343 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng Taọp 1: Cụ Nhieọt ẹieọn P S CC BI TP Chng 1: 1.1: b, d, f. 1.2: PTQ; khụng. 1.3: a) y = 2 x 2 ; b) x 20 y = ; c) y = 2x 2 1; d) z = 2x +1; e) 1 100 y 25 x 22 =+ ; f) (x 5) 2 + (y 4) 2 = 400. 1.4: 39,4km/h. 1.5: 43,6km/h. 1.6: 62,3 km/h. 1.7: k v v 3 2 s 0 0 = ; 0tb v 3 2 v = . 1.8: ; 2 tb )a 2 2 xb v)b tb = . 1.9: . 1.10: t s/m5,11v;s/m10v);6,8,0(v tb === 1 = 1s; t 2 = 2s; t 3 = 3s; s = 0,77m/s. 1.11: a) 1,6cm; 3m ; b) 2s; 2,4cm; 565m. 1.12: a) y= 2x 2 + x; b) ; c) )16,0(a);2,2(v == 2 nt s/m28aa == ; R = 70,7cm; d) t = 0,25s; e) 0,57m. 1.13: 2 3 23 c bS4 1ca; bS2 c R +== . 1.14: )A1( B2 a v 2 o += . 1.15: k v 3 v2 s oo = ; 3 v v 0 tb = . 1.16: a) 4 x y 2 = ; b) 45 0 . 1.17: a) 2 x xy 2 = ; c) t = 1s d) a t = 3,98m/s 2 ; a n = 0,44 m/s 2 ; R = 745m; e) 42m. 1.18: b) t = 1/; = 2 r s 0 . 1.19: = sin2 0 . 1.20: 3 0 tb = . 1.21: s = 85m. 1.22: t 1 = 0,894s; t 10 = 0,145s. 1.23: s = At. 1.24: a) = 3,14 rad/s; b) v = 1,02 m/s; a t = 1,02 m/s 2 ; a n = 3,2 m/s 2 ; a = 3,36 m/s 2 ; c) s = 0,51m. 1.25: 15 = rad/s 2 ; 240 vũng. 1.26: 22m. 1.27:b)70,7s c) 2500m; d) a t = 7m/s 2 , a n = 7,14m/s 2 , R = 35000m. 1.29: 2 2 2 1 2211 vv vv t + + = ; 2 2 2 1 1221 min vv |vv| d + = . 1.30: m802/ad)b;s25 vu au t)a 22 === = Chng 2: 2.5:a) f ms = àmg; a= m F àg; b)f ms = à(mg Fsin); g m )sin(cosF a à à + = c) F ms = à(mg + Fsin); g m )sin(cosF a à à = . ẹAP SO CAC BAỉI TAP 344 2.6: )N(106 )sin( cosP T AC = + = ; )N(137 )sin( cosP T BC = + = . 2.8: 1e 1e . k g v t.gk2 t.gk2 + = AB AB mm mm ga + = . 2.9: k v s;evv 0 kt 0 == . 2.10: 21 21 mm mm ga + à = ; m 2 khụng b trt khi m 2 à 1 m . 2.11: 21 12 m4m mm2 ga + = 2.12: g m )sin(cosF)sin(cosF a 21 à à+à+ = . 2.13: F ht = mg.tg; F cd = cos mg . 2.14:a) a = 1m/s 2 ; T 12 = 7,2N; T 23 = 1,8N; t = 2s; b) cú, sau 1s. 2.15: a) )cos mm mm (singa 21 2211 + à+à = ; 21 2121 mm cosg)(mm Q + àà = ; b) 21 2211 min mm mm tg + à+à = . 2.16: a) à+ cossin m m 1 2 ; 21 21 mm )cos(sinmm ga + à+ = ; b)sin > àcos v à cossin m m 1 2 ; 21 12 mm m)cos(sinm ga + à = ; c) à+ cossin m m 1 2 , nu sin àcos hoc à+ 2 1 m cossin m à cossin m 1 , nu sin > àcos. 2.17: a) ) R v cosg(mQ 2 = , ti nh cu. 2.19: 6m/s; 2.20: 2kgm/s; 5m. 2.21: gv = . 2.22: tm Ft v 0 à = . 2.23: ) tm m ln(uvv 0 0 0 à += . 2.24: L = L z = - ẵ mv o gt 2 cos; L = - ẵ mv 0 3 cos.sin 2 . 2.25: 2,7.10 40 kgm 2 /s 2.26: ; tb2M = b/at = ; M = 2 ab . 2.27: 3 4 0 2 0 r Rm T = ; 2 0 0 r R = . 2.28: . 2.30: = pxrL'L 0 g)mm)((F 2121max + à + à = . 2.31: 1 m m4 m m 1 m m4 m m ga 2 1 2 1 0 1 2 1 1 ++ + = ; m 1 i xung khi 20 20 1 m4m mm m + ; 345 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng Taọp 1: Cụ Nhieọt ẹieọn 2.32: à à + = sincos cossin ga max0 . 2.33: g min = ; . )g(mT 2 = 2.34: s/m10 gR v min = à = . 3.35: a) )cos(sing)sin(cosa 2 t 0 à+à+ = ; Chng 3: 3.1: 2,83kg. 3.2: 982kg. 3.3: 546kg. 3.5: tng m = 3m. 3.6: chn trc Ox, Oy trựng vi OA, OC thỡ ) 10 a7 , 2 a (G . 3.7: = 3 R4 x G ; 2 3 R4 x G = . 3.8: a) = 3 a4 x G ; b) = 3 b4 x G . 3.9: 8 R3 z G = . 3.10: 22 2 r R ar OG = ; 6 R OG = . 3.11: 33 3 r R ar OG = ; 14 R OG = . 3.12: )cb(2 acbc2b x 2 G + ++ = ; 4 ab3 x G + = . 3.13: 2 R h . 3.14: xem vớ d 2. 3.15: 4,5s. 3.16: 0,02rad/s 2 . 3.17: 140cm/s; 20cm/s. 3.18: a) R2 |vv| ; 2 vv v 2121 G = + = ; b) R2 vv ; 2 |vv| v 2121 G + = = . 3.19: 4,4m; 2270 vũng; 76 vũng/phỳt. 3.20: 10Nm; 17,3Nm; 20Nm; 0Nm; 2Nm; 1,3Nm; kim ng h. 3.22: 4,6Nm. 3.23: )RR(m 2 1 2 2 2 1 + . 3.24: 2 mR 10 3 ; 33 55 r R rR m 10 3 . 3.25: 2 mR 4 1 ; 2 mR 2 3 . 3.26: 2 mR 2 1 . 3.27: a) )rR(m 4 1 22 + ; 2 mR 16 5 ; b) 22 22 22 r R dmr )rR(m 2 1 + ; 2 mR 24 13 . 3.28: 33 55 r R rR m 5 2 . 3.29: 2 ma 3 1 ; )ba(m 12 1 22 + . 3.30: 2 m 3 1 . 3.31: a) 2m(a 2 + b 2 ); b) 2mb 2 ; c) 2ma 2 . 3.32: a) 2ma 2 ; b) ma 2 ; c) 2ma 2 ; d) 4ma 2 . 3.33: R r cos; R/Im )cos(cosF a 0 2 0 G = + = ; < 0 : sang phi; > 0 : sang trỏi; = 0 : quay ti ch. 3.34: ; mm2 m2 ga o + = o o mm2 gmm T + = ; o oo o o m3m2 gm)mm( T; m3m2 )mm(2 ga + + = + + = . ẹAP SO CAC BAỉI TAP 346 3.35: o21 21 m 2 1 mm mm ga ++ = ; o21 21 m 2 1 mm )cos(sinmm ga ++ à+ = . 3.36: m3 F2 a = . 3.37: 3 0 tb = . 3.38: 0,05Nm; 0,1Nm; 3.39: 34,6rad/s; 3.40: t 2 mR 0 2 Chng 4: 4.1: 10(kJ) 4.2: 0(J). 4.3: 17J. 4.4: 6J. 4.5: 25J 4.6: 16,7kW. 4.7: 36MW. 4.8:7200N. 4.9: 30km/h. 4.10: a) 2W; b) 2 kgmv P 2 0 max = . 4.11: 396Nm. 4.12: 19,8kJ; 1320W. 4.13: 200W; 400W. 4.14: 500J; 250W. 4.15: 2kJ; 212kJ. 4.16: bỏnh . 17: 10kJ. 4.18: Nng lng tng tỏc. 4.19: b a2 r < : y; b a2 r > : hỳt; 2 2 max a27 b F = 4.20: a) Khụng; b) Cỏc elớp; c) khụng, cỏc elớpxụit . 4.21: a) khụng ; b) cú. 4.22: k4 mg3 ; k2 gmg3 ; k2 mg . 4.23: r > r C : hỳt; r < r C : y. 4.24: H/2; H. 4.25: 3 2 ;g3 . 4.26: 2,5; 2; 1; )Rh(g 7 10 ; )Rh(g 3 4 ; )Rh(g ; qu cu khi tr cỏi vũng. 4.27: R g . 4.28: 15,5m/s. 4.29: 20%. 4.30: 6,25kW. 4.31: 2 m kx 2 1 ; )xx( m k 22 m . 4.32: 3kg. 4.33: g2.)mM( vm 2 22 + . 4.34: . 4.35: 9kg; 1/9kg. 4.37: += j4i3v H h k = ; t )gh2gH2(m F + = Chng 5: 5.1: 2,6.10 8 m/s. 5.2: 3,2. 5.3: m = 8,6.10 -27 kg. 5.4: 8,19.10 -14 J. 5.5: 2,985m/s. 5.6: x = 137,7 km; t = - 374,7 às. 5.7: t 1 = 0; t 2 = - 2,5 às. 5.8: a) V = rb rb tt xx = - 1,44.10 8 m/s; b) t b - t r = 4,39.10 -6 s = 4,39 às; c) 4,39às. 5.9: u = 0,806 c. 5.10: u = 0,946 c. Chng 6: 6.3: 2 B 2 A BA SS hg2 .S.SL = . 6.4: gh2v = . 6.5: 5m. 6.6: a) 20cm 3 ; 10g; b) ni lờn, chỡm xung; c) 666 kg/m 3 ; d) k 1/3. 6.7: a) 600 lớt; b) lõu hn, vỡ vn tc chy 347 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng Taọp 1: Cụ Nhieọt ẹieọn gim dn. 6.9: 5m; khụng. 6.10: 500N. 6.11: 2 2 2 2 1 2 1 t. S S g 2 1 t.gH2 S S Hh += ; g H )12( S S t 1 2 1 = ; g H2 S S t 1 2 2 = . 6.12: g'. 1 S S v 2 1 PP h 2 B 2 A 2 AAo + . 6.13: c) H/2. 6.14: 700J. 6.15: a) 61,5%; b) )( )D( V 211 12 = Chng 7: 7.1: 29,5 lớt; 8,9 at. 7.2: 7,5 kg. 7.3: a) 1 2o o1 2 V pp pp V = ; b) 21 2211 o VV VpVp p + + = . 7.4: a) a3 p R3 p2 T oo max = ; b) a R .e p T o max = . 7.5: omin aTR2p = . 7.6: 2.10 18 phõn t/cm 3 . 7.7: 5,74 atm; an ton. 7.8: 1,83g/lớt. Chng 8: 8.1: sinh cụng A =1000J; nhn nhit Q = 2500J. 8.2: sinh cụng A = 1184J; nhn nhit Q = 1184J. 8.3: 30,8%. 8.4: 2324J. 8.5: 1454W. 8.6: 72J. 8.7: 150J; 90J. 8.8: 2,7kg; 25%. 8.9: 6,21.10 21 J. Chng 9: 9.1: b) F d = 2,3.10 39 F hd . 9.2 = 4.10 16 rad/s; v = 2,2.10 6 m/s. 9.3: thiu 1,25.10 13 electron. 9.4: 1 21 2 21 2 F qq4 )qq( F + = . 9.5: 7 mgtg q sin 1,1.10 C k = = . 9.6: a) 1,35.10 5 V/m; b) 3,1.10 4 V/m; c) 1,92.10 4 V/m; d) 1,5.10 4 V/m; e) AN = 20cm, BN = 40cm. 9.7: = d 'rr )'rr)('r( 4 1 )r(E )( 3 o , = d 'rr )'r( 4 1 )r(V )( o 9.8: a) E x = -2ax; E y = -2ay; E z = -2bz; b) nhng elipsoid trũn xoay. 9.9: r r . 2 E o o = ; V = 0 0 rC 2 + . 9.10: 22 o hah2 a E + = ; 22 aah V2kln h ++ = . 9.11: a)E A > E B ; V A > V B ; b) E A > E B ; V A < V B ; E A = E B = E C ; V A = V C > V B . 9.12 : 45 0 . 9.13 : a)A BC = A AD = 0; b) A AC = A DC ; c) khụng thay i. 9.14: E A = E B ; V A = V B ; A AB = 0. 9.15 : 2k sin E R = ; V = 2k. ẹAP SO CAC BAỉI TAP 348 9.16 : a) 11 E2k|| x2ax =+ ; 2a x V2k||ln x = b) 22 4ka | | E ah = + ; V = 0 Chng 10 : 10.2 : a) 8,85pF; b) a)ad( S C o + = ; c) a d S C o = . 10.3 : a) Q = Q o = C o U o ; C = o C 2 1+ ; U = o U 1 2 + ; b) E = d)1( U2 o + ; c) Q chỡm = o Q 1 + ; d) 0 C)1(2 Q)1( W o 2 o < + = . 10.4: a) C = 8àF; Q 1 = Q 2 = Q 3 = 44àC; Q 4 = 132àC; b) 8 cỏch. 10.5: - 19,2àJ. 10.6: a) Q 1 = 48àC, U 1 = 12V; Q 2 = 72àC, U 2 = 12V b) Q 1 = 16àC, Q 2 = 24àC; U 1 = U 2 = 4V. 10.7: C 2 = 5àF. 10.8: a) K m: 43 43 21 21 CC CC CC CC C + + + = , Q 1 = Q 2 = U CC CC 21 21 + , Q 3 = Q 4 = U CC CC 43 43 + ; b) K úng: 4321 4231 CCCC )CC)(CC( C +++ + + = , 4321 421 1 CCCC U)CC(C Q +++ + = , 4321 312 2 CCCC U)CC(C Q +++ + = , 4321 423 3 CCCC U)CC(C Q +++ + = , 4321 314 4 CCCC U)CC(C Q +++ + = ; e U . CCCC CCCC n 4321 3241 e +++ = ; 4 2 3 1 e C C C C 0n == . 10.9: o o U C C U = = 8000V. 10.10: U BA = 2V. 10.11: Q = 1,59àC; Q = 10,6àC. 10.12: U2 mgd q = . 10.13: U = 20V. 10.14: cm1,2)2s( U4 Us x o =+= . 10.15: 2 2 o dU2 U . Chng 12 : 12.1 : a) )ba2ba(S ba)ba( R 22 22 +++ ++ = ; b) S a . )ba2ba)(ba( )baba(bba)ba( R 22 2222 ++++ ++++++ = ; 349 Giaựo Trỡnh Vaọt Lớ ẹaùi Cửụng Taọp 1: Cụ Nhieọt ẹieọn c) S . ba2ba( ba)ba(ab2 R 22 22 +++ +++ = . 12.2 : I = 3A, U AB = 1,5V; a) K m: Q 1 = Q 2 = 0,3àC, U 1 = 1V, U 2 = 0,5V; b) K úng: U 1 = 0,9V, Q 1 = 0,27àC, U 2 = 0,6V, Q 2 = 0,36àC. 12.3: I 1 = 1,5A, I 2 = 2,5A, I 3 = 4A; U 1 = 1,1V, U 2 = 1V, U 3 = 1,2V. 12.6: s a: R = 15; s b: R = 5. 12.7: K m: U = 2V, lch sang phi; K úmg: U = 1,86V, lch sang phi. 12.8: a) 6 búng; b) 23A. 12.9: a) 781 A; A; A 999 ; b) 12 21 12 Er Er E1,7 rr + == + 5V v 12 12 rr r0,25 rr = = + ; c) 21 12 12 Er Er R1 2(E E ) ,75 + = = ; d) 2 12 Er R1, EE == 5 ; e) 1 1 1 E I4 r ==A , 2 2 2 E I3A r == 12.10: a) I 1 = 1,2A (ngun thu), I 2 = 0,4A (ngun phỏt), I 3 = 0,8A (ngun phỏt); b) U 1 = 4,8V, U 2 = 1,2V, U 3 = 5,6V; c) Cụng sut tiờu th ca ngun 1: P 1 = 13,44W, hiu sut np in: H 1 = 89,3%; P 2 = 8W, H 2 = 96%; P 3 = 24W, H 3 = 92%; d) oo cc ngun E 3 thỡ c 3 ngun u phỏt: I 1 = 0,8A, I 2 = 2A, I 3 = 2,8A; U 1 = 3,2V, U 2 = 6V, U 3 = 19,6V; P 1 = 8W, P 2 = 40W, P 3 = 84W; H 1 = 92%, H 2 = 80%, H 3 = 72%. 12.11: a) U = 22V; b) U = 12,2V; c) U = 9,6V, U = 2,44V; d) 92mA, 18mA. 12.12 : I 1 = 3,01A; I 2 = 2,78A; I 3 = 1,93A; I 4 = 1,08A; I 5 = 0,23A; I 6 =0,85A. 12.13: Q 1 = 2,5àC; Q 2 = 2,25àC; Q 3 = 0,25àC. 6.14: U = 50,8V; I tng, U gim. 12.15: a) A = Q = 60J; b) A = 60J, Q = 21J. 12.16: 2kW. 12.17: a) 6 dóy //, mi dóy 10 ngun; P max = 65,25W; b) cú 6 cỏch mc: 3, 4, 5, 6, 10, 12 dóy //. 12.18: a) Cn ớt nht 6 ngun mc theo 2 cỏch sau: C1: mc ngun thnh 1 dóy 6 ngun ni tip v mc ốn thnh 2 dóy //, mi dóy 4 ốn; C2: mc ngun thnh 2 dóy //, mi dóy 3 ngun v mc ốn thnh 4 dóy //, mi dóy 2 ốn; b) 20 ốn, mc theo 2 cỏch: C1: mc ngun thnh 1 dóy 15 ngun ni tip v mc ốn thnh 2 dóy, mi dóy 10 ốn; hoc mc ngun thnh 5 dóy, mi dóy 3 ngun v mc ốn thnh 10 dóy, mi dóy 2 ốn. 12.19: a) 4; b) 2,4; 50%; 5,6, 64,3%; c) 1,2A. 12.20: 4 cỏch; 8 cỏch. 12.21: Loi 3: 5, 10, 15 cỏi v tng ng loi 5: 8, 5, 2 cỏi. 12.22: loi (5, 3, 1/3) cú (4, 18, 78) hoc (8, 11, 81) hoc (12, 4, 84) cỏi. 12.23: 5 cỏi; 6 cỏi. Chng 13: 13.1: a) B = 0; b) B = 5,7.10 5 T. 13.2: M thuc on I 1 I 2 , cỏch I 2 l d/3; M nm ngoi on I 1 I 2 cỏch I 1 v I 2 ln lt l 2d v d. 13.3: H = 31,8A/m. 13.4: a) B O1 = B O2 = 2,1.10 - 5 T; B M = 1,4.10 5 T ; b) B O1 = B O2 = 1,7.10 5 T; B M = 0. 13.5: B = 6,8.10 5 T. 13.6: a)h = 0; b) H = 79,6A/m. 13.8: F = 2,45N. 13.9: F = 0,8N. 13.10: a) theo chiu KH; b) à = 2 2lnaI oo m ; c) Khung dõy b kộo cng v tin v gn I o bi lc kộo à = 4 II F oo . 13.11: v = 36,3.10 6 m/s; W = 6,2.10 6 J; T = 5.10 9 s; L = 9,9.10 6 kgm 2 /s. 13.12: v o = 7,6.10 6 m/s. 13.13: b) v = 2.10 6 m/s theo phng vuụng gúc vi v ; B E ẹAP SO CAC BAỉI TAP 350 c) r = 2,3 cm. 13.14: a) 25,12.10 5 Wb; b) 5,02.10 4 J. 7.15: b) v = 0,67mm/s; n o = 2,8.10 23 ht/cm 3 . Chng 14: 14.1: a) U = 0,5V; b) U = 0,25V. 14.2: a) E o = 1,23V; b) = BScost. 14.3: U = 0,25V; u cỏnh trỏi cú in th cao. 14.4: a) 10 7 W; b) 0,04àC. 14.5: I max = 1,6A. 14.6: B = 0,3T. 14.7: E c = 0,3V; b) I = 10A; c) F = 3N; d) P c = 3W; e) P = 2W; f) P n = 5W. 14.8: cd qua hai thanh kim loi: ++ = 2 t t2r4 BD I 22 ; cng dũng in qua hai on vũng dõy: = 2 t II 1 ; = 2 t2 II 2 . . 4 2 3 1 e C C C C 0n == . 10 .9: o o U C C U = = 8000V. 10 .10 : U BA = 2V. 10 .11 : Q = 1, 59àC; Q = 10 ,6àC. 10 .12 : U2 mgd q = . 10 .13 : U = 20V. 10 .14 : cm1,2)2s( U4 Us x o =+=. 13 .3: H = 31, 8A/m. 13 .4: a) B O1 = B O2 = 2 ,1. 10 - 5 T; B M = 1, 4 .10 5 T ; b) B O1 = B O2 = 1, 7 .10 5 T; B M = 0. 13 .5: B = 6,8 .10 5 T. 13 .6: