Answers to Even-Numbered Problems

Transcription

1 Answers to Even-Numbered Problems Chapter Answers given in problem statement. 1.4 (a) l D 13:90 m; (b) m D 9: kg; (c) F D 98:30 kn; (d) M D 10:39 kn m. 1.6 (a) l D 25:4 m; (b) m D 53:4 kg; (c) F D 11:4 kn; (d) I mass D 2:60 N m s (a) l D 60:37 ft; (b) m D 0:2961 slug; (c) F D 476:6 lb; (d) M D 7656 in: lb: 1.10 (a) l D 60:2 in:; (b) m D 4:46 slug; (c) F D 20:1 lb; (d) M D 291 in: lb: 1.12 (a) p D 3:63 lb=in: 2 ; (b) E D 29:010 6 lb=in: 2 ; (c) I area = 5:65 in: 4 ; (d) I mass =109 in: lb s m D 0:115 kg: 1.16 g theory D 9:822 m=s 2 : 1.18 F D 2: N: 1.20 F D 0:5649 lb: 1.22 (a) D 65:7 kn=m 3, D 6: kg=m 3 ; (b) D 20:9 kn=m 3, D 2: kg=m 3 ; (c) D 0:314 kn=m 3, D 32:0 kg=m 3 ; (d) D 21:4 kn=m 3, D 2: kg=m b D 7:087 in:; h 1 D 23:62 in:; h 2 D 19:69 in:; L D 6:562 ft; W D 3239 lb :217 lb (a) D 0:621 rad; (b) D 0:0188 mrad; (c) D 266 ı ; (d) D 0:0146 ı. Chapter (a) ER D :0 ı ; (b) ER D 1: ı. 2.4 (a) ER D 88:39 118:1 ı, or if desired, this vector may be stated using a positive angle as ER D 88:39 241:9 ı ; (b) ER D 138:5 14:67 ı. 2.6 (a) ER D 243:6 34:80 ı, or if desired, this vector may be stated using a positive angle as ER D 243:6 325:2 ı ; (b) ER D 9: :3 ı. 2.8 (a) ER D 6:32 71:6 ı ; (b) ER D 7:21 56:3 ı ; (c) ER D 17:0 m 45:0 ı ; (d) ER D 45:0 ı F 2 D 1035 N, R D 267:9 N D 16:0 ı or 104 ı (a) ER D 12:14 19:23 ı, or if desired, this vector may be stated using a positive angle as ER D 12:14 340:8 ı ; (b) ER D 7:134 76:20 ı F D 1:60 kn, D 90 ı. Possible choices for F kn a 30 2 kn sin 30 a 3 kn 3 kn sin 60 1 Last modified: July 6, 2012

2 2.18 (a) ı ; (b) ı ; (c) P D 607 N; (d) D 0 ı, P D 304 N F 1 D 19:28 kn, D 0 ı F 1 D 246 N, D 60 ı (a) j EF a j D 25:9 lb, j EF b j D 96:6 lb; (b) j EF a j D 29:9 lb; j EF b j D 112 lb EF a D 164:4 50 ı, EF b D 352:5 90 ı ˇ D 90 ı, F OC 0 D 200 lb ER D. 18 O{ C 35 O / kn EF D 1:60 O kn (a) ER D. 304 O{ C 200 O / N; (b) ER D. 53:6 O{ 233 O / N; (c) P D 607 N; (d) D 0 ı, P D 304 N D 60 ı, F 1 D 246 N, EF 1 D. 213 O{ C 123 O / N (a) ER D. 15 O{ 4 O / kn, R D 15:52 kn; (b) ER D.3 O{ 28 O / kn, R D 28:16 kn; (c) s D 0:6667; (d) OR D 0:1483 O{ C 0:9889 O (a) Er AB D.4 O{ 3 O / m; (b) Er BA D. 4 O{ C 3 O / m; (c) Ou AB D 4 5 O{ 3 5 O ; (d) Ou BA D 4 5 O{ C 3 5 O ; (e) EF AB D.9:6 O{ 7:2 O / kn; (f) EF BA D. 9:6 O{ C 7:2 O / kn ER D. 93:6 O{ C 541 O / N, j ERj D 549 N, ER D :8 ı ER D. 168:9 O{ 207:0 O / N D 267:2 230:8 ı, R D 267:2 N Er AB D.3:235 O{ C 12:07 O / m, Er BC D.2:585 O{ C 1:077 O / m, Er CD D.5:734 O{ 4:015 O / m, Er DE D.2:236 O{ 1:118 O / m, Er AE D.13:79 O{ C 8:018 O / m F 2 =F 1 D 1: D 30:65 ı, ER D. 735:9 O{ C 436:1 O / lb, R D 855:4 lb D 33:7 ı, R D 6:42 kn. y Possible choices for F R O x A α 12 kn 8 kn 2.54 (a) Not safe; (b) Safe (the working load multiplier is 70%, determined using linear interpolation); (c) Safe (the working load multiplier is 96%, determined using linear interpolation). 2 Last modified: July 6, 2012

3 2.56 R x D 100 N, R y D 200 N, R t D 13:40 N, R n D 223:2 N (a) R x D 21:61 N, R y D 48:30 N; (b) R t D 8:375 N, R n D 52:25 N (a) R x D 213 N, R y D 51:7 N; (b) R t D 187 N, R n D 114 N Er AB D. 20 O{ C 48 O / mm, x B D 165 mm, y B D 48 mm Er AC D. 50 O{ C 120 O / mm, x C D 135 mm, y C D 120 mm Er OA D.95 O{ C 56 O / mm; Er OB D.68 O{ C 92 O / mm; Er OC D.17 O{ C 160 O / mm; x B D 68 mm; y B D 92 mm: 2.68 x D 36 ı ; 144 ı. q 2.70 With D x D y D, D 54:74 ı ; 125:3 ı 1, cos D 3 D 0: EF D. 59:24 O{ 162:8 O C 100 O k/ N, EQ D.114:3 O{ C 228:6 O 157:1 O k/ N, ER D.55:05 O{ C 65:81 O 57:14 O k/ N EF D. 4:59 O{ C 26:8 O C 12:6 k/ O lb, EQ D.39:8 O{ C 30:0 O 33:4 k/ O lb, EP D.50:0 O{ 70:7 O C 50:0 k/ O lb, ER D.85:2 O{ 13:9 O C 29:2 k/ O lb EP D. 1:33 O{ C 0:766 O C 1:29 O k/ kn, EQ D. 2:67 O{ C 2:67 O C 1:33 O k/ kn, EF D.2:12 O{ C 1:50 O C 1:50 O k/ kn, ER D. 1:87 O{ C 4:93 O C 4:12 O k/ kn EF D.12:5 O{ 14:5 O C 16:1 O k/ N where x D 60 ı ; y D 125 ı ; D 50 ı ; EP D.49:4 O{ C 53:0 O C 19:4 O k/ N where x D 48:8 ı ; y D 45 ı ; D 75 ı ; ER D.61:9 O{ C 38:5 O C 35:5 O k/ N where x D 40:3 ı ; y D 61:6 ı ; D 64:0 ı :16 km (a) x D cos 1.sin h cos v /, y D cos 1.cos h cos v /, D cos 1.sin v / D.90 ı v /; (b) x D 75:5 ı ; y D 64:3 ı ; D 30 ı : 2.84 h D 33:7 ı ; v D 59:0 ı Er AD D. 80:09 O{ 150:2 O 90:00 k/ O cm EF BE D. 44:4 O{ C 77:8 O 44:4 k/ O lb; EF EB D.44:4 O{ 77:8 O C 44:4 k/ O lb EF BA D.23:62 O{ 16:24 O 8:857 k/ O lb, EF BC D 1500 lb O EF BA D.16:60 O{ 24:88 O 2:262 k/ O lb, EF BC D 1500 lb O x E ; y E ; E / D.80; 60; 120/ mm, EF EG D. 47:1 O{ C 52:9 O C 70:6 k/ O N. 3 Last modified: July 6, 2012

4 2.96 EF CD D. 2:4 O{ C 1:8 O k/ kn, EF BE D 5 kn O k EF CD D. 0:8208 O{ 2:255 O C 1:800 O k/ kn, EF BE D 5 kn O k x D cos 1.sin cos /, y D cos 1.sin sin /, D (a) F B =F A D 1:51; (b) Spokes on side B are more severely loaded; (c) Essay-type answer (a) 128 ı ; (b) A k D 4:33 lb, A? D 5:50 lb; (c) EA k D.4:04 O{ C 0:578 O 1:44 O k/lb, EA? D.1:96 O{ 2:58 O C 4:44 O k/lb (a) 145:7 ı ; (b) A k D 10:73 N, A? D 7:335 N; (c) EA k D.1:431 O{ 3:578 O C 10:02 O k/ N, EA? D.2:569 O{ C 6:578 O C 1:982 O k/ N d D 5:77 cm, D 41:4 ı D 4:70 ı, ˇ D 9:43 ı, a D 12:2 in:, b D 12:0 in: F k D 67:4 N, F? D 73:9 N, The bead slides toward C Answer given in problem statement F D 1:79 kip, EF D.0:808 O{ C 0:0659 O 1:60 O k/ kip F D 5:83 N F k D.0:937/F, F? D.0:349/F: W D 45:0 N (a) F k D 44:25 N, F? D 23:28 N; (b) F k D 41:31 N, F? D 28:17 N :0 lb :5 lb: ET k D. 3:537 O{ C 1:179 O 1:769 O k/ lb, ET? D.4:648 O{ C 3:265 O 7:120 O k/ lb, The bead slides toward B F k D 1:71 N, F? D 60:0 N, The bead slides toward A :93 km=h The shortest distance is 209:5 m, The point where the road is closest lies outside of segment CD v D.1:149/s :7 mm :0 in: (a) and (b) 350 O k Nmm (a). 120 O{ 2 O 26 k/ O mm 2 ; (b).120 O{ C 2 O C 26 k/ O mm 2 ; (c) Essay-type answer; (d) Answer given in problem statement (a). 118 O{ 426 O 360 O k/ in.lb.; (b).118 O{ C 426 O C 360 O k / in.lb.; (c) The results of Parts (a) and (b) are vectors with equal magnitude but opposite direction; (d) Answer given in problem statement Essay-type answer (a) Yes; (b) EM O D O{ C O / in.lb: (a) Essay-type answer; (b) Ou D 0:192 O{ C 0:192 O C 0:962 O k; (c) 364 cm :5147 ı, The surface is not sufficiently level Ev n D. 2:92 O{ 7:87 O 6:30 O k/ km/s, Ev t D. 3:62 O{ 1:95 O C 4:11 O k/ km/s, jev n j D 10:5 km=s; jev t j D 5:82 km=s (a) Since Er 1 Er AB D 0; the vectors Er 1 and Er AB are perpendicular; (b) Or 2 D 0:8920 O{ 0:03678 O 0:4506 O k; (c) P AB D 50:55 N, P 1 D 281:3 N, P 2 D 958:3 N (a) Since Er AB Er CD D 0; the vectors Er AB and Er CD are perpendicular; (b) Or D 0:8909 O{ 0:4483 O 0:07284 k; O (c) P AB D 412:2 lb, P CD D 162:4 lb, P r D 404:6 lb. NOTE: The first printing of this book has an error in the last sentence of the statement for Part (c). The force referenced in the last sentence should be 600 lb (not 50 N). This error is corrected in the second and subsequent printings of the book :57 mm (a) and (b) 23.4 Nm. 4 Last modified: July 6, 2012

5 :8 kn P 4:6 kn (a) ER D. 2:29 O{ C 2:72 O 1:45 k/ O kn; (b) ET D.2:29 O{/ kn The distance from point A to point B is 3058 ft and the length of the power line is 2796 ft P? D. 0:970/P, P k D.0:243/ P :672 ı, The surface meets the drainage specification P k D 7:66 kn, P? D 6:43 kn, EP k D. 3:48 O{ 3:48 O 5:87 k/ O kn, EP? D.3:48 O{ C 3:48 O 4:13 k/ O kn (a) x D 125:5 ı ; (b) Or D 0:2632 O{ 0:7291 O C 0:6318 k; O (c) P r D 12:08 N (a) x D 107 ı, y D 114 ı ; (b) 0:520 O{ C 0:693 O C 0:500 k O (or 0:520 O{ 0:693 O 0:500 k). O ft Answers given in problem statement. Chapter T AB D 217:0 lb (tension), T BC D 176:9 lb (tension), T BD D 200 lb.tension/. 3.4 T AB D 92:65 N.tension/, T BC D 54:50 N.compression/, T BD D 49:05 N.tension/. 3.6 D 50 ı, T AB D 128:6 lb, T BC D 153:2 lb, T BD D 200 lb. 3.8 R C D R D D 31:8 lb (a) T 1 D 251 lb, R D 141 lb; (b) T 2 D 149 lb, R D 141 lb (a) F D 17:9 N; R A D 17:9 N; R B D 98:1 N; R D 52:2 N (b) The system is in equilibrium and blocks A and B may move with constant velocity, but they will not accelerate. (c) The system is not in equilibrium, block B will accelerate to the right, and block A will accelerate downward T AB D 5:13 kn, T AC D 0:340 kn F AB D 1580 N, F AC D 1500 N T AB D 259:1 N T AC D 2:294 lb. 5 Last modified: July 6, 2012

6 3.22 (a) T AB D 175 N; (b) T CD D T CE D 109 N; (c) Essay-type answer T ABC D 169:8 N, R D 268:8 N (a) Answer provided in problem description; (b) F D 2T cos ; (c) Essay-type answer T ACB D 2620 N; T CDE D 4530 N: 3.30 m D 547 kg Q max D 2041 lb T CD D 5710 N, T BA D 3710 N, T CB D 4290 N, W D 1140 N W max D 2:4 kn (a) System (a): T D W, system (b): T D 1 2 W, system (c): 1 2 W, system (d): 1 4 W ; (b) Essay-type answer W D 218 lb. 1 3 W, system (e): 1 3 W, system (f): 3.42 T BH D 540 lb; T HE D 540 lb; T BC D 717 lb; T EF D 586 lb; W A D 322 lb; W G D 369 lb; W D D 108 lb: 3.44 D 46:8 ı, T D 86:2 N W 1 D 11:3 N, W 2 D 32:6 N d D 45 in., T ABC D 54:17 lb D 30 ı ; intermediate answer: F BD D.5 lb/.cos 30ı Csin 30 ı / cos 30 ı cos sin 30 ı sin. 6 Last modified: July 6, 2012

7 3.52 T AC D 3460 lb, T AE D 6000 lb, T AG D 4240 lb, ı D 6:00 in: 3.54 ı A D 14:72 mm, ı B D 27:80 mm ı A D 5:2 in., ı B D 4:9 in., ı C D 4 in, ı D D 2:4 in (a) L AB D 94:3 cm; L AD D 120 cm; (b) x D 104 cm; y D 46:7 cm P D 10:39 lb, R D 5:196 lb (a) 10:0 N, 8:00 N; (b) 7:00 N, 5:00 N k D 167 lb=in., L 0 D 21:0 in: 3.66 ı D 0:587 in:, F 1 D 128 lb, F 2 D 345 lb, F 3 D 128 lb (a) P D 6000 N, T AB D 8000 N; (b) x A D 229:2 mm, y A D 71:11 mm ı D 3:42 mm (a) d D 95:49 in., F 1 D 1082 lb (compression), F 2 D 1082 lb (tension); (b) d D 86:40 in., F 1 D 3264 lb (compression), F 2 D 1736 lb (compression) ı A D 4:355 mm, ı B D 5:547 mm, F 1 D 119:2 N, F 2 D 665:6 N, F 3 D 609:7 N (a) ı D 1:17 in:; (b) ı D 1:99 in: 3.78 W D 13:33 lb D 83:62 ı (a) F D 2.2 N=mm/ F max D 0:600 N; (d) Essay-type answer. q.5 mm/ 2 C.2 mm ı/ 2 p 29mm q.5 mm/ 2 C.2 mm ı/ 2.2 mm ı/ C.0:3 N=mm/ı; (b) Answer not provided; (c) 7 Last modified: July 6, 2012

8 3.84 F max D 3:333 kn m D D 91:7 kg W D 500 N T AO D 698:5 lb, T AB D 833:3 lb, T AC D 541:7 lb, T AD D 1000 lb. r 3.92 (a) W D 3k 1 p d; (b) d D 16:9 in: r 2 Cd P D 533 lb P D 532 lb P D 1450 lb T AB D 365:8 lb, T BD D 292:3 lb, T BE D 339:8 lb, T BH D 1200 lb. 8 Last modified: July 6, 2012

9 3.102 (a) F AE D 420 lb, F AC D 120 lb, F AD D 120 lb; (b) F EB D 120 lb F AB D F AC D 780 lb, R D 800 lb W D 400 N, R 1 D 291 N, R 2 D 72:8 N, ER 1 D.28:2 O{ C 198 O C 212 O k/ N, ER 2 D. 68:3 O{ C 22:3 O 11:8 O k/ N P D 107 N, ER D.32:0 O{ C 42:6 O 107 O k/n W D 68:52 lb :5 N F ED D 280 lb, F EF D 360 lb, F FB D 210 lb, F EA D 380 lb, F F C D 210 lb, 60 lb must be added to traffic light E (a) T AB D 96:75 lb, T AC D 114:3 lb; (b) k AB D 297:4 lb=in:, k AC D 461:4 lb=in: Essay-type answer For scenario (a): T AB D 4000 lb, for scenario (b): T AD D 2611 lb T AE D 44:6 lb, T AD D 69:6 lb, T DF D 192 lb, T DG D 274 lb, T ABCD D 100 lb T AB D 2625 lb, T BC D 1250 lb, T BD D 2125 lb, T CD D 750 lb, T CE D 1000 lb D 19:1 ı, T AB D 153 N FS D 1: F D 90:1 N. 9 Last modified: July 6, 2012

10 3.132 ı 1 D 10:0 mm, ı 2 D 10:0 mm T AB D 9:33 kn, T AC D 9:33 kn, T AD D 16:0 kn, T AE D 8:00 kn T AB D 8:40 kn, T AC D 4:40 kn, T AD D 8:00 kn, T AE D 8:00 kn T AB D 275:4 lb, R y D 130:9 lb, R n D 479:8 lb P D 30 lb, T BE D 70 lb, reactions for collar B: R Bx D 60 lb, R By D 30 lb, reactions for collar E: R Ex D 60 lb, R E D 40 lb The bead slides toward B T AC D 1650 lb, T BC D 106 lb, T CD D 2330 lb, F CE D 1410 lb, F CF D 1410 lb, T BG D 600 lb, P D 106 lb (a) T AB D 5000 lb, T AC D 7071 lb, d D 5:063 in.; (b) P D 3884 lb; (c) Essay-type answer. Chapter 4 Note: Throughout Ch. 4, unless otherwise stated, answers for two-dimensional problems are reported using positive values for counterclockwise moments and negative values for clockwise moments. Answers for three-dimensional problems are reported using positive values for moments that act in the positive coordinate directions and negative values for moments that act in the negative coordinate directions. 4.2 (a) d D 6:00 in:, M B D 150 in:lb; (b) M B D 150 in:lb; (c) M B D 150 in:lb; (d) M B D 150 in:lb; (e) EM B D 150 k O in.lb. 4.4 (a) d D 14:1 mm, M B D 42:4 Nmm; (b) M B D 42:4 Nmm; (c) M B D 42:4 Nmm; (d) M B D 42:4 Nmm; (e) EM B D 42:4 k O Nmm. 4.6 M A D p 2 sin C3 cos 5 knm sin C4 cos 4.8 (a) F D 20:1 lb; (b) F D 56:1 lb; (c) k D 13:0 lb=in F D 640 lb, D 140 ı (a) M A D 30:0 knm; (b) M A D 35:0 knm; (c) M A D 38:0 knm (a) Q D 10:0 kn; (b) W D 5:00 kn, D 53:1 ı. Hint: In Part (b), the value of W you determine must not produce a moment about point A that exceeds 20 knm for any possible value of Open-end wrench: EM O D.194:2 O C120 k/ O in:lb, ratchet-wrench: EM O D. 121:4 O{ 194:2 O C 73:65 k/ O in:lb, the open-end wrench is probably more effective F D 100 N (a) and (b) EM A D.184:6 O{ C 3:077 O 129:2 O k/ knm. 10 Last modified: July 6, 2012

11 4.22 (a) EM B D.3570 O{ C 286 O 3000 O k/ in.lb; (b) EM O D.8030 O{ C 514 O 3000 O k/ in.lb (a) EM A D O{ C 7200 O / Nmm; (b) EM B D.29;600 O / Nmm (a) EM B D O{ 2880 k/ O ftlb; (b) EM A D O{ C 1920 O 2880 k/ O ftlb; (c) EM O D O{ C 7680 O 2880 k/ O ftlb F D 1:75 kn (a) F D 240 N, (b) EM O D 288 O{ Nm; (c) Essay-type answer Points A and B lie on a line that is parallel to the line of action of the force (a) M AB D 1900 N mm, EF D. 3:85 O{ C 9:23 k/ O N, EF D.3:85 O{ 9:23 k/ O N is also acceptable; (b) M AB D 472 Nmm; (c) M AB D F D 92:6 lb F D 115 N. Twisting occurs at both fittings on pipe OA M Strength AB D 8 in.lb, M Strength BC D 4:992 in.lb (a) EM A D.2:29 O{ C 10:3 O C 2:29 k/ O Nmm, M AB D 8:00 Nmm; (b) EM B D.12:0 O{ 6:00 k/ O Nmm, M AB D 8:00 Nmm; (c) Essay-type answer M a D 19,850 Ncm: 4.46 M AB D 817:5 Ncm M BCD D 263:8 in.lb. NOTE: The first printing of this book has an error in the figure for this problem. The y coordinate of point D should be 25 in:, hence its location is D.10; 25; 28/ in. This error is corrected in the second and subsequent printings of the book M OB D 12:5 Nm (a) EM A D.9830 O{ C 1940 O C 7770 O k/ Nmm, M a D Nmm; (b) EM O D O{ Nmm, M a D Nmm EF D.13:4 O C 6:71 O k/ lb, M GH D 537 in.lb EQ D.6 O{ C 6 O C 3 O k/ lb, M BC D 290 in.lb M a D 17;400 ftlb, D 90 ı. 11 Last modified: July 6, 2012

12 4.60 M OBA D cos sin.1:8 knm/ P max D 1546 N M D 144 in.lb: 4.66 (a) Q D 120 N; (b) The answer does not change F B D 80 lb, ˇ D 70 ı, M D 3363 in.lb (a) M D 96:6 Nmm; (b) M D 96:6 Nmm (a) F A D 200 N, D 22:62 ı, M D 2400 Ncm; (b) F 1 D F 2 D 123:8 N; (c) Q 1 D Q 2 D 133:3 N; (d) M A D 2400 Ncm F B D 18:93 lb EM D.200 O{ 600 O k/ Nm: 4.78 d D 1:92 m (a) EM D. 800 O{ 200 O / Nm; (b) Essay-type answer The forces F are resolved into horizontal and vertical components as shown. The two vertical forces F cos 30 ı constitute one couple. The two horizontal forces F sin 30 ı and the horizontal force F constitute another couple Force systems (a) and (c) are equivalent Force systems (a) and (d) are equivalent, and force systems (b) and (c) are equivalent For force system (b), F D 2 kip and P D 4 kip; for force system (c), there are no values for F and P such that force systems (a) and (c) will be equivalent; for force system (d), F D 5 kip and P D 1 kip F Rx D 1490 lb, F Ry D 102 lb, M R 5110 in.lb. The original force system and the force system at point O are shown below EF R D.144:5 O{ C 2091 O C 17,000 O k/ lb, EM RO D. 31,650 O{ C 2402 O 795:2 O k/ ftlb F Rx D 0:500 kn, F Ry D 3:87 kn, 2:58 m to the right of the bearing at C. 12 Last modified: July 6, 2012

13 4.96 F Rx D 49:24 lb, F Ry D 41:32 lb, x D 9:342 in (a) EF R D O k/ N, EM RO D.6:94 O{ 12:0 O / Nm; (b) EF R D O k/ N,.x; y/ D. 3:86 mm; 6:67 mm/: (a) EF R D. 5:00 O{ C50:0 O 10:0 O k/ nn, EM RB D.120 O{ 60:0 O k/ nnm; (b) EF R D. 5:00 O{ C50:0 O 10:0 O k/ nn, EM RO D.220 O{ C 800 O C 3890 O k/ nnm (a) EF R D.10:0 O / kn, EM RA D.25:0 O{ C 4:00 O C 20:0 O k/ kn m; (b) F Rx D 0, F Ry D 10:0 kn, F R D 0, M RAx D 25:0 knm, M RAy D 4:00 knm, M RA D 20:0 knm EF R D 2F O k, EM R D 3P r O k,.x; y/ D.0; r/ EF R D.2:00 O{ C 3:00 O 4:00 O k/ N, EM RA D.9:00 O{ C 8:00 O 4:00 O k/ Nm EF R D F. O C k/, O EM R D F a 1 2. O C k/, O.x; y/ D. 2 1 a; b/ EM R D.150 O{ C 104 O 200 O k/ Nm: F D 444:4 N (a) M a D 256 Nm; (b) Ou D 0:530 O{ C 0:662 O C 0:530 O k F D 300 lb M a D 311:0 in.lb M D 9638 Nmm P D 10 lb, Q D 5 lb, R D 0, S D 20 lb, M D D 10 in:lb (a) F Rx D 0:880 lb, F Ry D 0:660 lb, M O D 0:552 in. lb; (b) F Rx D 0:880 lb, F Ry D 0:660 lb, y D 0:627 in: (a) F Rx D 0, F Ry D 1800 lb, F R D 0, M Ax D 8700 ftlb, M Ay D 0, M A D 26;700 ftlb; (b) F Rx D 0, F Ry D 1800 lb, F R D 0, x D 12:2 ft, D 7:83 ft EF R D. 30:0 O{ 120 O 22:5 O k/ lb, EM RO D. 990 O{ C 60:0 O C 1180 O k/ in.lb. Chapter 5 Note: Throughout Ch. 5, unless otherwise stated, the following conventions apply. Answers for two-dimensional problems are referred to an xy coordinate system where x is horizontal with positive to the right, and y is vertical with positive upward. Answers are reported so that positive forces act in positive coordinate directions, and positive moments are counterclockwise. For three-dimensional problems, moments are reported using positive values for moments that act in the positive coordinate directions. 5.2 A D 23:5 N, B D 107 N. 13 Last modified: July 6, 2012

14 5.4 F D 120 lb, B D 213 lb, A D 53:5 lb, essay-type answer. 5.6 T DE D 258:1 lb, N D 377:6 lb, T BC D 77:30 lb. 5.8 B D 42:9 N (force supported by one link), A x D 68:6 N, A y D 31:4 N If 0 ˇ < 51:32 ı, the spool will roll to the left, and if 51:32 ı < ˇ 180 ı, the spool will roll to the right d D 3:10 ft (a) A y D 3 2 F C 1 3 P, A x D 0, D y D 3 1 F C 2 3 P ; (b) A x D 0:192F C 0:385P, A y D 3 2 F C 1 3 P, D D 0:385F C0:770P ; (c) A y D F CP, D x D 0, M D D 1 3 L.F C2P /; (d) A x D 0, A y D F CP, M A D 3 1 L.F C2P / A y D 1:88 kn, E y D 2:12 kn, E x D 2:00 kn A x D 0, A y D 3:00 kip, P y D 1:00 kip C y D 11;300 lb, D y D 6170 lb A x D 0, B y D P, M A D P a C y D 1516 lb, A x D 845:2 lb, A y D 582:5 lb (a) T D 75 lb, B x D 112:4 lb, B y D 49:41 lb; (b) F CD D 134:2 lb, B x D 12:44 lb, B y D 139:4 lb C n D 11;940 N, B x D 10;880 N, B y D 6856 N (a) P D 50 N; (b) Rollers B and C make contact, A y D 0, B y D 10 N, C y D 100 N, D y D Rollers B and C make contact, A y D 0, B y D 40:8 lb, C y D 231 lb, D y D Rollers A and C make contact, A y D 193 lb, B y D 0, C y D 198 lb, D y D (a) A D 498 lb; (b) Essay-type answer (a) > 75:5 ı ; (b) > 90:0 ı 5.40 Essay-type answer F x D 9:08 lb, F y D 6:91 lb, E y D 19:1 lb T t D 759:7 N, B x D 777:3 N, B y D 389:1 N G D 4:66 N, N D 17:4 N, D 17:0 ı A x D 0, A y D 200 lb, T D 600 lb A x D 21:92 lb, A y D 54:22 lb, T D 28:61 lb F BE D 4:472 kn, C x D 2 kn, C y D 1 kn. NOTE: The first printing of this book has an error in the figure for this problem; the location of point E was not given. Point E is located 0:4 m from the vertical line passing through point C. This error is corrected in the second and subsequent printings of the book (a) A x D 2:59 kn, A y D 35:2 kn, B y D 54:8 kn; (b) A x D 7:59 kn, A y D 41:2 kn, B y D 59:5 kn F BE D 143:5 lb, A x D 64:62 lb, A y D 89:42 lb T D 1:66 kip (tension in cable BCD), A x D 1:66 kip, A y D 0:55 kip T DE D 2:76 kip, F DF D 2:36 kip. 14 Last modified: July 6, 2012

15 5.60 (a) Complete fixity, statically determinate; (b) T D 10:68F ; Additional results: C x D 2:000F, C y D 11:32F (a) Partial fixity, statically indeterminate; (b) The cable tension cannot be determined; Additional result: The equations of static equilibrium require F D 0. If F 0, then the equations of static equilibrium cannot be satisfied, and dynamic motion occurs F D 13:6 lb Q D 191:5 N, C x D 63:40 N, C y D 170:6 N F s D 200 lb, P D 81:84 lb, A x D 127:4 lb, A y D 77:75 lb The pretwist of the torsional spring is turns, P D 11 lb (a) D 4:58 ı ; (b) D 36:7 ı ; (c) Essay-type answer Essay-type answer 5.76 A x D 0, A y D F h 1 kl 2 i F kl 2 2.k t C kl 2, C / y D 2.k t C kl 2 /, M A D FL 2 h 1 kl 2 i k t C kl For structure (a), full fixity and statically determinate; for structure (b), full fixity and statically indeterminate; for structure (c), full fixity and statically determinate; for structure (d), partial fixity and statically determinate; for structure (e), full fixity and statically determinate; for structure (f), partial fixity and statically indeterminate D D 0:314 N, L D 1:34 N ı D 2:40 mm, D 1:49 ı (a) T EA D 1:33 kip, B x D 0, B y D 3:33 kip; (b) T EA D 12:3 kip, B x D 0, B y D 20:3 kip; (c) T EA D 15:9 kip, B x D 0, B y D 25:7 kip ABC is a 3-force member and BD is a 2-force member ABDE is a multiforce member and BC is a 2-force member force member force member ABCD is a multiforce member and DE is a 2-force member Multiforce member force member F AB D 318 kn to begin opening the dump when D 0 ı ; F AB D 0 when the center of gravity G of the dump and its contents is immediately above point O. 15 Last modified: July 6, 2012

16 5.102 C x D 0:333 kn, C y D 0:667 kn, T AD D 1:25 kn, M Cx D 0, M Cy D 2:00 knm, M C D 3:33 knm A x D 0, A y D 0, A D 10 lb, M Ax D 120 in.lb, M A D 0, F D 20 lb (a) Partial fixity and statically determinate; (b) T D 27 lb, A x D 18:0 lb, A D 9:00 lb, M Ax D 54:0 in.lb, M A D T AD D 50:75 kn (b) 2, 0, 4, 1, 3; (a) A x D 0, A y D 0, A D 2F, M Ax D 2F r, M Ay D 0, M A D 2P r B x D 0:01 lb, B y D 0: lb, B D 0:1150 lb, M Bx D 0:08571 in.lb, E y D 0: lb, E D 0:0850 lb F D 3:21 kn, C x D 3:00 kn, C y D 0:429 kn, C D 2:07 kn, M Cx D 0:343 knm, M C D 0:600 knm. 16 Last modified: July 6, 2012

17 5.118 A D 5:77 kn, C D x 2:89 kn, D y D 5:00 kn, D D 0, M Dy D 0, M D D 9:23 knm Statically determinate, Q D 833:3 lb, A x D 1667 lb, A y D 0, A D 4313 lb, C x D 2500 lb, C D 162:5 lb (a) Statically indeterminate; (b) T CF D 2289 N (a) A x D 38 kn, A y D 50 kn, M A D 1281 knm; (b) T BF D 153:8 kn; (c) T BF D 93:76 kn Essay-type answer; partial answer: the propellers rotate counterclockwise T D 163 N, A D 83:2 N, B D 163 N A x D 7:00 N, A y D 26:1 N, M A D 276 Ncm T D 16:74 lb, T JK D 14 lb k t D 1:034 in:lb=rad, 0 D 3:142 rad (a) F D 3:29 N; (b) F D 11:5 N; (c) F D 20:1 N (a) Statically indeterminate; (b) F AE D 833:3 lb (compression), T C G D 1167 lb (tension), B x D 1732 lb, B y D 666:7 lb For structure (a), full fixity and statically determinate; for structure (b), partial fixity and statically indeterminate; for structure (c), full fixity and statically indeterminate; for structure (d), partial fixity and statically determinate; for structure (e), partial fixity and statically determinate; for structure (f), full fixity and statically indeterminate. 17 Last modified: July 6, 2012

18 5.142 (a) Essay-type answer; (b) T 1 D 15:7 lb, T 2 D 21:5 lb, O x D 13:3 lb, O y D 11:5 lb, O D 19:4 lb P D 444:4 lb, A x D 307:2 lb, A y D 204:5 lb, A D 355:6 lb, B x D 209:5 lb, B y D 54:50 lb (a) Full fixity and statically determinate; (b) A y D 0, A D 60:0 lb, B x D 40:0 lb, B D 40:0 lb, M Ay D 200 in.lb, M A D 80:0 in.lb d Object 1 could never be in equilibrium; Object 2 could be in equilibrium c Object 1 could be in equilibrium; Object 2 could never be in equilibrium. Chapter T AB D 500 lb, T AC D 0, T BC D 625 lb, T BD D 375 lb, T CD D 625 lb, T CE D 0, T DE D 500 lb. 6.4 P D 3200 lb. 6.6 P D 8000 lb. 6.8 T CE D 3:75 kn, T DF D 3:66 kn T AB D 4:00 kn, T AC D 0, T BC D 7:21 kn, T BD D 6:00 kn, T CD D 5:00 kn, T CE D 6:00 kn, T DE D 7:21 kn P D 10:0 kn P D 6:66 kn :92: :77: 6.20 T AB D F, T AE D p 2F, T CD D 0, T CE D 0, T DB D p 2F, T DE D F, T EB D F T AB D 3333 lb, T AC D 2667 lb, T BC D 4667 lb, T BE D 3771 lb, T CE D 2667 lb T AB D 5:66 kn, T AD D 4:00 kn, T BC D 7:07 kn, T BD D 2:24 kn, T BE D 3:00 kn, T BF D 4:47 kn, T CF D 5:00 kn, T DE D 3:00 kn, T EF D 3:00 kn. 18 Last modified: July 6, 2012

19 6.26 BD, CD, GH AB, CD, EF BD, CD, EF (a) F G, DG; (b) T F G D 0, T DG D 0, T AC D 12:0 kn, T AB D 10:4 kn, T CB D 4:00 kn, T BD D 10:4 kn, T GH D 8:00 kn, T FH D 6:93 kn, T EG D 8:00 kn, T CE D 8:00 kn, T DE D 8:00 kn, T CD D 4:00 kn, T DF D 6:93 kn T AB D 3 kip, T AC D 6:25 kip, T AD D 3:75 kip, T BD D 4 kip, T CD D 5 kip, T CE D 15 kip, T CF D 6:25 kip, T DF D 6:75 kip (a) BG, DI, EJ, DE, CD, CH ; (b) T BG D 0, T CH D 0, T AB D 3:00 kip, T AF D 5:20 kip, T BC D 3:00 kip, T CF D 7:21 kip, T F G D 6:00 kip, T C G D 5:00 kip, T GH D 3:00 kip; (c) T DI D 0, T EJ D 0, T DE D 0, T CD D 0, T CJ D 14:4 kip, T IJ D 9:00 kip, T CI D 10:0 kip, T HI D 3:00 kip T AB D 0, T AD D 20 lb, T BC D 0, T BD D 29:15 lb, T BF D 29:15 lb, T CF D 30 lb, T DE D 15 lb, T DG D 65 lb, T EF D 15 lb, T EG D 29:15 lb, T EH D 29:15 lb, T FH D 85 lb, T GH D 15 lb T BD D 0:577P, T CD D 0:577P, T CE D 0:289P T CE D 5:667 kn, T DE D 4:807 kn, T DF D 9:000 kn F CD D 485:3 lb, F CI D 159:1 lb, F IJ D 970:6 lb (a) DE, HI, JK, LM, NO; (b) eliminate DE, HI, LM, essay-type answer; (c) T GH D 5 8 Q (a) HI, JK, LM ; (b) eliminate JK, essay-type answer; (c) T F G D 2:00 kn (a) Statically determinate; (b) T CD D 8:00 kip, T DE D 0, T AD D 10:4 kip, T BD D 10:4 kip T CE D 18,667 lb, T DE D 5833 lb, T EF D 3000 lb, T EG D 14,000 lb T GI D 10;000 lb, T HI D 4167 lb, T IJ D 0, T IK D 4000 lb, T IL D 3333 lb (a) T J T D 40:2 kn; (b) T HJ D 30:0 kn, T IJ D 14:1 kn, T JK D 0, T JM D 0:563 kn, T JL D 0:796 kn (a) Statically indeterminate; (b) mechanism; (c) statically indeterminate; (d) statically determinate T HJ D 12 kip, T HK D 0, T IK D 0, T IL D 12 kip (a) For truss (a): T AB D 1:41W, T BD D W, T DF D 1:41W, T AC D W, T CE D W, T EF D W, T BC D W, T CD D 0, T DE D W ; for truss (b): T AB D 1:12W, T BD D 0:500W, T DF D 1:12W, T AC D 0:500W, T CE D 0:500W, T EF D 0:500W, T BC D W, T CD D 0, T DE D W ; (b) Essay-type answer; (c) Essay-type answer; (d) Essay-type answer P crit D k t =L (a) Partial fixity; (b) statically determinate; (c) T AB D 0, T AC D 0, T AD D 4:00 kn, T BC D 0:417 kn, T BD D 2:13 kn, T BE D 0:838 kn, T CD D 2:13 kn, T CE D 0:838 kn, T DE D 1:33 kn T AC D 76:04 N, T BC D 0, T CD D 0, T CF D 77:71 N, T C G D 0, T CH D 72:5 N Statically determinate T MJ D 10:0 kn T J G D 15:0 kn Last modified: July 6, 2012

20 6.78 A x D 430:8 N, A y D 1984 N, T DH D 1259 N, T BE D 2333 N, C x D 1400 lb, C y D 1067 N Essay-type answer Horizontal force applied by the operator is Q D 20:8 lb to the right, T AE D 6:67 lb; for the following results, absolute values are reported: B x D 5:77 lb, B y D 6:67 lb, C x D 26:6 lb, C y D 6:67 lb Horizontal force applied by the operator is Q D 47:7 N to the right, F BE D 64:0 N; for the following results, absolute values are reported: A x D 55:7 N, A y D 10:7 N, C x D 103 N, C y D 10:7 N N when h D 0:9 m D y D 440:7 lb, T BE D 1740 lb D y D 640:5 lb, T BE D 1131 lb T BG D 200 lb, T CG D 240 lb, T DG D 200 lb (b) F AD D 3390 lb; (a) 6.96 (b) T 1 D 283 N, T 2 D 283 N; (c) A 1x D 260 N, A 1y D 225 N, A 2x D 260 N, A 2y D 225 N; (a) 6.98 The chair is safe from collapsing. Intermediate answer: H y D 21:33 N (compression). NOTE: In the first printing of this book, the hint should refer to the reaction at point H (not point G). This error is corrected in the second and subsequent printings of the book. 20 Last modified: July 6, 2012

21 6.100 (b) F CF D 27;200 lb; (a) P D 27:30 lb F FH D 22:5 N, F BF D 70:8 N (a) The structure is not a truss, essay-type answer; (b) C y D 5 kn, A x D 0, A y D 4 kn, T DG D 2:00 kn, T BE D 3:00 kn, T FH D 4:00 kn, T AD D 3:00 kn, T DE D 3:00 kn, T EF D 3:00 kn, T CF D 3:00 kn, B x D 3:00 kn, B y D 1:00 kn (a) Statically indeterminate; (b) HQ and IQ, (c) F DG D p 2 kn T BP D 813 lb, T BO D 813 lb, T CD D 100 lb T BG D 36:46 lb, T CF D 1620 lb (a) The structure is not a truss; (b) Statically indeterminate; (c) E x D 0, E y D 1:25 kn, H y D 1:75 kn, T BF D 0, T CH D 1:094 kn, T DH D 1:094 kn T AD D 163 lb, T AB D 115 lb, T BE D 163 lb, T BD D 115 lb, T GI D 0, T HI D 85:0 lb, T EH D 184 lb, T DG D 184 lb, T EG D 35:0 lb. 21 Last modified: July 6, 2012

22 6.118 (b) F AE D 525 lb; (a) Chapter Nx; Ny/ D.0; 65:0/ mm Nx; Ny/ D.1:18; 1:18/ in Nx; Ny/ D.60:8; 30:0/ mm Nx; Ny; Ń/ D.2:31; 2:12; 1:42/ in Nx; Ny/ D ; 9 20 / in Nx; Ny/ D. 6 5 ; 3 2 / m Nx; Ny/ D ; Nx; Ny/ D.5:602; 5:167/ in Nx; Ny/ D.48:0; 16:0/ in y 1 D 2x, y 2 D 92 C 4x,. Nx; Ny/ D.16:44; 13:16/ cm Nx; Ny/ D.3:429; 1:429/ m Answer given in problem statement c 1 D b= p a, c 2 D b=a 3,. Nx; Ny/ D a; 3 7 b/ L D R 12 cm 3 cm 1 3 p 10 dx D 9:487 cm, Nx D R 12 cm 3 cm x 1 3 p 10 dx 9:487 cm D 7:5 cm, Ny D R 12 cm 3 cm.2c x 3 / 1 3 p 10 dx 9:487 cm D 4:5 cm. R 1 in: 0 x p 1C9x 7.30 (a) Nx D 4 R 1 in: dx R 1 in: p ; Ny D 0 x 3p R r1c r 1 1C9x 4 in: 2 dx 0 1C9x 4 R 1 in: p ; (b) Nx D 0 y1=3 13 y 2=3 R dy 1 in: 2 0 y 1C 13 y 2=3 dy r dx 0 1C9x 4 dx R 1 in: 2 ; Ny D r 0 1C 13 y 2=3 R 1 in: 2 ; dy 0 1C 13 y 2=3 dy (c). Nx; Ny/ D.0:609; 0:366/ in. s s R 2 r r x R x 1C p r p 2 dx r 7.32 (a) Nx D 2 x s 2 r r 2 x 2 1C p x dx r 2 ; Ny D 2 x s 2 2 ; (b). Nx; Ny/ D.0; 2 r/. x x 1C dx 1C dx R r r p r 2 x V D 60:32 in. 3,. Nx; Ny; Ń/ D.1:389; 0; 0/ in Nx D R d A D 4938 m, d B D 3: km. R r r p r 2 x The center of gravity is located on the horizontal member of the antenna, at a distance of 133 in: from the left-hand end. 22 Last modified: July 6, 2012

23 7.42. Nx; Ny; Ń/ D.2:98; 0; 0/ in Ń D 2:675 cm m c D 680 g Nx; Ny; Ń/ D.1:07; 0; 0:876/ in The center of mass is located 1:46 m to the right of point A and 1 m above point A, T D 639 N; B x D 553 N; B y D 118 N Nx D 1:447 in., m D in (a) Nx D R r=2 0 x 0 2.r 2 x 2 /dxc R r r=2 x 0.r2 x 2 /dx R r= r 2 x 2 /dxc R r r=2 0.r2 x 2 /dx, Ny D 0; Ń D 0; (b) Nx D r R a 2dx 0 (a) Nx D 0 h2 1 x2 a 2 R a 2dx, Ny D 0; Ń D 0; (b) h2 x a R L 0 x 0 R 2. L x / 2=3 2 R x 2 L dx (a) Nx D R L 0 0 R 2. L x / 2=3 2, Ny D 0; Ń D 0; (b) Nx D R x L dx 7.60 (a) Ny D R 1 cm V D 283 mm 3, A D 226 mm CxCx 2 / 0 2xŒ1Cx 2 x dx R 1 cm ; (b) Nx D xŒ1Cx 2 x dx 10 cm V D 1: mm 3, A D 1: mm V D 8h 3, A D h 2.11 C 8 p 2/ V D 19:8 in. 3, W D 0:118 lb (a) V D 4: mm 3 ; (b) A outside D 34:610 3 mm 2 ; (c) A inside D 12:210 3 mm V D 7 12 R3, A D 4.11 C p 5/R (a) w D 2:78 lb=in. for 0 x 36 in:; (b) w D 1:85 lb=in. for 0 x 18 in:, w D 3:70 lb=in. for 18 in: x 36 in:; (c) w D 1:85 lb=in. C.0:0514 lb=in. 2 /x for 0 x 36 in:, (d) w D 1:85 lb=in. C.0:103 lb=in. 2 /x for 0 x 18 in:, w D 5:56 lb=in..0:103 lb=in. 2 /x for 18 in: x 36 in: 7.76 A x D 0, A y D 33:3 lb, B y D 66:7 lb A x D 0, A y D 49:1 kn, M A D 98:1 knm (a) Nx D 21:0 in:; (b) & (c) A x D 0, A y D 22:2 lb, B y D 77:8 lb (a) Nx D 1:67 m; (b) & (c) A x D 0, A y D 49:1 kn, M A D 81:8 knm (a) a D 35 8 in. lb, b D lb ; (b) w.x D 0/ D 4:375 lb=in:, w.x D 4 in:/ D 0:625 lb=in:; (c) Essay-type answer; (d) in. A D 17:96 lb, B D 17:04 lb (a) a D 800 N=m, b D 0, c D 8:00 N=m 3 ; (b) d D 800 N=m, f D 20 m A x D 0, A y D 4:00 kn, B y D 16:0 kn. 23 Last modified: July 6, 2012

24 7.90 A x D 0, A y D 40:0 kip, B y D 40:0 kip A x D 0, A y D 6:08 kip, B y D 4:92 kip C x D 0, C y D 12:0 kn, M C D 24:0 knm A x D 0, A y D 80 kip, C y D 80 kip A x D 0, A y D w 1 a C w 2.L a/, M A D 1 2 w 1 a2 C 1 2 w 2.L2 a 2 / a D 0:524 kn=m, b D 1:21 kn=m 2, c D 0:0556 kn=m 3, F D 23:0 kn, Nx D 4:05 m k t D 87:71 knm=degree A x D 0, A y D 0, A D W, M Ax D WR T D d T D 39:0 lb D 0:235 rad D 13:5 ı. 2 /, M Ay D 2 WR, M A D T BC D 13,333 lb, T DF D 12,000 lb (a) T D 40:7 lb; (b) T D 323 lb T B D 414 N, T C D 414 N, T D D 684 N F EG D 381 lb Nx; Ny/ D.4:487; 8:153/ cm Nx; Ny/ D.0; 20:2/ mm Nx; Ny/ D ; 1/ m Nx; Ny; Ń/ D.34:7; 0; 0/ mm (a) Let o D 0:002 g=mm 3, i D 0:003 g=mm 3, Nx D Ń D 0; (b). Nx; Ny; Ń/ D.3:20; 0; 0/ mm Nx D 3 4 m. R 1 cm 0 x.1cx (a) Nx D 2 / 2 dx R, Ny D Ń D 0; (b) Nx D 5 1 cm 0.1Cx 2 / 2 dx 8 cm (a) Nx D R 2 km 1 km xp 1C4x 2 R 2 km 1 km R 2 km p, Ny D 1 km x2p 1C4x p 2 ; (b). Nx; Ny/ D.0:801; 1:48/ km. 1C4x 2 1C4x 2 R 2 km 1 km R 6 mm 0 xf i x/2 C o Œ.3C 1 6 x/ x/2 g dx R 6 mm 0 f i x/2 C o Œ.3C 6 1 x/ x/2 g dx Nx; Ny/ D.42:00; 11:03/ in., A x D 508:6 lb, A y D 0, B x D 508:6 lb, B y D 218:0 lb V D 4 3 r3, A D 4r V D 3180 cm 3, A D 867 cm A x D 0, A y D 1700 lb, B y D 1300 lb B y D 640 lb, C x D 0, C y D 1460 lb where pin C is located 6 ft from the left-hand end of the beam A x D 0, A y D 2:17 kn, C y D 3:83 kn where roller C is located 2 m from the right-hand end of the beam A x D 46:8 lb, A y D 281 lb, C x D 187 lb., Ny D 0, d D 12:5 mm. 24 Last modified: July 6, 2012

25 Chapter N H D 34:7 lb, V H D 197 lb, M H D 1180 in.lb, N J D 480 lb, V J D 0, M J D N E D 200 lb, V E D 346 lb, M E D 0, N F D 200 lb, V F D 346 lb, M F D 8310 in.lb 8.6 N F D 3:20 kn, V F D 4:27 kn, M F D 0, N G D 3:20 kn, V G D 4:27 kn, M G D 10:7 knm, N H D 0:800 kn, V H D 1:07 kn, M H D 10:7 knm, N I D 0:800 kn, V I D 1:07 kn, M I D 13:3 knm. 8.8 N F D 11:2 kn, V F D 1:60 kn, M F D 0, N G D 11:2 kn, V G D 1:60 kn, M G D 4:00 knm, N H D 8:80 kn, V H D 1:60 kn, M H D 4:00 knm, N I D 8:80 kn, V I D 1:60 kn, M I D N D D 0, V D D 100 lb, M D D 0, N E D 0, V E D 100 lb, M E D 150 in.lb, N F D 70:7 lb, V F D 70:7 lb, M F D 238 in.lb N H D 2:00 kn, V H D 2:00 kn, M H D 0, N I D 2:00 kn, V I D 2:00 kn, M I D 5:60 knm: 8.14 N L D 2:00 kn, V L D 2:00 kn, M L D 3:20 knm, N O D 2:00 kn, V O D 2:00 kn, M O D N R D 5:83 kn, V R D 0 kn, M R D 0, N A D 4:00 kn, V A D 0, M A D 4:20 knm N H D 400 lb, V H D 693 lb, M H D 1390 ftlb, N I D 400 lb, V I D 693 lb, M I D N L D 400 lb, V L D 693 lb, M L D 1390 ftlb, N M D 0, V M D 800 lb, M M D Essay-type answer V Ax D 0, V Ay D 150 lb, N A D 0, M Ax D 2400 in.lb, M Ay D 0, M A D 3600 in.lb N Bx D 0, V By D 0, V B D 120 N, M Bx D 8:40 Nm, M By D 12:6 Nm, M B D V Dx D 0, N Dy D 0, V D D 120 N, M Dx D 13:8 Nm, M Dy D 14:4 Nm, M D D V D 2:50 kn, M D.2:50 kn/x for 0 x 3 m; V D 7:50 kn, M D.7:50 kn/.4 m x/ for 3 m x 4 m (a) V D P, M D P x for 0 x 1 3 L; V D 0, M D 3 1 PL for 1 3 L x 2 3 L; V D P, M D P.L x/ for 2 3 L x L; (b) Essay-type answer V D 125 lb, M D.125 lb/ x for 0 x 8 ft; V D 125 lb, M D. 125 lb/.16 ft x/ for 8 ft x 16 ft V D 1000 lb, M D lb/.20 ft x/ V D. 8 kn=m/ x, M D. 4 kn=m/ x Last modified: July 6, 2012

26 8.40 V D 1200 N.600 N=m/ x C.50 N=m 2 / x 2, M D.1200 N/ x.300 N=m/ x 2 C.16:7 N=m 2 / x Essay-type answer w 0 D 550:5 lb=ft V D 3:00 N, M D 8:00 N mm C.3:00 N/ x for 0 x 2 mm; V D 1:00 N, M D.1:00 N/ x for 2 mm x 4 mm; V D 2:00 N, M D 12 Nmm C.2:00 N/ x for 4 mm x 6 mm V D 3:00 N, M D 8:00 Nmm C.3:00 N/ x for 0 x 2 mm; V D 0, M D 0 for 2 mm x 6 mm: 8.50 Essay-type answer V D 100 lb=ft.6 ft x/ C 1000 lb, M D 50 lb=ftœ.12 ft/x x 2 C.1000 lb/ x for 0 x 6 ft; V D 100 lb=ft.6 ft x/ 1000 lb, M D 50 lb=ftœ.12 ft/x x 2 C.1000 lb/.12 ft x/ for 6 ft x 12 ft V D 1000 N, M D.1000 N/ x for 0 x 1 m; V D 100 N, M D.100 N/.9 m C x/ for 1 m x 2 m; V D 1100 N, M D.1100 N/.3 m x/ for 2 m x 3 m. 26 Last modified: July 6, 2012

27 8.56 V D.0:202 kip=in./ x, M D.0:101 kip=in./x 2 for 0 x 20 in:; V D 10:0 kip C.0:202 kip=in./ x, M D 200 kip in..10:0 kip/ x C.0:101 kip=in./x 2 for 20 in: x 79 in:; V D. 0:202 kip=in./.99:0 in: x/, M D.0:101 kip=in./.99:0 in: x/ 2 for 79 in: x 99 in: 8.58 V D. 8 kn=m/ x, M D. 4 kn=m/ x V D 36 kn.8 kn=m/ x C. 1 3 kn=m2 / x 2, M D 96 knm C.36 kn/ x.4 kn=m/ x 2 C. 1 9 kn=m2 / x V D 4000 lb.15 lb=ft/œ.40 ft/x x 2, M D.4000 lb/ x.5 lb=ft 2 /Œ.60 ft/x 2 x 3, M max D 15;400 ftlb at x D 8:45 ft V D 1 6 w 0 L w 0.x 1 L x2 /, M D w 0. L 6 x 1 2 x 2 C 1 3L x3 /, M max D.0:0160/w 0 L 2 at x D.0:211/L and M max D. 0:0160/w 0 L 2 at x D.0:789/L V D 2P, M D 3 2 PL C 2P x for 0 x L 2 ; V D P, M D 2 1 PL C P.x 1 2 L/ for L 2 x L. 27 Last modified: July 6, 2012

28 8.68 V D. 25 lb=ft 2 / x 2 25, M D. 3 lb=ft 2 / x 3 for 0 x 4 ft; V D 1800 lb.25 lb=ft 2 / x 2, M D 7200 ftlb C.1800 lb/ x lb=ft2 / x 3 for 4 ft x 12 ft V D. 1:00 kn=m/ x, M D. 0:500 kn=m/ x 2 for 0 x 1:3 m; V D 6:86 kn.1:00 kn=m/.x 1:30 m/, M D 7:22 knm.5:56 kn/ x.0:500 kn=m/ x 2 for 1:3 m x 4 m; V D 14:0 kn.1:00 kn=m/.x 4:00 m/, M D 25:0 knm.10:0 kn/ x.0:500 kn=m/ x 2 for 4 m x 5:5 m V max D 4P at x D 0, M max D 10P d at x D V max D 45:0 N just to the left of x D 30 mm, M max D 1130 Nmm at x D 30 mm V max D 10:0 lb just to the right of x D 17 in:, M max D 16:0 in.lb at x D 4 in: 8.78 Beam 1: Shear diagram (b), Moment diagram (g); Beam 2: Shear diagram (a), Moment diagram (g); Beam 3: Shear diagram (d), Moment diagram (f) N F D 6:19 kip, V F D 0:940 kip, M F D 0, N G D 6:19 kip, V G D 0:940 kip, M G D 4:00 kipft. 28 Last modified: July 6, 2012

29 8.82 N E D 833 N, V E D 833 N, M E D 0, N F D 1180 N, V F D 0, M F D 69:0 Nm, N G D 833 N, V G D 833 N, M G D V D 12 kn.0:750 kn=m 2 / x 2, M D.12 kn/ x.0:250 kn=m 2 / x 3 for 0 x 4 m; V D 36 kn.12 kn=m/ xc.0:750 kn=m 2 / x 2, M D 32 knm C.36 kn/ x.6 kn=m/ x 2 C.0:250 kn=m 2 / x 3 for 4 m x 8 m V D 12 kn.0:750 kn=m 2 / x 2, M D.12 kn/ x.0:250 kn=m 2 / x 3 for 0 x 4 m; V D 36 kn.12 kn=m/ xc.0:750 kn=m 2 / x 2, M D 32 knm C.36 kn/ x.6 kn=m/ x 2 C.0:250 kn=m 2 / x 3 for 4 m x 8 m; see V and M plots for Prob V D 60 N, M D 12;000 Nmm C.60 N/ x V D 60 N, M D 21;000 Nmm C.60 N/ x for 0 x 150 mm; V D 240 N, M D 48;000 Nmm C.240 N/ x for 150 mm x 200 mm V max D 1750 lb for 15 ft x 20 ft, M max D 8750 ftlb at x D 15 ft (a) V D 4 kn. 1 3 kn=m2 / x 2 ; (b) M D. 4 kn/ x. 1 9 kn=m2 / x 3 ; (c) V max D 9:00 kn at x D 3 m, M max D 15:0 knm at x D 3 m; (c) 29 Last modified: July 6, 2012

30 8.96 (a) M D. 2 kip=ft/ x 2 ; (b) V D 56 kip.8 kip=ft/ x C. 3 1 kip=ft2 / x 2 ; (c) V max D 20:0 kip at x D 6 ft, M max D 72:0 ftkip at x D 6 ft; (c) 8.98 (a) M D 132 kn m.17 kn/ x C.0:5 kn=m/ x 2 ; (b) V D 16 kn.4 kn=m/ x C. 1 3 kn=m2 / x 2 ; (c) (a) V D 25 lb=ft 2 x 2 ; (b) M D 800 ftlb 25 lb=ft 2 x 3 =3 ; (c) Chapter N D 52:1 lb, F D 10:3 lb, the box remains at rest on the ramp. 9.4 P D 471:4 N. 9.6 D tan h D 60:0 cm N D 1: lb, F D 8: lb : The dam will not slide or tip when the reservoir is completely full. 30 Last modified: July 6, 2012

31 9.16 The dam will not tip and will fail by sliding P D 47:4 N T D 1:940 N (a) D 1:103, safe from tipping; (b) D 0:3540, safe from tipping; (c) D 0:2680, safe from tipping (a) min D 0:289; (b) The answer to Part (a) will change, essay-type answer; (c) The answer to Part (a) does not change, essay-type answer P 1 D 0:6344 lb Q D 0:0915 lb s D 0: P D 0:900 lb will cause all books to slide together on the table A D B D 0: Nine books may be lifted s D 0: Q D 7:70 lb P D 10:6 N The truck is not capable of pulling the dumpster P D 7:00 kn s D T BD D 789:9 lb (a) P D 4:56 N; (b) T CD D 6:58 N, essay-type answer (a), (b), & (c): 73:0 lb :494 lb P 16:95 lb M A D 23:1 Nm. 31 Last modified: July 6, 2012

32 9.60 M A D 575 in.lb (a) P D 14:1 N; (b) P D 4:27 N W D 35:3 lb W B D 53:8 lb, surface C will stick while motion is impending at A and B (a) T CD D 89:86 lb; (b) The assumption of no tipping is correct D 0: N D 156 kn, F D 14:7 kn, D 0:0943, N and F are located 0:730 m to the left of point A h D 9 mm P D 1:60 lb, the roll of paper will tip (a) It is not possible to descend the hill with uniform speed; (b) It is possible to descend the hill with uniform speed, Q D 16:03 lb P D 56:2 lb, slip is impending at E and there is no slip at B and C W D 4402 N, M A D.5532 N/ r A where r A is the radius of pulley A T 0 D 57:4 lb. Chapter Essay-type answer I x D 568 a 4, I y D 328 a I x D 0:0404 in. 4, I y D 0:0570 in I x D 1 12 bh3, I y D 1 12 hb Answer provided in problem statement I y D 16 r4 0, J O D 8 r4 o, essay-type answer J A D 4 r4 o Essay-type answer (a) I x D 2:74 mm 4 ; (b) I y D 11:0 mm (a) I x D 0:305 mm 4 ; (b) I y D 1:60 mm (a) I x D 0:500 in. 4 ; (b) I y D 0:375 in c 1 D b= p a, c 2 D b=a 3, I x D 1 10 ab I x D 0:305 mm I x D 4: mm 4, I y D 4: mm 4, k x D 105 mm, k y D 33:1 mm I x D 117 in. 4, essay-type answer k x D 23:1 in: For the rectangular cross section: I x D 108 in. 4, I y D 108 in. 4 ; For the I cross section: I x D 428 in. 4, I y D 76:0 in I x D 4: mm 4, I y D 1: mm Last modified: July 6, 2012

33 10.38 I x D 37:6 in. 4, I y D 10:9 in (a) I x1 D 1820 mm 4 ; (b) I x2 D 2550 mm (a) d D 4:00 in:; (b) I x D 128 in. 4 ; (c) I y D 704 in (a) d D 2:00 mm; (b) I x D 88:0 mm 4 ; (c) I y D 64:0 mm (a) d D 65:0 mm; (b) I x D 1: mm 4 ; (c) I y D 1: mm Answer provided in problem statement I y D 1 4 mr2 where m D r 2 t I y D m. 1 4 R2 C 1 3 L2 / where m D R 2 L I D 3 5 m. 1 4 R2 C L 2 / where m D 1 3 R2 L I y D 3 5 m. 1 3 b2 C h 2 / where m D 4 3 abh Essay-type answer (a) I x D 1 R r= r 2 x 2 / 2 dx C I x D 4: slugin I y D 1 3 ma2 where m D 1 2 ha (a) I y D R L 0 where m D LR (a) I x D 2 R L 0 t 0.2 x L I y D 1: kgcm I x D where m D 12 7 R I D 16 7 mr2 where m D 12 7 R3. R r r=2 0.r2 x 2 / 2 dx; (b) I x D r R4 Œ. x L /4=3. x 2L /4 dx C R L 0 R2 x 2 Œ. x L /2=3. x 2L /2 dx; (b) I y D m L2 C7689 R I O D 0:0217 slugft 2, essay-type answer I y D 1 3 m.a2 C c 2 / I B D 20;700 kgmm I A D 9: slugin I x D 0:497 slugin I B D 0:0778 kgm I x D 1:61 slugin I D 0:627 slugin I y D 3:53 slugin I y D 5: slugft J O D 4.r4 o r 4 i / (a) I y D R 4 m 0 x 2. p x q Rx 3 / L q1 C R2 L dx; (b) I 2 x D 20 9 mr2 where m D 3 4 t 0 RL 1 C R2 L x/ dx; (b) I y D 20:6 m c 1 D 6, c 2 D 1 3, c 3 D 1; (a) I y D R 9 in: 0 x (a) I y D 2 R 1 in: 0 x 2.x 1/ 2 dx; (b) I y D 0:0667 in I x D 2: mm 4, I y D 3: mm (a) d D 1:183 in:; (b) I x D 5:56 in I D 3 10 mr2 where m D 1 3 r2 h I x D 1700 kgmm 2 : I D 3040 kgmm 2 : I x D 0:0113 kgmm 2 : I x D 1 R h x2 dx C I y D 1: kgm 2 : R 2h h 2 x2 dx (a) I x D 1: mm 4 ; (b) I x D 5: kgmm I x D 13:3 slugin I D 16:7 slugin x p x/ dx; (b) Iy D 286 in Last modified: July 6, 2012