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9. A lever is 3 ft. long. Where must the fulcrum be placed so that a weight of 300 lb. at one end shall be balanced by 50 lb. at the other? 10. Two horses of unequal strength must be hitched as a team. The one is to pull 360 lb., while the other pulls 288 lb. In a doubletree 50 in. long, where must the pin be placed to permit an even pull?

11. In the differential wheel and axle (Fig. 483) the rope is wound in opposite directions on two axles of different diameter. For a complete revolution of the axle the weight is lifted by a distance equal to one half the difference between the circumferences of the two axles. If the crank has a radius of 2 ft., the larger axle a diameter of 6 in., and the smaller one a diameter of 4 in., find the mechanical advantage of the arrangement. (See differential pulley, p. 119.)

FIG. 483. Differential windlass

12. With the aid of Fig. 484 describe the process of winding and setting a watch. The rocker R is pivoted at S; Ccarries the mainspring and E the hands; S. P. is a light spring which normally keeps the wheel A in mesh with C. Pressing down on P, however, releases A from C and engages B with D. What mechanical principles do you find involved? What happens when M is turned backward?

13. A 150-lb. man runs up a flight of stairs 60 ft. high in 10 sec. What is his horse power while doing it? How do you account for the result?

14. A thousand-barrel tank at a mean elevation of 50 ft. is to be filled with water. How much work must be done to fill it, assuming a barrel of water to weigh 260 lb.? How long would it take a 2-horsepower electric motor to fill it?

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FIG. 484. Winding and setting mechanism of a stem-winding watch

15. What must be the horse power of an engine which is to pump 10,000 1. of water per second from a mine 150 m. deep? (Take 76 kilogram meters per second = 1 horse power.)

16. A water motor discharges 100 1. of water per minute when fed from a reservoir in which the water surface stands 50 m. above the level

of the motor. If all of the potential energy of the water were transformed into work in the motor, what would be the horse power of the motor? (The potential energy of the water is the amount of work which would be required to carry it back to the top of the reservoir.)

17. A rifle weighing 8.5 lb. discharges a bullet weighing 0.4 oz. with a velocity of 2600 ft. per second. What is the kinetic energy of the bullet; the velocity of recoil of the rifle; the kinetic energy of the rifle?

CHAPTER VIII. 1. What fractional part of the air in a room passes out when the air in it is heated from -15°C. to 20°C.? (−15°C. = 258° A.; 20°C. 293° A.)

2. If the volume of a body of gas at 20°C. and 76 cm. pressure is 500 cc., what is its volume at 50°C. and 70 cm. pressure?

3. An automobile tire contained air under a pressure of 70 lb. per square inch at a temperature of 20°C. On being driven, the temperature of the air rose to 35°C. What was the increase in pressure within the tire?

4. Find the density of the air in a furnace whose temperature is 1000°C., the density at 0°C. being .001293.

5. When the barometric height is 76 cm. and the temperature 0°C., the density of air is .001293. Find the density of air when the temperature is 38°C. and the barometric height is 73 cm. Find the density of air when the temperature is 40° C. and the barometric height 74 cm.

6. If an iron steam pipe is 60 ft. long at 0°C., what is its length when steam passes through it at 100°C.?

7. If iron rails are 30 ft. long, and if the variation of temperature throughout the year is 50°C., what space must be left between their ends?

8. If the total length of the iron rods b, d, e, and i in a compensated pendulum (Fig. 151) is 2 m., what must be the total length of the copper rods e if the period of the pendulum is independent of temperature?

9. Two metal bars, one aluminium and the other steel, are both 100 cm. long at 0°C. How much will they differ in length at 30°C.? (See table on page 140.)

CHAPTER IX. 1. Name three uses and three disadvantages of friction. 2. There is a Pelton wheel at the Sutro tunnel in Nevada which is driven by water supplied from a reservoir 2100 ft. above the level of the motor. The diameter of the nozzle is about 1⁄2 in., and that of the wheel but 3 ft., yet 100 H. P. is developed. If the efficiency is 80%, how many cubic feet of water are discharged per second?

3. A turbine having an efficiency of 80% was supplied with 200 cu. ft. of water per second at a head of 50 ft. What horse power was developed?

4. How many calories of heat are generated by the impact of a 200kilo bowlder when it falls vertically through 100 m.? (The mechanical equivalent of heat 427 g.m.)

5. Thousands of meteorites are falling into the sun with enormous velocities every minute. From a consideration of the preceding example account for a portion, at least, of the sun's heat.

6. The kinetic energy of mass motion of an automobile running 20 mi. per hour was 37,344 ft. lb. In stopping this car how many B.T.U. were developed in the brakes?

7. 400 g. of aluminium at 100° C. were dropped into 500 g. of water at 20° C. The water equivalent of the calorimeter was 40 grams. Find the resultant temperature. (See table on page 160.)

8. A copper ball weighing 3 kg. was heated to a temperature of 100° C. When placed in water at 15° C. it raised the temperature to 25° C. How many grams of water were there? (See table on page 160.)

9. 100 g. of water at 80° C. are thoroughly mixed with 500 g. of mercury at 0° C. What is the temperature of the mixture?

10. A piece of platinum weighing 10 g. is taken from a furnace and plunged instantly into 40 g. of water at 10° C. The temperature of the water rises to 24° C. What was the temperature of the furnace?

11. How many grams of ice-cold water must be poured into a tumbler weighing 300 g. to cool it from 60° C. to 20° C., the specific heat of glass being .2?

12. If you put a 20-g. silver spoon at 20° C. into a 150-cc. cup of tea at 70° C., how much do you cool the tea?

13. Which would be heated more, a lead or a steel bullet, if they were fired against a target with equal speeds?

14. If the specific heat of lead is .031 and the mechanical equivalent of a calorie 427 g. m., through how many degrees centigrade will a 1000-g. lead ball be raised if it falls from a height of 100 m., provided all of the heat developed by the impact goes into the lead?

15. A car weighing 60,000 kilos slides down a grade which is 2 m. lower at the bottom than at the top and is brought to rest at the bottom by the brakes. How many calories of heat are developed by the friction?

16. Explain why the cylinder of an automobile-tire pump becomes hot when the pump is being used. Why is the air cooled as it escapes from the valve of an automobile tire?

CHAPTER X. 1. What is the temperature of a mixture of ice and water? What determines whether it is freezing or melting?

2. Why does ice cream seem so much colder to the teeth than ice water?

3. If water were like gold in contracting on solidification, what would happen to lakes and rivers during a cold winter?

4. Equal weights of hot water and ice are mixed, and the result is water at 0° C. What was the temperature of the hot water?

5. Which is the more effective as a cooling agent, 100 lb. of ice at 0° C. or 100 lb. of water at the same temperature? Why?

6. What temperature will result from mixing 10 g. of ice at 0° C. with 200 g. of water at 25° C.?

7. From what height must a gram of ice at 0° C. fall in order to melt itself by the heat generated in the impact?

8. If dry air were placed in a closed vessel when the barometer was 76 cm., and if a dish of water were then introduced within the closed space, what pressure would finally be attained within the vessel if the temperature were kept at 18° C.?

9. If there were moisture on the face, would fanning produce any feeling of coolness in a saturated atmosphere?

10. Would fanning produce any feeling of coolness if there were no moisture on the face?

11. Explain the formation of frost on the window panes in winter. 12. In the fall we expect frost on clear nights when the dew point is low, but not on cloudy nights when the dew point is high. Can you see any reason why a large deposit of dew should prevent the temperature of the air from falling very low?

13. Why does the distillation of a mixture of alcohol and water always result to some extent in a mixture of alcohol and water?

14. How much heat is given up by 30 g. of steam at 100° C. in condensing to water at the same temperature?

15. A vessel contains 300 g. of water at 0° C. and 130 g. of ice. If 25 g. of steam are condensed in it, what will be the resulting temperature? 16. To convert 1 g. of water at 0° C. into steam at 100° C. requires 636 calories. When the boiling point of water is 100° C., how many of these calories are used to vaporize the water? At an elevation where water boils at 90° C., how many calories are required for the vaporization? (Specific heat of steam = 0.5.)

17. Bearing in mind that the cooler the water the less the kinetic agitation of its molecules, why should you expect a larger result at 90° C. than 536 calories?

18. When the steam gauge of a locomotive records 250 lb. per square inch, the steam is at a temperature of 406° F. Explain how the steam produces this great pressure.

19. If the average pressure in the cylinder of a steam engine is 10 kilos to the square centimeter, and the area of the piston is 427 sq. cm.,

how much work is done by the piston in a stroke of length 50 cm.? How many calories did the steam lose in this operation?

20. The total efficiency of a certain 600-horse-power locomotive is 6%; 8000 calories of heat are produced by the burning of 1 g. of the best anthracite coal; how many kilos of such coal are consumed per hour by this engine? (Take 1 H.P. = 746 watts and 1 calorie per second = 4.2 watts.)

CHAPTER XI. 1. Why are the pipes that carry steam from the boiler to the radiators often covered with cellular asbestos? Why is the cellular structure an advantage?

2. Explain the cause of the sea breeze which occurs in coast regions on summer afternoons.

3. Is the draft through the fire of a kitchen range pushed through or drawn through? Explain.

4. Why should steam radiators be installed on the cold side of a room, for example, near outside walls or windows?

5. Describe all the processes involved in the transference of heat energy from the fire under the steam boiler in a cellar to the rooms containing the radiators.

CHAPTER XII. 1. If a bar magnet is floated on a piece of cork, will it tend to float toward the north? Why?

2. The dipping needle is suspended from one arm of a steel-free balance and carefully weighed. It is then magnetized. Will its apparent weight increase?

3. When a piece of soft iron is made a temporary magnet by bringing it near the N pole of a bar magnet, will the end of the iron nearest the magnet be an N or an S pole?

4. To which do isogonic lines as a rule correspond most nearly, the parallels or the meridians?

5. Lines connecting those places on the earth where the inclination of the dipping needle is the same are called isoclinic lines. Do isoclinic lines in general trend approximately N and S or E and W?

6. With what force will an N magnetic pole of strength 6 attract, at a distance of 5 cm., an S pole of strength 1? of strength 9?

CHAPTER XIII. 1. Why is repulsion between an unknown body and an electrified pith ball a surer sign that the unknown body is electrified than is attraction?

2. If you charge an electroscope and then bring your hand toward the knob (not touching it), the leaves go closer together. Why?

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