is illustrated in Fig. 160. The free-wheel ratchet is shown in Fig. 161. The pawls a and b enable the pedals and chain wheel WV to stop while the rear axle continues to revolve. Roller bearings are shown in Fig. 162. Oils and greases prevent rapid wear of bearings by lessening friction.
FIG. 160. The bicycle pedal
FIG. 161. Free-wheel ratchet
175. Fluid friction. When a solid moves through a fluid, as when a bullet moves through the air or a ship through the water, the resistance encountered is not at all independent of velocity, as in the case of solid friction, but increases for slow speeds nearly as the square of the velocity, and for high speeds at a rate considerably greater. This explains why it is so expensive to run a fast train; for the resistance of the air, which is a small part of the total resistance so long as the train is moving slowly, becomes the predominant factor at high speeds. The resistance offered to steamboats running at high speeds is usually considered to increase as the cube of the velocity. Thus, the Cedric, of the White Star Line, having a speed of 17 knots, has a horse power of 14,000 and a total weight, when loaded, of about 38,000 tons, while the Mauretania, of the Cunard Line, having a speed of 25 knots, has engines of 70,000 horse power, although the total weight when loaded is only 32,500 tons.
QUESTIONS AND PROBLEMS
1. Mention three ways of lessening friction in machinery.
2. In what respects is friction an advantage, and in what a disadvantage, in everyday life? Could we get along without it?
3. Why is a stream swifter at the center than at the banks?
4. Why does a team have to keep pulling after a load is started?