the existence of these mysterious super X rays that can pass through six feet of solid lead is a definitely established fact.

512. Practical value of physics. Thirty years ago no one had dreamed of any practical application of present or future knowledge of electronic phenomena. Today all our broadcasting, most of our wireless, nine tenths of all long-distance wire telephony, all our transmission of pictures by wire, and a host of other useful developments have resulted directly from that knowledge. In view of what physics has done, is doing, and yet can do for the progress of the world, can anyone be insensible either to its value or to its fascination?

APPENDIX

SUPPLEMENTARY QUESTIONS AND PROBLEMS

CHAPTER I. 1. The 200-meter run at the Olympic games corresponds to the 220-yard run in our local games. Which is the longer and how much?

2. What is the weight in metric tons of a cube of lead 2 m. on an edge?

3. One kilogram of alcohol is poured into a cylindrical vessel and fills it to a depth of 8 cm. Find the cross section of the cylinder.

4. Find the length of a lead rod 1 cm. in diameter and weighing 1 kg.

5. A bottle filled with mercury weighed 700 g. The bottle empty weighed 20 g. Find the capacity of the bottle in cubic centimeters.

CHAPTER II. 1. A swimming pool has a sloping bottom 75 ft. long and 30 ft. wide. The water is 9 ft. deep at one end and 4 ft. deep at the other. Find the total force on the bottom; on the end which measures 9 ft. by 30 ft.

2. Deep-sea fish have been caught in nets at a depth of a mile. How many pounds pressure are there to the square inch at this depth? (Specific gravity of sea water 1.026.)

=

3. If the pressure at a tap on the first floor reads 80 lb. per square inch, and at a tap two floors above, 68 lb., what is the difference in feet between the levels of the two taps?

4. Forty years ago standpipes were generally straight cylinders. Today they are more commonly of the form shown in Fig. 484. What are the advantages of each form?

5. What pressure per square inch is required to force water to the top of the Woolworth Building in New York City, 780 ft. high?

6. If the vessel which is shown in Fig. 13 (1) (p. 18) has a base of 200 sq. cm. and if the water stands 100 cm. deep, what is the total force on the bottom?

7. If the weight of the empty vessel in Fig. 13 (1) is small compared with the weight of the contained water, will the force required to lift the vessel and water be greater

or less than the force exerted by the water against the bottom? Explain.

8. A hydraulic press having a piston 1 in. in diameter exerts a force of 10,000 lb. when 10 lb. are applied to this piston. What is the diameter of the large piston?

9. The specific gravity of milk is 1.032. How would its specific gravity be affected by removing part of the cream? by adding water? May these two changes be made so as not to alter its specific gravity at all?

10. A stone has a weight of 300 g. and a volume of 90 cc. What is its apparent weight

when submerged in kerosene having a specific FIG. 484. A water gravity of .79?

11. A block of wood 15 cm. by 10 cm. by

reservoir

4 cm. floats in water with 1 cm. in the air. Find the weight of the wood and its specific gravity.

CHAPTER III. 1. Explain the process of making air enter the lungs; of making lemonade rise in a straw.

2. If a circular piece of wet leather having a string attached to the middle is pressed down on a flat, smooth stone, as in Fig. 485, the latter may often be lifted by pulling on the string. Why do the stone and the leather not separate while you are lifting them?

3. Why does not the ink run out of a pneumatic inkstand like that shown in Fig. 486?

FIG. 485

FIG. 486

4. If a small quantity of air should get into the space at the top of the mercury column of a barometer, how would it affect the readings? Why?

5. If the pressure at a depth of 30 in. (2 ft.) in mercury is 1 atmosphere, at what depth in feet would you expect the pressure of water to be 1 atmosphere? 2 atmospheres? 3 atmospheres? (Specific gravity of mercury = 13.6.)

6. Calculate the number of tons of atmospheric force on the roof of an apartment house 50 ft. x 100 ft. Why does the roof not cave in?

7. If Glaisher and Coxwell rose in their balloon until the barometric height was only 18 cm., how many inhalations were they obliged to make in order to obtain the same amount of air which they could obtain at the surface in one inhalation?

8. At the earth's surface 1 cc. of air weighs .00129 g. If this were the density all the way up, to what height in kilometers would the atmosphere extend? How many miles?

9. How high will a lift pump raise water if it is located upon the side of a mountain where the barometer reading is 71 cm.?

10. If a diver's tank has a volume of 2 cu. ft. and contains air under a pressure of 40 atmospheres, to what volume will the air expand when it is released at a depth of 34 ft. under water?

11. A gas tank having a capacity of 2 cu. ft. contained acetylene at a gauge pressure of 1845 lb. per square inch. When the gauge pressure got down to 915 lb. per square inch, how many cubic feet of the gas were used?

CHAPTER IV. 1. If a vessel with a small leak is filled with hydrogen at a pressure of 2 atmospheres, the pressure falls to 1 atmosphere about four times as fast as when the same experiment is tried with air. Can you see a reason for this?

2. Find the pressure to which the diver was subjected who descended to a depth of 304 ft. Find the density of the air in his suit, the density at the surface being .00128 g. per cubic centimeter and the temperature being assumed to remain constant. Take the pressure at the surface as 30 in.

CHAPTER V. 1. A cake of ice weighing 200 lb. is held at rest upon an inclined plane 12 ft. long and 3 ft. high. By the resolution-and-proportion method find the component of its weight that tends to make the ice slide down the incline. With what force must one push to keep the ice at rest? How great is the component that tends to break the incline?

2. A boy pulls a loaded sled weighing 200 lb. up a hill which rises 1 ft. in 5 measured along the slope. Neglecting friction, how much force must he exert?

3. A man was let down over a cliff on a rope 500 ft. What was his period as a pendulum?

4. Explain why the toy in Fig. 487 will not lie upon its side, but rises to the vertical position. Does the center of gravity rise?

5. Where is the center of gravity of a hoop? of a cubical box? Is the latter more stable when empty or when full? Why?

6. Where must the center of gravity of the beam of a balance be with reference to the supporting knife-edge C? (Fig. 5, p. 6.) Why? Could you make a weighing if C and g coincided? Why?

FIG. 487

7. A body starting from rest and moving with uniformly accelerated motion acquired a velocity of 60 ft. per second in 5 sec. Find (1) the acceleration; (2) the average velocity during the 5 sec.; (3) the total distance traversed in 5 sec.

8. How long will it take a trolley car starting from rest with an acceleration of 2.5 ft./sec.2 to travel 100 ft.?

9. A ball shot straight upward near a pond was seen to strike the water in 10 sec. How high did it rise? What was its initial speed?

10. What force supports an airplane

in flight?

11. If a weight is dropped from the roof to the floor of a moving car, will it strike the point on the floor which was directly beneath its starting point?

12. If one ball is thrown horizontally from the top of a tower and another dropped at the same instant, which will strike the earth first? (Remember that

FIG. 488

the acceleration produced by a force is in the direction in which the force acts and proportional to it, whether the body is at rest or in motion. See second law.) If possible, try the experiment with an arrangement like that of Fig. 488.