Answer sheet for Dynamics, Cheat Sheet of Law

Download Answer sheet for Dynamics and more Cheat Sheet Law in PDF only on Docsity! 701 Problem Answers Chapter 1 1/1 1/2 1/3 1/4 1/5 (a) (b) 1/6 1/7 1/8 1/9 1/10 1/11 022 or 432 348 km 1/12 1/13 On earth: On moon: 1/14 1/15 [MLT1]  [MLT1] RB  2.21RA  2.19, Rem  0.001677 Rem  286 000 Res  1656 d  346 V  1.770 Wh  186.0 lbgh  29.9 ft/sec2, Wrel  882.2 NWabs  883.9 N, h  0.414R F  (5.73i  3.31j)109 N 3.14(1011)i N 1.255(1010)i N 27, 1.392i  18j, 19.39i  6j, 178.7k, 21.5 m  0.01294 slugs  0.1888 kg, W  1.853 N W  14 720 N  3310 lb, m  102.8 slugs W  801 N 180-lb person: m  5.59 slugs  81.6 kg Chapter 2 2/1 2/2 7.89 sec 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12 2/13 2/14 2/15 2/16 2/17 (a) (b) 2/18 2/19 2/20 2/21 2/22 2/23 2/24 2/25 2/26 (a) (b) t  0.0555 sect  0.0370 sec, s  2250 m s  330 m s  713 m v  99.8 mi/hra  1.168 ft/sec2, t  3.26 ss  3.26 m, v  0.8 m/s %s  64 m%a  0.5 m/s2, s  1.819 kmt  65.5 s, v  25.6 m/sv  21.9 m/s, v  1.25 m/svav  0.75 m/s, tacc  0.8 seca  31.2 ft /sec2,v  25 ft /sec, tAC  2.39 sec vB  56.4 ft/sec downt  4.24 sec,h  49.4 ft, t  40.8 sh  2040 m, v2  139.0 ft/sec s  213 ft s  5  3t  15t2  2 3 t3 m v  3 – 30t  2t2 m/s D  1.419 m%s  1.248 m, a  3.61g %s  24 m a  constantD  45 mm,%s  27 mm, a  150 mm/s2 a  15 m/s2v  42 m/s,s  72 m, t  2.11 sec, v  75 m/s (When a problem asks for both a general and a specific result, only the specific result might be listed below.) 702 Problem Answers 2/27 2/28 2/29 2/30 2/31 2/32 2/33 2/34 2/35 2/36 2/37 2/38 2/39 2/40 Particle 1: Particle 2: Particle 3: 2/41 2/42 2/43 2/44 2/45 2/46 2/47 2/48 2/49 (a) (b) 2/50 (a) (b) 2/51 2/52 2/53 (a) (b) 2/54 2/55 2/56 2/57 2/58 2/59 2/60 2/61 2/62 2/63 2/64 2/65 2/66 2/67 2/68 2/69 2/70 2/71 2/72 2.57 ft above B 2/73 right of B 2/74 2/75 2/76 2/77 2/78 2/79 2/80 2/81 2/82 2/83 2/84 2/85 2/86 2/87 2/88 2/89 2/90 2/91 2/92 2/93 2/94 2/95 2/96 2/97 2/98 2/100 2/101 2/102 2/103 2/104 2/105 2/106 an  36.7 ft/sec2, at  20 ft/sec2 tA  8.97 s, tB  8.89 s, 2.50 m tA  8.97 s, tB  9.92 s, 23.9 m S  266 m a  0.269 m/s2 v  5.30 ft/sec, an  25.0 ft/sec2 v  71.3 km/h at  8.39 ft/sec2 vA  11.75 m/s, vB  13.46 m/s x  1242 ft, y  62.7 ft V  90  B 2 , V  45, 60, 67.5 h  583 ft, tƒ  12.59 sec, d  746 ft vx l 0, vy l  g k (v0 sin V  g k )(1  ekt)  g k ty  1 k vy  v0 sin V  g k ekt  g k x  v0 cos V k (1  ekt)vx  (v0 cos V)ekt, ƒ2  1ƒ1, ƒ2  1 2 Ri  0.667 v0 2 g , ti  1.155 v0 g s  1.046 km, t  17.75 s h  1.227 m B  0.445, h  500 ft E  7.76 ft 31.0  V  34.3 or 53.1  V  54.7 umax  1.135 m/s, umin  0.744 m/s 20.6  v0  22.4 ft/sec s  455 m, t  13.35 s R  46.4 m, V  23.3 V1  26.1, V2  80.6 u  14.41 m/s R  2970 m V  48.7 or V  53.6 v  70.0 ft/sec, s  11.85 ft V  5.57 V  21.7 V  14.91 V  50.6, 2.50 ft v0  77.1 ft/sec, V  31.1 v0  16.33 ft/sec, V  66.8 u  343 m/s Rmax  v0 2 g v0  3.67 m/s, d  1.340 m (y  2)3  144x2, v  30 ft/sec t  24.7 sec, h  1.786 mi v  13.45 in./sec, a  26.8 in./sec2 v  24.2 ft/sec, a  25.3 ft/sec2 Vx  26.6a  4.47 mm/s2, v  8.94 mm/s, Vx  63.4 v  6.20i  3.36j m/s, V  27.9 aav  5 m/s2, V  53.1 vav  20.6 m/s, V  76.0 t  105 sec, amax  11.73 ft/sec2 v  g c(ect 1)  k c  b (ebt ect) vƒ  78.5 ft/sech  120.8 ft, x  0.831 ft D  0.693/k, t  1 kv0 s  1268 ms  1206 m, v  v0  kxx  v0 k (1ekt),v  v0ekt, v  [v0 1n  c(n1)t]1/(1n) v  4990 ft/secv  6490 ft/sec, v  12,290 ft/secv  13,040 ft/sec, s  416 m%t  10 s, D  1 2C2 ln 1  C2 C1 v0 2 vmax { 18 m/s c  3v0 2  6gym 2ym3 D  65.3 ft, %s  6.67 ft, s5  3.67 ft t  50.8 s K  1.073(103) ft1, t  25.4 sec v  2K(L  D/2) LD s  v0 k sin (kt), v  v 2 0  ks2 s  v0t  1 6 kt3, v  v0  1 2 kt2 s  v0 k (1  ekt), v  v0ekt c  v0 2  2gym ym 2 D  3710 ft s  5810 ft v  178.9 ft/sec t  2.74 seca  8.72 ft/sec2, t  16.67 s a  6.67 m/s2, t l P vmax  35.9 ft/sec v  38.9 km/h v  1.587 in./sec t  0.917 s s  972 ft h  1.934 kmvm  120 m/s, D D D D D D Problem Answers 705 2/246 2/247 2/248 2/249 (a) (b) (c) 2/250 V  90 at t  0.526 sec at t  0.324 secV̇max  3.79 rad/s Vmax  110.4 at t  0.802 sec a  30.3 m/s2 a  0 a  30.3 m/s2 v  113.5 ft/seck  0.00323 ft1, vt  99.8 ft/sec, t  1.473 s, x  0.1178 m aB  7.86 mm/s2 up 3/1 3/2 (a) (b) Crate does not stop 3/3 (a) no motion, (b) down incline 3/4 3/5 3/6 3/7 3/8 up 3/9 up incline 3/10 3/11 (a) , (b) 3/12 (a) (b) 3/13 3/14 3/15 3/16 3/17 3/18 up 3/19 3/20 3/21 (a) (b) right 3/22 Not possible 3/23 3/24 (a) (b) 3/25 3/26 3/27 3/28 3/29 down incline up, 3/30 3/31 3/32 right down, 3/33 down, T  8.21 NaB  2.37 m/s2 T  46.6 NaB  9.32 m/s2 aA  1.364 m/s2 v  2P S  NkgL x  201 m T  105.4 NaB  0.725 m/s2 aA  1.450 m/s2 T  171.3 N k  5 lb/in. n  66.0% C  tan1a  g sin V g cos V  aA  aB  0.667 m/s2 aA  1.095 m/s2, aB  0.981 m/s2 Nk  0.555 a  1.390 m/s2 a  0, Nk  0.429 TA  75.0 N, TB  55.4 N FA  4080 lb F  0.0206 lb a  5.66 m/s2 T1  39,200 lb, T100  392 lb T  1042 N 12 s a  0.513 m/s2 a  0.257 m/s2, a  16.10 ft/sec2 a  6.44 ft/sec2 a  g(sin V1  sin V2) a  4.96 m/s2 a  3.58 ft/sec2 su  807 m, sd  751 m n  sin V  ag F  2890 N R  846 N, L  110.4 N; R, L l 0 a  3.45 ft/sec2 t  5.59 s, x  19.58 m t  1.784 s, x  6.24 m 3/34 3/35 (a) (b) left 3/36 Case (a), 3/37 3/38 3/39 (a) (b) 3/40 (a) (b) 3/41 3/42 3/43 No motion 3/44 3/45 3/46 (a) (b) 3/47 3/48 (a) (b) 3/49 3/50 (a) (b) 3/51 3/52 3/53 3/54 3/55 3/56 3/57 (a) (b) 3/58 3/59 3/60 3/61 3/62 3/63 3/64 3/65 3/66 3/67 3/68 F  165.9 N T  1.76 N, FV  3.52 N D  45.0 kN, L  274 kN NA  3380 N, NB  1617 N F  920 lb s  v0 /kg k  cos2 V vA  140.7 ft/sec, vB  163.8 ft/sec at  22.0 ft/sec2 an  0.818g, F  2460 lb V̇  3.37 deg/s NA  241 NvB  54.2 m/s, W  1.064 rad/s N  8.63 rev/min Ns  0.540 N  0.0241 lb P  4 lb (side A) V  45.3 R  0.271 lbR  0.25 lb, R  1.173 N, at  7.21 m/s2 v̇  16.10 ft/sec2N  1.374 lb, NA  10.89 N, NB  8.30 N T  16.14 NT  8.52 N, T  138.0 N, a  0.766 m/s2 v0  11.19 km/s P  9.66aB  0.322 aA  4.83 ft/sec2P  54 lb: aA  aB  0.1789P  3.2227  P  54 lb: 0  P  27 lb: V  5.88, 47.2 v  2100 m/s t  0.0768 s, y  0.01529 m vs  0.327 m/s h  127.4 mh  55.5 m, tan1 1Ns  V  Q 2 a  1.406 m/s2 v  7.43 m/s a  0.714 m/s2a  0, ax  32.2(14 – 30x), v  14.47 ft/sec * * * * * * Chapter 3 D D D D 2/251 2/252 2/253 2/254 vmax  10 in./sec at t  0.330 sec, x  2.45 in. amax  10.76 m/s2 at V  0 and t  0 amin  9.03 m/s2 at V  44.3 and t  0.237 s B  42.2, R  101.3 m sB  150 m t  10 s and 2.52 m/s2 atsB  0, (aA/B)min sB  557 m, (aA/B)max  6.12 m/s2 at t  0 and sB  1264 m, (vA/B)min  10 m/s at t  23.6 s and (vA/B)max  70 m/s at t  47.1 s and 706 Problem Answers 3/69 3/70 3/71 3/72 3/73 3/74 Dynamic: Static: 3/75 3/76 3/77 3/78 3/79 3/80 3/81 3/82 3/83 3/84 3/85 3/86 3/87 3/88 3/89 (a) (b) (c) 3/90 3/91 3/92 3/93 3/94 3/95 3/96 3/97 (a) (b) 3/98 3/99 3/100 3/101 3/102 3/103 3/104 3/105 (a) and (b) 3/106 3/107 (a) (b) 3/108 (a) (b) 3/109 (a) (b) 3/110 (a) (b) 3/111 3/112 3/113 3/114 3/115 3/116 3/117 3/118 3/119 At Halfway: 3/120 (a) (b) (c) (d) 3/121 3/122 3/123 (a) (b) (c) 3/124 3/125 (a) (b) , (c) 3/126 3/127 3/128 3/129 3/130 3/131 3/132 3/133 3/134 3/135 3/136 (a) (b) 3/137 (a) (b) (c) 3/138 3/139 3/140 3/141 (a) (b) 3/142 (a) (b) (c) down 3/143 3/144 3/145 W  88.1 lb N  m5g  kRm (3 – 22) vC  4gR  kR2 m (3 – 22) vB  2gR  kR 2 m (3 – 22) y  0.224 m NE  35.3 N NC  10.19 NNC  77.7 N, E  54.2 mmvB  9.40 m/s, v  3.43 m/s, x  48.5 mm v  3.65 ft/sec v  5.46 ft/sec xss  93.2 mm xmax  186.4 mmv  0.496 m/s, v  70.9 mi/hr Pup  35.2 hp, Pdown  3.17 hp P30  5 hp, P60  16 hp E  29.4 mm v  1.734 m/s, v  1.889 m/s v  7.80 ft/sec k  8.79 kN/m Pin  36.8 kW E  0.1445 m vC  3.59 m/s vA  3.44 m/s v  17.48 ft/sec v  5.30 m/s s  4R 1  Nk3 NC  7mgNB  4mg, k  5mg(h  d) d5 P  0P  287 W,P  0, v0  6460 m/s v  13.37 ft/sec P  2670 hpP  6530 hp, P  3270 hpF  61,200 lb, F  6960 N P  136.7 kWB: P  193.4 kW, e  0.892 %Q  1620 JR  4.05 kN, R  4.05 kN, P  52.2 N v  7.08 ft/sec Q  903 kJ e  0.764 v  1.881 m/s P  0.393 hp, P  293 W v  6.55 ft/secv  5.93 ft/sec, x  98.9 mmv  2.56 m/s, s  1.226 ms  1.853 m, s  0.349 ms  0.663 m, P  0.400 hp v  8.10 m/s Q  1.835 J v  2gh R  3340 lb k  974 lb/in. v  17.18 ft/sec Uƒ  672 ft- lb vB  3.05 m/s U1–2  2.35 JU1–2  60 J, N  mg (1  4k2x2)3/2  0 s  r 2Nk ln v0 2  v0 4  r2g2 rg  N  81.6 N, R  38.7 N v  5.52 m/s Vmax  Q 2 , T  mg(3 sin V  3 cos V  2) T  2.53 N, R  1.028 N (lower side) r̈  1.153 ft/sec2, V̈  2.72(108) rad/sec2 ṙ  9620 ft/sec, V̇  1.133(104) rad/sec F  1562 lb F  2260 lbF  1562 lb, at  10 m/s2, NA  NB  4.83 N, T  5.23 N at  10 m/s2, NA  NB  2 N, T  2.83 N P  8.62 lb vV  r0W0 cosh W0t vr  r0W0 2 (eW0t  eW0t), r  r0 2 (eW0t  eW0t) P  2.21 N, N  14.22 N k  1  RW2 g , W  99.655 N 7  4.77 rad/s N  1 4QNsg rB  2  1 T  2.52 lb, N  0.326 lb (side B) F  4.39 N x  118.8 mm, N  25.3 N R  2.14  1.913 cos V N, vB  2.06 m/s v  149.4 ft/sec, vmin  0, vmax  345 ft/sec v  L 2Q g b , N  2mg Fr  5.89 N, FV  10.19 N Fr  4.79 N, FV  14.00 N S  3000 km, v̇  6.00 m/s2 P  27.0 N, Ps  19.62 N 1.414  t  5 s T1  0.0707  0.0354t2 N  0.0707  0.0354t2 0  t  1.414 s T2  0.0707  0.0354t2 N  0.0707  0.0354t2 W  5.01 rad/s v  gr tan V D D D D D D Problem Answers 707 3/146 3/147 3/148 3/149 (a) (b) 3/150 3/151 3/152 3/153 3/154 3/155 (a) (b) 3/156 3/157 3/158 3/159 3/160 3/161 3/162 3/163 3/164 3/165 3/166 3/167 3/168 (a) (b) 3/169 3/170 (a) (b) 3/171 3/172 3/173 3/174 3/175 3/176 3/177 3/178 3/179 down 3/180 3/181 (a) (b) 3/182 left 3/183 3/184 3/185 left 3/186 3/187 3/188 (a) (b) right 3/189 3/190 3/191 right 3/192 3/193 3/194 3/195 3/196 3/197 3/198 3/199 3/200 (a) (b) (c) 3/201 3/202 3/203 3/204 3/205 3/206 3/207 3/208 knots 3/209 3/210 3/211 3/212 (a) (b) (c) 3/213 3/214 3/215 3/216 (a) (b) (c) 3/217 3/218 3/219 3/220 3/221 (a) (b) 3/222 3/223 3/224 3/225 3/226 3/227 3/228 3/229 3/230 3/231 (a) (b) 3/232 HO  1 2mgut2k HO  2mv0 3 sin2 V cos V gHO  0, A: (ḢO)z  0, B: (ḢO)z  0.120 kg [m2/s2 vB  47 850 m/s, vP  58 980 m/s W  W0/4, n  3/4 W  0.1721 rad/s CW dW dr  2W r ḢB  1.113k lb-ft vP  17,723 mi/hr t  15.08 s V̇   2m1 m1  4m2  v1 L HO  2mrgr, ḢO  0 HO  mr2gr, ḢO  mgr W  5v 3L HO  mv(ci  ak), ḢO  F(bi  aj) (HO)2  34i  0.1333j  19.6k kg [m2/s VH V  389 N [m [ s, VM V  260 N [m T  24 J HO  23.2k kg [m2/s G  8.49i  8.49j kg [m/s HO  69.3 kg [m2/s v2  40.0 mm/s vB  mA mB 2gl 1  mA/mB v  9.10 m/s v  7.23 m/sv  3.10 m/s, R  43.0 N, C  8.68 Rx  559 lb, Ry  218 lb s  r Nk  mA mA  mC 2 v  5.20 R  472 lb, a  4660g, d  0.900 in. v1  0, v3  0.468 m/s, v5  5.30 m/s, v7  0 v  6.61 m/s v  15.62 ft/sec, V  50.2 v  17.82 mi/hr, V  54.7 v  0.1935 km/h v  0.663 km/h R  12,150 lb aB  195.6 ft/sec2aA  97.8 ft/sec2, v  13.33 mi/hr v2  1.423 m/s down incline, t  8.25 s v  3.42 m/s t  4 min 33 sec v  F0 mb 1  ebt, s  F0 mb t  1 b (ebt  1) R  14.96 kN v1  0, v3  2.42 ft/sec, v5  6.44 ft/sec, v7  0 vƒ  0.00264 m/s, Fav  59.5 N v1  0.417 m/s, v3  8.96 m/s ẋ1  2.05 m/s left, ẋ2  0.878 m/s v  190.9 m/s, V%E V  17.18(103) J T  2780 N v4  2.69 m/sv1  0, v  5.86 ft/sec t  12.18 min ẋ1  2.90 m/s right, ẋ2  0.483 m/s v  2.10 m/s R  423 lb vC  1.231 m/s V%E V  2230 ft- lbv  2.44 mi/hr, t  7.73 s vB  1.652 m/s Nk  0.302 %R  568 N V%E V  13 480 J, n  99.9% v2  188.5i  74j  47k m/s F  3.03 kN 1.7 N [ s v  gr Q2  4 Q V̇  1.045 rad/s v  0.522 m/sk  111.9 N/m, v  1.143 m/s v  1.005 m/sm  0.528 kg, V  43.8 (vB)max  0.962 m/s k  155.1 N/m v2  35.1 km/h E  vm/k v  20.4 mi/hr xmax  105.9 mm, vmax  1.493 m/s, x  27.2 mm vB  26 300 km/h v  3.43 ft/sec v  4.93 m/s P  2.86 lb v  0.331 m/s v  1.641 ft/secv  3.06 ft/sec, k  86.8 N/m, v  1.371 m/s vB  8.54 ft/sec vA  0.616 m/s, vB  0.924 m/s V̇  4.22 rad/s k  393 N/m, v  1.370 m/s, V̇  2.28 rad/s x  0.510 in.v  3.84 ft/sec, Uƒ  2.36 J, Fav  3.38 N v0  6460 m/s v  1.248 ft/sec D D D