1. Gii thiu mn hc: S tn ch: 2 (30 tit) nh gi:Kim tra cui k (thi vit): m Ln bng lm bi tp c cng im

2. Ni dung: Tnh hc ng hc imTi liu: C l thuyt ( Sanh) BT c l thuyt (Trn Vn Un) BT c l thuyt (V Duy Cng) 3. Phn 1: Tnh hc1. Cc khi nim c bn, cc tin tnh hc, linkt v phn lc lin kt2. H lc phng3. Ma st4. H lc khng gianTrong phn tnh hc s gii quyt hai bi ton c bn :- Thu gn h thc v dng n gin.- Tm iu kin cn bng ca h lc. 4. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:1. Vt rn tuyt iVt rn tuyt i l vt m khong cch gia haiim bt k ca vt lun lun khng i gi tt l vt rn 5. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:2. Trng thi cn bngTrong mt h quy chiu, vt rn cn bng khitrng thi chuyn ng ca vt khng i:- ng yn- Chuyn ng thng u 6. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:3. Lc-Lc l i lng c trng cho tc dng tng h c hc cavt ny i vi vt khc m kt qu lm thay i chuyn nghoc bin dng ca cc vt-Biu din lc:1. im t lc2. Phng, chiu ca lc3. Cng hay tr s ca lc. 7. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:4. Mt s khi nim khcH lc: H lc l tp hp nhiu lc cng tc dng ln vt rn.k hiuH lc tng ng: Hai h c cng tc dng c hcHp lc: Hp lc l mt lc tng ng vi h lcH lc cn bng: l h lc m di tc dng ca n, vt rnt do c th trng thi cn bng=0 8. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:4. Mt s khi nim khcNgu lc:H lc 2 lc song song ngcchiu, cng ln v khc gi.Cc c trng:+ Mp cha 2 lc gi l mp tc dng ca ngulc+ d: cnh tay n ca ngu lc+ Ngu lc l h lc c bit, c tc dng lmvt quay/ /,F F F F 9. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:5. Momen lc:a. Momen lc i vi 1 im:Mmen lc F i vi im O c xcnh bng cng thc: Phng: Vung gc mp(r,F) Chiu: quy tc tam din thun ln:FO( ) sinOM F FrsinFrFdH(d=OH: cnh tay n)( )OM F ( )OM F r F 10. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:5. Momen lc:a. Momen lc i vi 1 im:Biu thc gii tch:( )Ox y zi j kM F x y zF F F FOH/F OM ( )Oy z x yz xy z x yz xM F i j kF F F FF F ( )O ZM F 11. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:5. Momen lc:b. Momen lc i vi 1 trc:Mmen lc F i vi im Oc xc nh bng cngthc:Lin h:1( )ZM F Fh ( ) ( )Z O ZM F M F 1( )ZM F Fh 12. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktI. Cc khi nim c bn:5. Momen lc:c. Momen ca ngu lc: ln:nh l: Tng momen cc lc ca ngu lc i vi im O btk bng momen ca ngu lc y. ngha: Tc dng lm quay ca ca ngu lc l nh nhau ivi mi tm quay.m AB F .m F d 13. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:1. Tin 1 (h 2 lc cn bng):iu kin cn v hai lc tcdng ln mt vt rn cn bng lchng c cng phng tc dng,ngc chiu nhau v cng tr s. 14. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:2. Tin 2 (thm bt h lc cn bng):Tc dng ca mt h lc ln mt vt rn khng thay inu ta thm vo hay bt i hai lc cn bng nhau .H qu trt lc : Tc dng ca mt h lc ln mt vt rnkhng thay i khi ta di im t ca lc trn phng tc dngca nCh : 2 tin ch ng cho vt rn tuyt iv d: 15. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:3. Tin 3 : (Hp hai lc)Hai lc tc dng ln vt rn t ticng mt im c hp lc t tiim xc nh bng ngcho ca hnh bnh hnh m cccnh chnh l cc lc 1 2F F F nh l I : Mt h lc ng quy tc dngln vt rn c hp lc t ti im ngquy v vct hp lc bng tng hnh hcvct cc lc thnh phn 16. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:3. Tin 3 : (Hp hai lc)Hai lc tc dng ln vt rn t ticng mt im c hp lc t tiim xc nh bng ngcho ca hnh bnh hnh m cccnh chnh l cc lc 1 2F F F nh l II : Nu ba lc tc dng lnmt vt rn cn bng cng nm trongmt phng v khng song song nhauth ba lc phi ng qui. 17. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:4. Tin 4:ng vi mi lc tc dng ca vtny ln vt khc, bao gi cng cphn lc tc dng cng tr s,cng phng tc dng, nhngngc chiu nhau1 3F F 18. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktII. Cc tin tnh hc:5. Tin 5 (Ha rn vt)Nu di tc dng ca h lc no mt vt bin dng.Nh tin ny khi mt vt bin dng cn bng ditc dng ca mt h lc cho, ta c th xem vt nhvt rn kho st iu kin cn bng6. Tin 6 (Gii phng lin kt)Vt khng t do cn bng c th xem l vt t do cnbng nu thay lin kt bng cc phn lc lin kt 19. V d: 20. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktIII. Lin kt v phn lc lin kt1.Vt t do v vt chu lin kt:Vt t do: c th di chuyn v mi pha m khng b cn trVt chu lin kt: ngc li2. Lin kt v phn lc lin kt:Ti v tr lin kt tn ti cp lc c trng cho lin kt y-Phn lc lin kt l lc do vt gy ra lin kt tc dng lnvt chu lin kt. Lc cn li l p lc.-Lc khng phi l lc lin kt gi l lc hot ng. 21. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktIII. Lin kt v phn lc lin kt3.Mt s lin kt thng gp: 22. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktIII. Lin kt v phn lc lin kt3.Mt s lin kt thng gp:b. Lin kt bn l tr:c. Lin kt bn l cu: 23. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktIII. Lin kt v phn lc lin kt3.Mt s lin kt thng gp:d. Lin kt dy mm:e. Lin kt thanh: 24. Chng I: Cc khi nim c bn, cc tin tnh hc, lin kt v phn lc lin ktIII. Lin kt v phn lc lin kt3.Mt s lin kt thng gp:f. Lin kt ngm: 25. Chng II: H lc phngNi dung:-Thu gn h lc v dng ti gin-Tm iu kin cn bng-Kho st bi ton c th 26. Chng II: H lc phngI. Vector chnh v vector moment chnh1. Vector chnh:-L vector tng cc lc ca h-Phng php tnh ton: 2 pp+PP hnh hc (a gic lc):1 1 ... n iiR F F F F 27. Chng II: H lc phngI. Vector chnh v vector moment chnh1. Vector chnh:-L vector tng cc lc ca h-Phng php tnh ton: 2 pp+PP gii tch:Chiu trc, xc nh Rx, Ry:1 1 ... n kiR F F F F ,X k Y kX Yk kR F R F2 2,X YR R R 28. Chng II: H lc phngII. Vector chnh v vector moment chnh2. Vector moment chnh:-L vector tng cc moment cc lc thuc h i vi mttm-c im: h cc moment thnh phn cng phng(vung gc mp cha cc lc)+PP tnh: cng cc vector cng phng 29. Chng II: H lc phngII. Thu gn h lc v dng ti gin1. nh l di trc song song:Lc F t ti A tng ng lc F songsong cng chiu, cng ln nhng tti O v mt ngu lc c moment bngmoment ca F i vi O. 30. Chng II: H lc phngII. Thu gn h lc v dng ti gin2. Thu gn h lc phng v tm:H lc phng Fk bt k c th thu gn tng ng bngmt lc R v moment M0 ti im O ty sao cho:kiR F 31. Chng II: H lc phngI. Thu gn h lc v dng ti gin3. Dng ti gin:-H lc phng tng ng h lc cn bng nu:-H lc phng tng ng mt ngu lc nu:-H lc phng tng ng hp lc nu:-Nu th hp lc t ti O cch O 1 on:0, 0OR M 0, 0OR M 0, 0OR M 0, 0OR M OMdR 32. Chng II: H lc phngII. Thu gn h lc v dng ti gin4. Cc trng hp c bit:-H lc ng quy: im ng quy l tm thu gnkt qu-H ngu lc: vector chnh ca h ngu lc lun bng 0kt qu, 0OR F M 0, O OR M m 33. Chng II: H lc phngIII. iu kin cn bng ca h lc phng:1. iu kin cn bng:Vector chnh v moment chnh i vi tm bt k bng 02. Cch gii:a.b.c.(A,B,C khng thng hng)0, ( ) 0k O O kR F M m F 0, 0, ( ) 0k k O kX yk kF F M F0, ( ) 0 ( ) 0k A k B kXkF M F M F Ox AB( ) 0 ( ) 0 ( ) 0A k B k C kM F M F M F 34. Chng II: H lc phngIII. iu kin cn bng ca h lc phng:3. Cc i lng bt bin:-Vector chnh l i lng bt bin-Vector moment chnh ph thuc tm thu gn, theo cngthc: Tch v hng vector chnh v moment chnhbng nhau. ( )O O O OM M m R ( ) 0O O O O O O OM R M R m R R O O O OM R M R Const 35. Chng II: H lc phngIII. iu kin cn bng ca h lc phng:4. Lc tp trung v lc phn b:Lc tp trungLc phn b12Q qlQ ql 36. V d:xc nh phn lc v momen do ngm tc dng ln vt 37. Chng II: H lc phngIV. Bi ton h vt, bi ton vt lt1. Bi ton h vt-Kho st cn bng cc vt trong h cng lc-Phn bit 2 loi lc:+Ngoi lc: Fe+Ni lc: Fi-PP gii:a. Tch vt:i vi 1 vt ta c 3 ptcb, i vi h n vt 3n ptcbb. Ha rn:Xem ton h l vt rn, h ch chu tc dng ca ngoi lc, ta lp3 ptcb. Nu n s ln hn 3 th ta tch phi tch vt vit thm ptb sung. 38. Chng II: H lc phngIV. Bi ton h vt, bi ton vt lt1. Bi ton h vtV d 1: 39. IV. Bi ton h vt, bi ton vt ltI. Bi ton h vtV d 2: 40. IV. Bi ton h vt, bi ton vt ltI. Bi ton h vtV d 3: 41. IV. Bi ton h vt, bi ton vt ltI. Bi ton h vtV d 4: Bi ton ginCho gin chu lca. Tnh phn lc ti A v Bb. Tnh cc ng lc ca thanhAC,BCc. Tnh cc ng lc ca thanh cnli1 2( , )P P 42. IV. Bi ton h vt, bi ton vt ltI. Bi ton h vtNEXBYBYBXBXAYA ND- 43. Cc trng hp c bit:1. Bi ton n:Vt rn c th quay quanh trc c nhchu tc dng ca h lc phng vunggc trc quay*nh l: iu kin cn v ncn bng l tng momen cc lc tcdng i vi trc quay bng 0IV. Bi ton h vt, bi ton vt lt 44. IV.Bi ton h vt, bi ton vt ltCc trng hp c bit:2. Bi ton vt lt:Di tc dng ca h lc,vt c th mt lin kt vb lt-Moment lt-Moment giiu kin cn bng:g lM M1 2 3( ) ( ) ( )A A AM P M P M P 45. Cc trng hp c bit:3. Bi ton tnh nh v siu tnh:* Bi ton tnh nh:S n bng s ptcb* Bi ton siu tnh:S n ln hn s ptcbIV. Bi ton h vt, bi ton vt ltI. Bi ton h vt 46. Chng III: H lc khng gianI. Vector chnh v vector moment chnh1. Vector chnh:-L vector tng cc lc ca h-Phng php tnh ton: 2 pp+PP hnh hc (a gic lc)+PP gii tch(ch trong khng gian 3 chiu, ta c 3 trc Ox,Oy,Oz)1 1 ... n iiR F F F F 47. Chng III: H lc khng gianII. Vector chnh v vector moment chnh2. Vector moment chnh:-L vector tng cc moment cc lc thuc h i vi mttm( ) ( )( ) ( )( ) ( )X X k k kZ k kYY Y k k kX k kZZ Z k k kY k kXM m F y F z FM m F z F x FM m F x F y F 48. Chng III: H lc khng gianII. Thu gn h lc v dng ti gin1. nh l di trc song song:Lc F t ti A tng ng lc F songsong cng chiu, cng ln nhng tti O v mt ngu lc c moment bngmoment ca F i vi O. 49. Chng III: H lc khng gianII. Thu gn h lc v dng ti gin2. Thu gn h lc v tm:H lc Fk bt k c th thu gn tng ng bng mt lc Rv moment M0 ti im O ty sao cho:kiR F 50. Chng III: H lc khng gianI. Thu gn h lc v dng ti gin3. Dng ti gin ca h lc khng gian:-H lc khng gian tng ng h lc cn bng nu:-H lc khng gian tng ng mt ngu lc nu:-H lc khng gian tng ng hp lc nu:-Nu th h lc khng gianl mt h lc xon.0, 0OR M 0, 0OR M 0, 0OR M 0, 0,OR M R OM 51. Chng III: H lc khng gianIII. iu kin cn bng ca h khng gian:1. iu kin cn bng:Vector chnh v moment chnh i vi tm bt k bng 02. Phng trnh cn bng:0, ( ) 0k O O kR F M m F 0, 0, 0,k k kX y zk k kF F F( ) 0 ( ) 0 ( ) 0X k Y k Z kM F M F M F 52. Chng III: H lc khng gian V d: 53. Chng III: H lc khng gian 54. Chng IV: Ma St1. M hnh lc y trong lin kt ta:Xt mt qu cu lin kt ta trn mt sn:Phn tch R thnh 2 thnh phn:N:phn lc vung gc (chng ln)Fms: phn lc tip tuyn, cn tr (xu hng) chuyn ngtrt ma st trt (ngh)N hp vi P to thnh ngu lc, cn tr chuyn ng lnca vt momen cn ln MlKL: lin kt ta chu tc dng bi h lcRNmsFmsR F N ( , , )ms lF N M 55. Chng IV: Ma St2. nh ngha:L phn lc do mt ta tc ng, cn tr (xu hng)chuyn ng tng i ca vt kho st trn mt ta.3. Tnh cht:- trng thi tnh (CB), lc ma st nghc tnh da vo iu kin cn bng.- trng thi gii hn (sp chuyn ng)NmsF,ms lF fN M kNPk(f,k: h s ma st trt, ln c xc nh bng thc nghim,khng ph thuc din tch tip xc)lM 56. Chng IV: Ma St4. Gii bi ton cn bng khi c ma st:-Vit iu kin cn bng.-Gii Fms, Ml-5. Nn ma st:- trng thi cn bng gii hn- Nh vy, mun vt cn bng th Rnm trong nn ma st,ms lF fN M kN 57. Chng IV: Ma StMt vi h s ma st thng gp:* f cn ph thuc vn tc, nhng ta thng kho stvt cn bng v vn tc nh, nn coi f khng i 58. Chng IV: Ma St6. V d 1:Tm iu kin cn bng 59. Chng IV: Ma St