APPENDIX

ANSWERS TO NUMERICAL PROBLEMS

Page 33. 1. 9.33 m. 2. 1099.08 ft. 3. 169.164 m.; 67.056 m. 4. 14,845+ sq. m. 5. 177.8 cm. ; 83 kg. 6. 349.23 km. 7. 16,000 c.c.; 976.3 cu. in. 8. 2562.9 kg. 9. 907.2 kg. 10. 50 liters; 50 kg. 110.23 lb. 11. Elastic limit, 32,085.5+ lb. per sq. in. ; tensile strength, 73,847.7+ lb. per sq. in. 12. 9.84.

;

Pages 67-69. 1. 11.34 mi. per hour; 16.63 ft. per sec. 2. 65.906 mi. per hour; 96.66 ft. per sec. 3. As 347,976: 704,000. 4. 160.8 ft. per sec.; 402 ft.; 144.72 ft. 5. 200.8 ft. per sec.; 602 ft.; 184.72 ft. 7. 2250 ft. 8. 5 sec.; 24.505 m. per sec.; 20 m. 9. 36.18 ft. 10. 24 ft.; 12 ft. per sec. 11. 20,000 dynes. 12. 5,881,200 dynes. 13. 72.11 lb. 14. 442.8 ft. 15. 38.09 ft. per sec. 16. 6 ft. 17. 5.76 ft. from the 36-lb. force; 100 lb. 18. 18.48 lb.; 36.95 lb. 19. 11.785 mi. 20. 79.67 ft. per min.; 159.35 ft. per min. 21. 4 ft.;

2 ft. 8 in.

22. 54.18 lb.

Pages 78-79. 1. 1568 ergs. 2. 47,040 ft. lb. 3. 352 kilogrammeters. 4. 235.248. 5. 588 ft. lb. 6. 4142 ft. lb. ; 3534 ft. lb. ; 608 ft. lb. 7. 8.85 H. P.; about 6600 watts. 8. 14,000 ft. lb.; 8000 ft. lb.; 14,000 ft. lb. 9. 115,200 ft. lb.; 1.16 H. P.; 115,200 ft. lb. 10. 6,170,709 ft. lb. 11. 535,102.3 ft. lb. 12. 11.52 H.P. 13. 4.77 sec.; 153.43 ft. per sec.; 1830 ft. lb.

Page 89. 1. 7.2; 7.68. 2. 80 lb. of 10-lb. ball. 4. 3.6 in. from head. weight. 7. 300,000 ft. lb. Page 96. 1. 223.46 cm. 5. 981.82.

3. 1.5 ft.;
5. 3 ft.

1.6 ft. from center 6. 4.54 cm. from

8. 12,299 ft. lb.

2. 1.108 sec. 3. 99.305 cm.

4. 99.289 cm.

Pages 114-118. 1. 90%.

2. 86.6%. 3. 92.3% nearly. 4. 41.6 lb. 5. 7.75 ft. to right of F. acting upward; 136 lb. by lever downward and 8. 41.6 lb.

136 lb. by F. upward. 6. 17.86; 188 lb.
10. 19; 1425 lb. 11. 880 lb.

7. 13.3 lb.
12. 63 in.

9. 25 lb.
the weight.

14. 120 lb. by man nearest stone; 80 lb.

13. 21 of by other.

15. 104.72 ft. per sec.

18. 20 in.

18 m.

16.

10 in.; 18 ft.

17. 2.25; 16.49 ft.; 53.4. 640 ft. 20. 324 lb.; 20 ft. 21. 104 kg.; 23. 200 lb. if applied at middle; 100 lb. if 29.16 lb. 25. 1759.3 lb. 26.in. per 27.in. or 1 in. 28. 22,619.52 lb. ;

30. 0.11.

19. 48.83 lb.;

22. 7; 89.14 kg. at top. 24. 58.33 lb. ; sec.; 2.094 in. per sec. 0.398 in. 29. 0.62.

2. 0.04 mm.

3. 418.5 ft.

2. 3840 lb. 3. 10,584 lb.
6. 528,417 lb.; 93,333.3 lb. ;
tons; 6250 lb.
4057.9 lb.; 15.

7. 100,473+ gal.; 419.73 tons; 846.66
9. 317.729 kg. 10. 55.12 lb. 11.
13. 90,000 lb. 14. 84,375 lb. 15. 2050 lb.
17. 10 ft. from top. 18. 480 kg.; 360 kg.; 288 kg.

Page 129. 1. One half as great.

Pages 143–146. 1. 662.08 lb. 4. 125 lb.; 125 lb. 5. 8500 lb. 60,000 lb. 8. 5500 lb. 12. 12,812.5 lb. 16. 20.83 lb.

19. 8584 kg.

8. 2.35.

1580 cu. in. 2. 187.5 lb.; 3. 3.84 in. 4. 229.25 lb. or 229.2*; 6. 0.96 in. 7. 165.7 tons. 10. 1.6; 200 g. 11. 21.568 or 21.59.* 13. 113.59 lb. or 113.36 lb.* 14. 18.42 g. 15. 156.25 lb. 17. 500 g. 18. 2.35; 2.35 g. per c. c. 20. 0.772. 21. 0.916. 22. 0.001293 g. per c. c.

12.

44.68 lb. 16.42 g.

Pages 154-156. 1. 1005.4 cu. in.; 62.5 lb.; 43.75 lb.; 43.75 lb. 1.328 in. 5. 8.43 ft. 9. 8.6; 8.6. or 44.63 lb.* 16. 93.75 lb.; 19. 331.8 cu. in.

Pages 189–190. 1. 375.7 g. per sq. cm. 2. 102.6 c. c. 3. 50,803.2 lb. 4. To about its volume. 5. Nearly 5588 lb. on each side; 22,352 lb. nearly. 6. 33.87 ft. 7. 98.6 lb. 8. 3653.7 kg 9. 176,721+ lb. 10. 17,733.7 ft. lb. 11. 33.77 ft. 12. 8125.23 mm.; 10.79 mm, 13. 42,336 lb. 15. 3.4 atmospheres. 16. 0.0135 atmosphere. 17. 32.97 ft. 18. T520 19. 13.35 lb. per sq. in.

Page 202. 1. 1135.2 ft. or 1136.5 ft. 2. 3389.27 ft. or 3391.5 ft. 3. 558.88 ft, or 559.25 ft. 4. 844.05 ft. or 844.87 ft. 5. 7.5 sec. nearly. 6. 10,692 ft. or 10,701.9 ft. 7. 2824.4 ft. or 2826.25 ft. 8. 3377.7 ft. or 3379.5 ft.; 16,888 ft. per sec. or 16,897.5 ft. per sec. 9. 4.3+. 10. 12,491 ft. nearly or 12,501.5 ft.

Page 220. 1. 8.84 in. 2. 12.78 in.

5. 255. 6. 16. 8. 330+; 310 nearly.

3. 329.34 m.

4. 2.

* Differing answers possible with different methods of solution, because the weight 62.5 lb. per cu. ft. of water, and the numbers in table on p. 150, are only approximate values.

Page 236. 1. 60; 53.3; 50. 8. 44.4 cm.; 64 cm.

66.6 cm. 3. 2.34 lb. 4. 100; 88.8; 80; 75; 66.6; 12 ft.; 6 ft. 6. 2 ft. 1.6 in. 7. 1 ft. 5 in. 9. 0.212 in.; 0.847 in. or 0.848 in. 10. 8640.

5.

10. 1.77 kg.
15. 42 min. 57.6 sec.

19. 9.78° C.

Page 280. 1. 0.1045 in. 2. 0.000016. 3. 0.04176 mm. 5. 3689.2 cu. ft. 6. 457.2 c. c. 7. 146.25 c. c. 9. 57.75° C. 10. 168° C. 11. Air at 23° C. 12. 8.9 g. 14. 13.505 g.; 16.881 g.; between 19° C. and 20° C.

Pages 286-287. 1. 17,000. 2. 810.

5. 7.52 cal.

6. 17.12 cal.

7. 36.4° C. 12. 11,520. 131.63 g.

11. 12.5 min.
16.

17.

Page 416. 1. 9.5 volts. 120 alternations per sec.

3. 0.1086.

8. 88.9° C.

13. 576.
28,680 cal.

Pages 379-380. 1. 349,920 cal. 2. 594,000 cal. 4. 35,700 cal. in the copper, 216,954 cal. in the iron.

14.

4.

8.

3. 2.78 lb.

Page 299. 1. 105,000. 2. 18° F. 5. 7068.6 ft. lb.; 14,137.2 ft. lb.; 1,498,543.2 ft. lb. ; 45.4 H. P. 1. 10,000. 2. pole; 240 maxwells. 4. 2513.28 maxwells. 5. 750 gausses.

Page 317.

Pages 361-362. 1. 16.87 ohms. 2. 102.52 ohms.
5. 1.177 amp. 6. 0.5 amp. 7. 0.127 amp.

4. 1.359 amp.

9. 0.151 amp. 10. 0.958 amp.; 1.585 amp. 11. 3.625 amp.

series and 2 in parallel.

ohms.

5. -40°. 10. 9.4° C.

1.09 cu. ft.

4.097 kg. 13. 58%.

4. 9.36 cal.

9. 51.8° C. 11,066.6 cal. 18. 157.89 g.

4. 3.21°.

3. 533.3 dynes.

Pages 392-393. 1. 1.89 volts; 2.835 volts; 4.725 volts; 5.67 volts. 2. 5 ohms. 3. 6 ohms. 4. 518,400 cal. 5. in lamp, fin rheostat. 6. 220 ohms; 55 ohms; 110 ohms; 73.3 ohms; 55 ohms; 44 ohms; 44 ohms. 7. 5.614 ohms. 8. 1.44 ohms. 9. 55 watts; 1.76 kilowatt hours. 10. 19.5 ohms; 11 lamps. 2. 37.5 amp. 3. 75 amp. 4. 1,800 r. p. m.; 5. 11,000,000. 6. 12,000,000.

3. 135.26 ohms. 8. 0.195 amp. 12. 6 in

3. 233,280 cal. 5. 75.6° C.

2. 6.77 amp.

4. 5 ohms; 7.2 ohms;

Pages 432-434. 1. 11.25 ohms; 16.25 3. 2.25 in. for + carbon; 1.125 in. for- carbon. 2.2 ohms; 9 amp. 5. 17.7 ohms; 6.6 ohms. 6. 0.5 ohm; 0.6 ohm. 7. 0.4 ohm; 21,555.5 c. p. 8. 385 watts; 0.55 watt per c. p. 9. 21.14 ohms; 10.29 ohms. 10. 220 ohms; 13.6 lamps; 18.2 lamps; 3.44 watts. as great.

11. 242.29 ohms; 2.497 watts; 14.94 lamps; 1.38 times 12. 2.5 amp. ; 6 amp. by one and 3.5 amp. by the other.

13. 1.15 amp.; 400 c. p. by carbon; 500 c. p. by metallized. 14. 47,520 cal.
for carbon; 43,148 cal. for metallized. 15. 0.429 amp.; 256.4 ohms.
16. 0.947 watt; 155.3 ohms. 17. 53 lamps.
18. 8.453 amperes.
Pages 442-443. 1. 5 in.
18 sec.
5. 35 min. nearly.

8. 9.19 m.
9. 256 c. p.
bright as kerosene lamp.

Pages 456-457. 1. 19°. 6. 2 ft. 7. 3 ft.; 9 in.

Page 473. 1. 4.5 in. 1:4. 6. 60 cm.

2. 62.5 ft. 3. 1.28 sec.
4. 8 min.
6. About 1245 days. 7. 1.45 m.
10. Incandescent lamp is 2.77 times as

2. 50°.

2. 9 in. 3. 3.2 in.

TABLE OF CONVERSION FACTORS

3. 12 ft.

To

4. in.

4. 0.2 in.

5. 1.5 in.

5. 4.8 in.;

The fact that the acceleration given v2 by Fe is can be obtained from a

r

consideration of Fig. 557. Suppose a body of mass M to be moving around the circle whose center is 0, with a uniform velocity v. The space AB, over which it passes in the time t, is Svt. (Formula 2, page 37.) Let the time t be taken as a very short time-so short that the arc AB is practically equal to the chord AB. On AB as a diagonal, complete the rectangle ADBC. The distance the body

or

E

FIG. 557

is drawn away from AC toward O, by the constant centripetal force, is practically equal to

Hence

N

(For page 63)

=

=

CB= AD at2. (Formula 4.) Now, by geometry,* AB2 = AD × AE, v2t2 = at2 × 2 r. v2 v2 ar, and a = =.

r

(For page 462)

F

B

D

с

Fig. 481 shows how the direction of a ray, leaving water, may be traced into air.

When the angle of incidence NPB, Fig. 558, is the critical angle, the angle of refraction, FBC, must equal 90°. This will be true when NB multiplied by four thirds, the index of refraction, equals the radius PB or BC.

From the similar triangles NPB and FBE, NB = FE.

FIG. 558

* AE is the hypotenuse of the right-angled triangle ABE, and BD is a perpendicular dropped upon it from the vertex of the right angle.