1. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 1TM TT CNG THC V L THUYT VT L 12-LUYN THII HC V CAO NGONG LC HOC VAT RAN1. Chuyen ong quay eu:Tc gc trung bnh tb ca vt rn l :=tb tTc gc tc thi :lim hay = ' (t)t t= 0Van toc goc = hang so.Toa o goc. = +t 0Van toc dai cua iem cach tam quay khoang r : v = r2. Chuyen ong quay bien oi eu:Gia tc gc trung bnh tb:=tb tGia tc gc tc thi :lim hay = ' (t)t t=0 Gia toc goc: = hang so.Van toc goc: = +t 0Toa o goc: 12 =0 +0t + t22 = 20Cong thc oc lap vi thi gian: 2 ( ) 03. Lien he gia van toc dai, gia toc cua mot iem tren vat ranvi van toc goc, gia toc goc:a v n22a r t = ; r= = ;ra = a2 + a2 = r2 2 + r2 4 = r 2 + 4 n taVect gia toc ar hp vi knh goc vi: 2 tan = =tan4. Momem:a. Momen lc oi vi mot truc quay co nh: M = F dP0arrOHnh 2F la lc tac dung;d la canh tay on (ng thang ha t tam quay vuong goc vi phng cua lcb. Momen quan tnh oi vi truc:= 2i i I mr (kg.m2)Vi : m la khoi lng,r la khoang cach t vat en truc quayPzOA rHnhvrt arn ar MO rrFLRHnhTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 2. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 2* Momen quan tnh cua thanh co tiet dien nho so vi chieu dai vi truc qua trung iem:I = 1 mL212* Momen quan tnh cua vanh tron ban knh R truc quay qua tam:I = mR2* Momen quan tnh cua a ac det truc quay qua tam:2I = 1 mR2* Momen quan tnh cua qua cau ac truc quay qua tam:2I = 2 mR5b. Momen ong lng oi vi mot truc:L = I (kg.m/s)RHnhHnhc. Momen quan tnh cua vat oi vi truc song song va cach truc qua tam G oan d .I I md2 G = + 5. Hai dang phng trnh ong lc hoc cua vat ran quay quanh mot truc co nh:M = I vaM = dLdt6. nh luat bao toan ong lng:Neu M = 0 th L = hang soAp dung cho he vat : 1 2 L + L = hang soAp dung cho vat co momen quan tnh thay oi: 1 1 2 2 I = I 7. ng nng ca vt rn quay quanh mt trc c nhW 1 I =ng nng W ca vt rn quay quanh mt trc c nh l : 22trong : I l momen qun tnh ca vt rn i vi trc quay l tc gc ca vt rn trong chuyn ng quay quanh trc2L2ng nng W ca vt rn quay quanh mt trc c nh c th vit di dng : W =Itrong : L l momen ng lng ca vt rn i vi trc quayI l momen qun tnh ca vt rn i vi trc quayng nng ca vt rn c n v l jun, k hiu l J.R8. nh l bin thin ng nng ca vt rn quay quanh mt trc c nh bin thin ng nng ca mt vt bng tng cng ca cc ngoi lc tc dng vo vt.1 1W = I I 2 = A122 22trong : I l momen qun tnh ca vt rn i vi trc quay1 l tc gc lc u ca vt rn2 l tc gc lc sau ca vt rnA l tng cng ca cc ngoi lc tc dng vo vt rnW l bin thin ng nng ca vt rn9. ong nang cua vat ran chuyen ong song phang:TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 3. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 312 2 C W = I + mv m la khoi lng cua vat, vC la van toc khoi tam212DAO ONG IEU HOA - CON LAC LO XOI. Dao ong ieu hoa:Dao ong ieu hoa la dao ong ma trang thai dao ong c mo ta bang nh luat dang sin( hoaccosin) oi vi thi gian .1. Phng trnh dao ong (phng trnh li o)x = Acos(t + )trong o :A, , la nhng hang so.A [m] la bien o ; [rad/s] la tan so goc [rad] la pha ban aut + [rad] pha dao ongGi tr i s ca li : x A C = ; x A CT = ln: |x|max =A (v tr bin) ; |x|min =0 (v tr cn bng)2. Van toc: v = Asin(t + ) (m)Gi tr i s ca vn tc:NPFhOxv A C = VTCB theo chieu dng ; v A CT = VTCB theo chieu am ln vn tc :v =A max (v tr cn bng ) ; 0 min v = ( hai bien )Chu y: vat i theo chieu dng v>0, theo chieu am v v = A2 x2 ; 24. Cong thc oc lap: 2 2222A2 a v4+=5. Tan so goc chu ky tan so:T m = k ; 2 2 ;m= = hoackFl0FhP lT = t ; t la thi gian thc hien N lan dao ong.Nf k= = ; hoacm122 f = 1T22NN1m= 1= m2 2T1T2m1km2T t= =N1T t= =21222 kN6. Moi lien he gia li o, van toc, gia toc:x = Acos(t + ) ;O(+)TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 4. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 4)2v = A t + =A t + + =A t + + = A t + +) cos(2sin( ) sin( ) cos( a = 2Acos(t + ) = 2Acos(t + + )** Van toc nhanh pha hn li o goc2** Gia toc nhanh pha hn van toc goc2** Gia toc nhanh pha hn li o goc 7. Nang lng dao ongW = 1 mv2 = 1m2A2 2 t + * ong nang: sin ( )22W = 1 Kx2 = 1KA2 2 t + Vi: k = m2t * The nang : cos ( )22* C nang: W = W + Wt =1 kA 2 =21 m2A 2 = W max = Wt max = Const2lu y:Con lac dao ong vi chu ky T, tan so f ,tan so goc th the nang, ong nang dao ong vichuKy T / 2 , tan so 2f, tan so goc 2 . Con c nang luon khong oi theo thi gian.* ng nng v th nng trung bnh trong thi gian nT/2 ( nN*, T l chu k dao ng) l:W 1 2 22 4= m A* Ti v tr c W = nWt ta c:+ To : (n + 1).1 kx221 kA2 x = =2A+n 1+ Vn tc:n +1 .n1 mv2 =21 m2A2 v = A2n+n 1* Ti v tr c Wt = nW ta c:+ To :n +1 .n1 kx221 kA2 x = A=2nn +1+ Vn tc: (n + 1).1 mv2 =21 m2A2 v = 2A+n 1x8. Lc phuc hoi: La lc a vat ve v tr can bang(lc ieu hoa),luon hng ve v tr can bangF kxr r= ; o ln F = k xTai VTCB: 0 min F = ; Tai vi tr bien : F = kA max9. Lc an hoi: la lc a vat ve v tr chieu dai t nhien l0Tai v tr co li o x:F k l x h = Vi 0 l = l l* Con lac co lo xo nam ngang: l = 0 do o h ph F = F* Con lac co lo xo thang ng: mg = kl = 300FhPPOPNl0FhPO(+) lTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 5. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 5+ Chieu dng thang ng hng xuong: F k l x h = ++ Chieu dng thang ng hng len : F k l x h = * Con lac nam tren mat phang nghieng mot goc so vi mat phang ngang:+ mg sin = kl+ Chieu dng hng xuong: F k l x h = ++ Chieu dng hng len : F k l x h = Lc an hoi cc ai: ( ) _ max F k l A h = +Lc an hoi cc tieu:Neu A l : Fh min = 0 ( v tr lo xo co chieu dai t nhien: Fh = 0)Neu A < l : ( ) _ min F k l A h = 10. Chieu dai t nhien lo , chieu dai cc ai lmax , chieu dai cc tieu lmin v tr lo xo co chieu dai t nhien: Fh = 0* l l l cb = + 0 (tai v tr can bang lo xo b dan)* l l l cb = 0 (tai v tr can bang lo xo b nen)* l l A cb = + max* l l A cb = min*A l l MNmax min = = , vi MN = chieu dai quy ao =2A2 2*l l +l max min cb2=11. Con lac lo xo gom n lo xo:Mac noi tiep: * o cng1 = 1 + 1 + ... +1k k k knt 1 2n * chu ky Tnt = 2mK1K2 m va 2 2nt kT 2 = T 2+T + ... +Tnt 12n Mac song song: * o cng n k = k + k + k +...+ k // 1 2 3* chu ky T// = 21 1 1 1m va 2 2// k= + +K+T T T T2n 212//MKK1 K2FAFBA BPmCon lac lo xo khi treo vat co khoi lng m1 th chu ky la T1 , khi treo vat m2 th chu ky la T2.** khi treo vat co khoi lng m = m + m th chu ky la : T 2 = T 2+ T21 2 12** khi treo vat co khoi lng m = | m m | th chu ky la : T 2 = | T 2 T2 |1 2 1212. Neu cac lo xo co o cng k1, k2kn, co chieu dai t nhien l1, l2, ln co ban chat giong nhauhay c cat t cung mot lo xo ko, lo th:n n l k =l k = l k ... = l k 0 0 1 1 3 313. Khong thi gian ngn nht vt i t v tr c to x1 n x2 t 2 1 = = vico x1 = 1Ax22sscoA=T/4X-AT/4-A/2 0 A/2T/6 T/12 T/12 T/6ATRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 6. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 6v ( 0 1,2 )14. Van toc trung bnh khi vat i t v tr x1 en x2 :v x tb x x2 1t t2 1t==15. Toc o trung bnh :V = St-A A022A32AT/8 T/8 T/6 T/12** Chu y: Trong mot chu ky van toc trung bnh bang 0 va toc o trungV = 4ATX16. Tnh qung ng ln nht v nh nht vt i c trong khong thi gian 0 < t < T/2 trongDH.Vt c vn tc ln nht khi qua VTCB, nh nht khi qua v tr bin nn trong cng mt khong thigian qung ng i c cng ln khi vt cng gn VTCB v cng nh khi cng gn v tr bin.S dng mi lin h gia dao ng iu ho v chuyn ng trn u.Gc qut : =t Qung ng ln nht khi vt i t M1 n M2 i xng qua trc sinS = A2max 2 sinS = A Qung ng nh nht khi vt i t M1 n M2 i xng qua trc cos )2min 2 (1 cosLu : + Trong trng hp t > T/2Tch t = n T + t2trong nN*;0 < t < T2Trong thi gianM2 M1P-A An T qung ng lun l n.2A.2P2 P1Do o, quang ng i c trong thi gian t > T/2 la:O2M-A PAx O xS = n A + A Min vi =tS = n A+ A Max va )22 2 sin22 2 (1 cos+ Tc trung bnh ln nht v nh nht ca vat trong khong thi gian t:Maxv StbMaxt=v S=v MintbMintvi SMax; SMin tnh nh trn.CON LAC N1. Phng trnh dao ong ieu hoa: khi bien o goc 00 10s = S0 cos(t + ) (m) vi : s = l ; S0 = l0 =0 cos(t + ) (rad) hoac (o)Vi s : li o cong ; So : bien o ; : li o goc ; 0 : bien o goc2. Tan so goc chu ky tan so: Khi bien o goc 00 10 = gl= 2 = 2T l gf gl12= =2 O1l1M(+)0ptOTn p pATRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 7. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 722NN1= 1= 2 2T1T212T t= =lN g1T t= =lN g21222 llN la so lan dao ong trong thi gian t3. Con lac vat ly: Tan so goc: = mgd ; Chu ky:IT Imgd= 2 = 24. phng trnh van toc khi bien o goc 00 10 :sin( ) 0 v = S t + (m/s)Gi tr i s ca vn tc :0 v S C = VTCB theo chieu dng ;0 v S CT = VTCB theo chieu am ln vn tc :max 0 v =S v tr cn bng ; 0 min v = hai bien5. Phng trnh gia toc (gia toc tiep tuyen) khi bien o goc 00 10 :a S t 2 s= 2 cos( + ) = s2)0(m/Gi tr i s ca gia tc :a = 2S C 0v tr bien am ; 0IH AOK0a 2S CT = v tr bien dng ln gia tc :a = S v tr bin ; a = 0 v tr can bangmax 0min 2Chu y: arluon hng ve v tr can bang (gia toc tiep tuyen), n arl gia tc hng tm.4a a2 a2 v s tp n = + = +Gia tc ton phn 4 22l6. phng trnh oc lap vi thi gian:2S = s + v ;0 22v222S 2= a + v ; a = 2S = 2lo 0 = + ; 2gl24 7. Van toc: Khi bien o goc o bat ky.* Khi qua li o goc bat ky:v2 = gl => 2 (cos cos ) 0 v = gl 2 (cos cos ) 0* Khi qua v tr can bang: = 0cos =1 2 (1 cos ) 0 v = gl C ; 2 (1 cos ) 0 v = gl CT* Khi hai bien: cos cos 0 0 0 = = v =Chu y: Neu 0 100 , th co the dung: 1 cos 0 = 2sin20 2=20 2 max 0 0 v = gl =S8. Sc cang day: Khi bien o goc 0 bat ky* Khi qua li o goc bat ky: (3cos 2cos ) 0 T = mg * Khi qua v tr can bang : 0 cos 1 (3 2cos ) vtcb max o = = T = T = mg TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 8. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 8* Khi qua v tr bien: 0 0 min 0 cos cos T T mg cos bien = = = =Chu y: Neu 100 ,0 th co the dung: 1 - cos 0 = 2220 0=2 2sin; (1 2 )max 0 T = mg + ; T mg 1= 202min*** Lc phuc hoi cua con lac n : F = mg sin = mg = mg s = m 2s phl9. Nang lng dao ong:1ong nang: (cos cos )20 W = mv = mgl 20(1 cos ) 1 W mgh mgl mgl t = = = Vi (1 cos ) h = l The nang: 22C nang: W =W +W = mgl (1 cos ) =W =W t 0 max t max Chu y: Neu 100 th co the dung: 2 = 2 0 =0o 2 21 cos 2sin0= m S = mg S = mgl = m l W 1 1 1 12 2 2 2 2 2 20 0 0 0l2 2 2 2* Ti cng mt ni con lc n chiu di l1 c chu k T1, con lc n chiu di l2 c chu k T2.** Con lc n chiu di l1 + l2 c chu k T 2 = T + T2221** Con lc n chiu di l1 - l2 c chu k T 2 = T T222110. Con lc n c chu k ng T cao h1, nhit t1. Khi a ti cao h2, nhit t2 th tac:T 2th=RT+Vi R = 6400km l bn knh Tri t, cn l h s n di ca thanh con lc.11. Con lc n c chu k ng T su h1, nhit t1. Khi a ti su h2, nhit t2 th tac:T h =R+2 2tT12. Con lc n c chu k ng T ti ni c gia tc g1. Khi a n ni c gia tc g2, th ta c:g =vi g = g g . con lc chy ng gi th chiu di dy tha:2 1 gTT222l l =1g g1Lu : * Nu T > 0 th ng h chy chm (ng h m giy s dng con lc n)* Nu T < 0 th ng h chy nhanh* Nu T = 0 th ng h chy ng* Thi gian chy sai mi giay la:TT =T* Thi gian chy sai mi ngy (24h = 86400s): 86400(s)T =12. Khi con lc n chu thm tc dng ca lc ph khng i:Lc ph khng i thng l:ur r* Lc qun tnh: F = maur r, ln F = ma ( F a)r rLu : + Chuyn ng nhanh dn u a v(v rc hng chuyn ng)TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 9. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 9r r+ Chuyn ng chm dn u a vur ur* Lc in trng: F = qEur ur, ln F = |q|E (Nu q > 0 F Eur ur; cn nu q < 0 F E)uur ur urKhi : P' = P + Fur)gi l trng lc hiu dng hay trong lc biu kin (c vai tr nh trng lc Puruur urg ' g Fm= +gi l gia tc trng trng hiu dng hay gia tc trng trng biu kin.Chu k dao ng ca con lc n khi :T lg = 2Cc trng hp c bit:urc phng ngang:+ Ti VTCB dy treo lch vi phng thng ng mt gc c: tan F* FP =+ g ' g2 (F )2= + ;mp = p g = gcos cosurc phng thng ng th g ' g F* Fm= urhng xung th g ' g F+ Nu Fm= +urhng ln th g ' g F+ Nu Fm= TEFP 'P13. o chu k bng phng php trng phng xc nh chu k T ca mt con lc l xo (con lc n) ngi ta so snh vi chu k T0 ( bit) camtcon lc khc .Hai con lc gi l trng phng khi chng i qua VTCB cng mt lc theo cng mt chiu.Thi gian gia hai ln trng phng lien tiep :TTT T00 =Nu T > T0 = nT = (n+1)T0. vi n Z+Nu T < T0 = nT0 = (n+1)T.CAC LOAI DAO ONG1. Dao ong t do: Dao ong t do la dao ong co chu ky hay tan so ch phu thuoc vao ac tnh cuahe dao ong, khong phu thuoc vao cac yeu to ben ngoai.VD: + Con lac lo xo dao ong trong ieu kien gii han an hoi.+ Con lac n dao ong vi bien o goc nho,bo qua sc can moi trng va tai mot a iemxac nh2. Dao ong tat dan: Dao ong tat dan la dao ong co bien o giam dan theo thi gian.Nguyen nhan: Nguyen nhan dao ong tat dan la do lc ma sat hay lc can cua moi trng.Cac lc nay luon ngc chieu vi chieu chuyen ong, nen sinh cong am v vay lam giam c nangcua vat dao ong. Cac lc nay cang ln th s tat dan cang nhanh.* Mt con lc l xo dao ng tt dn vi bin A, h s ma st .+ Qung ng vt i c n lc dng li l:W W = mgS kA2 = mgS 0 10 2S kA2= ;mg2t OTxTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 10. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 10Neu lo xo nam nghieng goc th:2S = kAmg2 cosA = mg = gk1 2 2 = => 2( ) 12+ o giam bien o trong mot chu ky: k A A kA mg4A24 4+ So lan dao ong trc khi dng:AgkA= =mgN AA24 4=+ Thi gian dao ong cho en luc dng:Agt T N T kAmg=4 2 = =* e m luon nam yen tren M th bien o cc ai la:A g (m +M)gk =2* e m khong trt tren M th bien o dao ong la:A g (m +M)g la he so ma sat gia m vak = 2mMk mHnh 1M3. Dao ong cng bc: Dao ong cng bc la dao ong cua he di tac dung cua mot ngoai lcbien thien ieu hoa, co dang: F = F cost 0 gom hai giai oan.* Giai oan chuyen tiep: dao ong cua he cha on nh, gia tr cc ai cua li o (bien o) ctang dan, cc ai sau ln hn cc ai trc.* Giai oan on nh: khi o gia tr cc ai khong thay oi(bien o khong oi) va vat dao ongvi tan so cua lc cng bc fLu y:Dao ong cua vat trong giai oan on nh goi la dao ong cng bc.Bien o phu thuoc vao quan he gia tan so ngoai lc f vi tan so rieng cua he f0.** S cong hng cBien o A cua dao ong cng bc at gia tr cc ai khi tan so cua lc cng bc bang tan sorieng cua he dao ong. ( ieu chnh tan so cua lc cng bc, ta thay khi ) flc=f rieng Max A = ANeu lc ma sat nho th cong hng ro net hn(cong hng nhon)N e u l c m a s a t l n t h c ong hng t ro net hn(cong hng tu)TONG HP DAO ONG1. Tong hp 2 dao ong ieu hoa cung phng, cung tan soGia s mot vat thc hien ong thi 2 DH cung phng, cung tan so:cos( ) 1 1 1 x = A t + va cos( ) 2 2 2 x = A t +Dao ong hp la: cos( ) 1 2 x = x + x = A t +A2 = A + A + A A ;2221Vi 2 cos( ) 1 2 2 1A Atan sin sin +1 1 2 2cos cosA A +1 1 2 2=* Neu hai dao ong thanh phanCung pha: = 2k th A=Amax = A + A1 2 Ngc pha: = (2k +1) th A=Amin = A A2 Vuong pha: = k + th 22(2 1)21 A = A + A2Lech pha nhau bat ky: 2 1 2 A A A A + AyxMAxAyA2yA1yM2M1AA11A2x A1xOA22 TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 11. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 11** Chu y: Neu e cho cos( ) 1 1 1 x = A t +va cho phng trnh tong hp x = x + x = A cos( t + ) .1 2 Tm x = A cos( t +) 2 2 2 Th: A 2 = A 2+ A 2 2 A A cos( ) ;2 11 1A Atan sin sin 1 1A Acos cos 1 1=2. Tong hp n dao ong ieu hoa cung phng, cung tan so:cos( ) 1 1 1 x = A t + , cos( ) 2 2 2 x = A t + , cos( ) n n n x = A t +Dao ong hp la: x= ... cos( ) 1 2 x + x + + x = A t + nThanh phan tren truc nam ngang ox: x n n A A cos A cos ... A cos 1 1 2 2 = + + +Thanh phan tren truc thang ng oy: y n n A A sin A sin ... A sin 1 1 2 2 = + + +2 2x y A = A + A ; tgAyAx =SONG C HOCI. nh ngha: Song c hoc la cac dao ong c hoc lan truyen theo thi gian trong mot moi trngvat chat. Co hai loai song: Song doc la song co phng dao ong trung vi phng truyen song Song ngang la song co phng dao ong vuong goc vi phng truyen song.* Lu y: song ngang ch truyen c trong moi trng ran va tren mat chat longII. Cac ai lng ac trng cua song1. Van toc song (toc o truyen song )v = van toc truyen pha dao ong, van toc phu thuoc vao nhiet o, tnh an hoi cua moitrng,mat o phan t. Trong mot moi trng xac nh v = const.* Moi si day c keo bang mot lc cang day va co mat o dai la th toc o truyen song tren day la:v =Chu y: Toc o truyen song khac toc o dao ong cua phan t vat chat co song truyen qua2. Chu ky va tan so songChu ky song = chu ky dao ong cua cac phan t co song truyen qua = chu ky cua nguon songTan so song = tan so dao ong cua cac phan t co song truyen qua = tan so cua nguon song:f = 1ToA3. Bc song: la quang ng song truyen trong mot chu ky, bang khoang cach gia hai iemgan nhau nhat tren cung mot phng truyen song giao ong cung pha. = vT = vf4. Bien o song AA song = A dao ong= bien o dao ong cua cac phan t co song truyen quaTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 12. GV. TRNG NH HUNG T: 0908.346.838 Trang 125. Nang lng song W: Qua trnh truyen song la qua trng truyen nang lngW W 1 m A song dao dong = 2 2_ 2a. Neu song truyen tren mot ng thang ( mot phng truyen song) nang lng cua songkhong oi, bien o khong oi W = const => A = constb. Neu song truyen tren mat phang(song phang) nang lng song giam t le quang ngtruyen song va bien o giam t le vi can bac hai quang ng truyen songW ~ 1 A~ 1M rrM Mc. Neu song truyen trong khong gian (song truyen theo mat cau) nang lng song giam t lebnh phng quang ng truyen song va bien o giam t le vi quang ng truyen songW ~ 1 A~ 1 M 2 rm MIII. Phng trnh songu = A cos ( t d ) = A cos( t d) = A cos t 2 dviM t du A t d M cos ( ) cos( ) cos 2 A t dA t d= + = + = +u = A t d + = A t d+ = A t dviM + t du A t d M cos ( ) cos ( ) cos 2 A t d= + A t d= + + = + + d d d d N M N MMNTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )rPhng trnh song tai mot iem trong moi trng truyen song la phng trnh dao ong cuaiem o.1. phng trnh truyen songa. Gia s phng trnh song tai O: u = AcostTh phng trnh song tai mot iem M cach O mot khoang d la:* Neu song truyen t O en M thvvv* Neu song truyen t M en O thvvTai mot iem M xac nh trong moi trng:M d = const : u la mot ham bien thien ieu hoa theo thi gian t vi chu ky T.Tai mot thi iem xac nh: t = const: M d = x : u la mot ham bien thien ieu hoa trong khong giantheo bien x vi chu ky .b. Gia s phng trnh song tai O: u = Acos(t + )Th phng trnh song tai mot iem M cach O mot khoang d la:* Neu song truyen t O en M thcos[ ( ) ] cos[( ) ] cos[ 2 ]vvv* Neu song truyen t M en O th+ vvIV. o lech pha:o lech pha dao ong gia hai iem M,N bat ky trong moi trng truyen song cach nguon O lanlt la dM va dN: :v= = 2* Neu M va N dao ong cung pha th:O vr MM vr Owww.MATHVN.comWWW.MATHVN.COM 13. GV. TRNG NH HUNG T: 0908.346.838 Trang 132 d d N M k2 d d = k (k)N M Z = k2 MN = * Neu M va N dao ong ngc pha th:2 d d N M(2k 1) = (2k +1) = + MN d d = k + N M (kZ )2(2 1)* Neu M va N dao ong vong pha th: d d N Mk = k + MN = + 2(2 1)22 (2 1)d d = k + N M (kZ )4(2 1)* Neu hai iem MN nam cung tren cung mot phng truyen song cach nhau oan d: = = 2 d( d = d d = MN )N M dMN v* Neu M va N dao ong cung pha th: d = k k N** Neu M va N dao ong ngc pha th:d = (k + 1 ( k N )d = k + hoac )2(2 1)2* Neu M va N dao ong vong pha th:d = k + (k N )4(2 1)SONG AMd1 dO M N1. nh ngha: Song am la song c hoc lan truyen trong moi trng vat chat nh ran, long, kh.Con ngi co the nghe tan so 16Hz f 2.104Hz (Am thanh)Song co tan so nho hn 16Hz la song ha am, song co tan so ln hn 20.000 Hz la song sieupI = W =I pL B = I suy ra LI 100L dB = I 1B =10 dB (dB: e xi ben)0 I = 10 W /m cng o am chuan ng vi f=1000HzI = cong thc ben L phai co n v BenL L I I21210 2 12 1 I2 L LITRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )am.Song am truyen c trong chat ran, long, kh khong truyen c trong chan khong, van tocsong am phu thuoc vao mat o phan t va tnh an hoi va ca nhiet o. Toc o truyen am giam dant ran, long, kh.2. o cao cua am. La ac trng sinh ly cua am phu thuoc vao tan so.Am co tan so ln goi la am cao(thanh), am co tan so thap goi la am thap ( tram )3. Cng o am I: la nang lng am truyen qua mot n v dien tch at vuong goc vi phngtruyen am trong mot n v thi gian.St .S(n v : W /m2 ) ; P = cong suat ; S la dien tch;Cng o am tai iem cach nguon oan R trong khong gian: =4 R24. Mc cng o am L:0( ) lgII= (B n v Ben)0( ) 10lgI12 2 = lg( ) lg( ) = lg( )100III1Chu y: Tai con ngi ch phan biet c hai am co mc cng o am hn kem nhau 10dB.5. Tan so cua am:Am c ban hay con goi la hoa am bac 1 la: f0d2www.MATHVN.comWWW.MATHVN.COM 14. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 14f k v k = ( k=1,2,3)f = v ( ch co 1 bo song); hoa am bac 2 th k=2; bac 3 th k=3;6. Am sac: la ac trng sinh l cua am, phu thuoc vao tan so va bien o (o th am) giup ta7. o to cua am: la ac trng sinh l cua am, phu thuoc vao tan so va mc cng o am8. Ngng nghe: La am co cng o nho nhat ma tai ngi con co the nghe c. Ngng9. Ngng au: Neu cng o am len ti 10W/m2 ng vi mc cng o am 130dB, oi vimoi tan so, song am gay cam giac nhc nhoi trong tai. Gia tr cc ai o cua cng o am goi langng au. Ngng au ng vi cng o am la130dB va hau nh khong phu thuoc vao tan so cuaam.Chu y: * khi nguon am hay may thu tien lai gan nhau th lay dau (+) trc vM va dau (-)Giao thoa song la s tong hp hai hay nhieu song ket hp trong khong gian, trong o co nhng choco nh bien o song tong hp c tang cng hay giam bt.I.Giao Thoa Ca Hai Sng Pht Ra T Hai Ngun Sng Kt Hp S1,S2 Cch Nhau Mt Khong l:S1* Mot ong sao hoac xaxophon co chieu dai l (mot au kn mot au h ) co tan so:s2Hoa am bac 2: f2=2f0 ; Hoa am bac 3: f3=3f0 ; Hoa am bac n: fn=nf0* Mt day an hai au co nh co chieu dai l song dng co tan so:2lAm c ban ng vi k=1 :1 2lf m v m = (m=1,3,5,7) ch co hoa am bac le.4lAm c ban ng vi m=1 thf = v (song co 1 nut va1 bung)1 4lHoa am bac 3: m=3 thf = 3v (song co 2 nut 2 bung )4l3Hoa am bac 5: m=5 thf = 5v (song co 3 nut 3 bung )4l5phan biet cac nguon am.nghe phu thuoc vao tan so cua am.(moi tan so khac nhau th ngng nghe khac nhau).10. Mien nghe c: Nam gia ngng nghe va ngng au.Vi tan so chuan 1000Hz ngng nghe la 0 dB, ngng au la 130 dB11. Hieu ng op_Ple:vM la toc o chuyen ong cua may thu = vs la toc o chuyen ong cua nguon amff v vMv vSmv la toc o truyen am trong moi trngtrc vS va lay dau ngc lai cho trng hp may thu va nguon tien ra xa nhau.* khi may thu ng yen th vM=0, khi nguon am ng yen th vS=0GIAO THOA SONGXt im M cch hai ngun ln lt d1, d21. TRNG HP CO PHA BAT KY:Phng trnh sng ti 2 ngun 1 1 u = Acos(2 ft + ) v 2 2 u = Acos(2 ft + )Phng trnh sng ti M do hai sng t hai ngun truyn ti:u ft d 1 1 Acos(2 2 ) Mu ft d = 1+ v 2= Acos(2 2 +) 2 M2 Phng trnh giao thoa sng ti M: uM = u1M + u2MTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 15. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 15u Ac d d c ft d d + + = 2 os 1 2 + os 2 1 2 + 1 2 M 2 2 A A c d d = + Bin dao ng ti M: 2 os 1 2M 2 vi 1 2 = Ch : * S cc i: (k Z)l k l + < < + + 2 2 l l k * S cc tiu: 1 + < < + 1 + (k Z)2 2 2 22. TRNG HP HAI DAO ONG KET HP CUNG PHAGia s phng trnh song tai hai nguon ket hp 1, 2 O O la:cos( ) 1 2 u = u = A t +Xet mot iem M cach hai nguon d1 = O1M,d2 = O2MPhng trnh song tai M do 1 2 O ,O truyen tiu = A cos( t 2 d 1 + )va cos( 2 2 M )1 u = A t d + M2 Coi A = constPhng truyen song tong hp tai M:= + = 2 cos ( ) cos ( ) 1 2 2 1 1 2 u u u A d d t d d M M Mo lech pha cua hai song t hai nguon truyen ti tai M: + + 2 d2 d1 == 2 cos ( ) 2 1 A A d d M Bien o song tong hp tai M: Md1 d2S1 S2T 2 T 1 T0 T1O1 O2 - 2 - 1 0 1 2iem co bien o tong hp cc ai Amax=2A (hai song gi ti cung pha)th: d cos ( d ) = 1 (d d ) = k d d = k , k = so nguyen2 1 2 1 2 1 iem co bien o tong hp cc tieu (hai song gi ti ngc pha) Amin =0 (hay triet tieu) d d d d kcos ( ) 0 ( ) (2 1) 2 1 2 1 = = + 2d d = k + k = so nguyen2(2 1) 2 1So cc ai giao thoa (hay so bung song trong khoang gia hai nguon , ) : 1 2 O O l < k < l So cc tieu giao thoa ( hay so nut song trong khoang gia hai nguonO O1, ) : 1 2 2l k l 1 < < 2 2 1 1 23. TRNG HP HAI DAO ONG KET HP NGC PHAGia s phng trnh song tai hai nguon ket hp 1, 2 O O la:cos( ) 1 u = A t va cos( ) 2 u = A t + = Acos(t)Xet mot iem M cach hai nguon d O M d O M 1 1 2 2 = , =Phng trnh song tai M do 1 2 O ,O truyen tiO1 O2T - 2 T - 1 T0 T1 T2TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 16. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 16u = A cos( t 2 d 1 )va cos( 2 2 M )1 u A t d M = 2 Coi A = constPhng trnh song tong hp tai M:u u u 2Asin (d d ) d d 2 1 sin t 2 1M 1 M 2 Mo lech pha cua hai song t hai nguon truyen ti tai M:= + = + + = 2 d2 d1 = 2 sin ( ) 2 1 A A d d M Bien o song tong hp tai M: * iem co bien o tong hp cc ai Amax =2A (hai song gi ti cung pha)th: d d d d ksin ( ) 1 ( ) (2 1) 2 1 2 1 = = + 2d d = k + k = so nguyen2(2 1) 2 1* iem co bien o tong hp cc tieu (hai song gi ti ngc pha) Amin= 0 (hay triet tieu) d sin ( d ) = 0 (d d ) = k d d = k k = so nguyen.2 1 2 1 2 1 * So cc ai giao thoa ( so bung song trong khoang gia hai nguon , ) : 1 2 O O12l k l 1 < < 2* So cc tieu giao thoa ( so nut song trong khoang gia hai nguon , ) : 1 2 O O l < k < l 4. HAI NGUON DAO ONG VUONG PHA:Gia s phng trnh song tai hai nguon ket hp O O la:1, 2 u Acost va = )1 2u = A t +cos( 2Xet mot iem M cach hai nguon d O M d O M 1 1 2 2 = , =Phng trnh song tai M do 1 2 O ,O truyen tiu = A cos( t 2 d 1 )va M )1 u A t d = + ( Coi A = const)M 2cos( 2 22Phng trnh song tong hp tai M:u u u A d d t d d M M M + + 2 cos ( ) 1 2 2 1 1 2cos ( )4= + = 4 A A d d M= Bien o song tong hp tai M: 2 cos ( ) 2 14* iem co bien o tong hp cc ai Amax=2A (hai song gi ti cung pha)th: d d d d k = = cos ( ) 2 1 2 11 ( )44d d = k + k = so nguyen2 1 4* iem co bien o tong hp cc tieu (hai song gi ti ngc pha) Amin =0 (hay triet tieu) d d d d k (2 1) cos ( ) 2 1 2 10 ( ) = = + 244 d d = k + + k = so2 4(2 1) 2 1nguyen* So cc ai giao thoa bang so cc tieu va bang:14l k l 1 < < 4TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 17. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 17** Tm so ng dao ong co bien o cc ai, cc tieu tren oan AB cach hai nguon lan ltla:A A d d1 2 , B B d d1 2 , .at A A A d d d1 2 = va B B B d d d1 2 = va gia s A B d < d .* Neu hai nguon dao ong cung pha:+ so iem cc ai: A B d k d ( vi k la so nguyen)+ so iem cc tieu: A B d (k + 0.5) d* Neu hai nguon dao ong ngc pha:+ so iem cc ai: A B d (k + 0.5) d+ so iem cc tieu: A B d k d** Chu y: Neu tnh tren oan AB th lay ca dau bang, trong khoang AB th khong lay daubang.SONG DNG1. nh ngha: La s giao thoa gia song ti va song phan xa hnh thanh cac nut va bung song conh trong khong gian goi la song dng2.Tnh chat: Song dng la trng hp ac biet cua giao thoa song: la s giao thoa cua hai songket hp truyen ngc chieu nhau tren cung mot phng truyen song.3. Khoang cach gia 2 nut song hay gia hai bung song bat ky: d d k BB NN = = ( k la so nguyen)24. ieu kien song dng 2 au co nh (nut) :Abung l = k , k = so bo song2bo song2So nut : N = k +1 nutSo bung: N k bung =*. Bc song ln nhat co the tao ra la: 2l max =Khoang cach gia mot nut song va 1 bung song bat ky:d = k + NB k = so nguyen,4(2 1)5. Phng trnh dao ong tong hp khi hai au co nh (song truyen t A)Gia s phng trnh song ti tai B la : u = Acos(t + )2 sin(2 )sin( )u = A d t + +l2B A x M6. ieu kien song dng mot au co nh (nut song) mot au t do(bung song)l = k + hoac4(2 1) l = k + hoac2 4dl = k + k = so bo song2( 1)2So nut : N = k +1 nutSo bung : N = k +1 bung*. Bc song ln nhat co the tao ra la: 4l max =7. Phng trnh dao ong tong hp khi co song dng mot au co nhmot au t do, tai M cach au t do mot oan d.dMBAB2TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 18. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 18Gia s phng trnh song ti au t do nhan c la : u = Acos(t + )2 cos(2 )cos( )u = A d t +MACH DAO ONG VA SONG IEN T1. ien tch ien tch gia hai ban tu C bien thien ieu hoa theo phng trnh (**)Ta co : = = = = qe Li u Lq q Lq qq = 2q (*) ( vi u=e; i=q; r =0 )LCC(*) la phng trnh vi phan luon co nghiem : 1 tan so goc(rad/s)0 cos( ) q = Q t + (**) Vi: = =LC2. Suat ien ong cam ng trong cuon day L (co r = 0)e = u = q = QO cos(t + )(v) q = Cu Q = CU0 0 CcVi u hieu ien the tc thi gia hai ban tuq ien tch gia hai ban tu thi iem t3. Cng o dong ien:Cng o dong ien chay trong cuon day L bien thien ieu hoa:i = q, Qsin(t + ) =Q sin(t + + ) oB = B t + +i = I t + + = I t + + )Hay: )2sin( ) cos( 0 02cos( 0Vi 0 0 I =Q cng o cc aiK+ -CALBTrong mach dao ong LC th u va q dao ong cung pha va cung cham pha /2 so vi i. = + /2 i u*****. Phng trnh c lp vi thi gian:2Q = q + i ; 2 2 2 22 20 22+ u2=i0 I = i + q ; 1 2020UI4.Chu ky tan so cua mach dao ong:Chu ky : Tan so: Bc song ien t trong chan khongT = 2 LC ; = c = . = 2 c = 3.108 m/s= 1 ; cT c LCLCf2f* Neu C gom C1// C2 th : 21 1 1f f fT 2= T 2+T va // 122= + va 22212// 2= 2+// 121 1 1T T T nt= + va 2* Neu C gom C1nt C2 th : 222121 1 1 f 2 = f 2+ f va nt 1222= +212nt1 1 1T T T* Neu L gom L1// L2 th: 2= + va 22212//1 1 1 f 2= f 2+ f va // 1222= +212//* Neu L gom L1nt L2 th: 21 1 1f f f ntT 2 = T 2+ T va nt 122= + va 222122 = + nt221** Lc ny : // 1 2 f f f f nt = hoc // 1 2 = nt hoc // 1 2 T T T T nt = ** Neu mach co L thay oi t min max L L va C thay oi t min max C Cth: max max max = c.2 L C va min min min = c.2 L CTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 19. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 195. Nang lng cua mach dao ong:2* Nang lng ien trng( tap trung tu C) thi iem t : Cu quW = q = = 2C11222Trong o: cos( ) 0 q = Q t +0 2W Q = t +cos ( )C22W 1 Li t =* Nang lng t trng (tap trung cuon cam L) thi iem t : 22Trong o: i = q'= I sin(t + + ) o hoac i = q = - Qosin(t + )W = 1 LI 2 2 t + t osin ( )2W = W + W = 1 Li +1Cu t * nh luat bao toan nang lng: 2 222* Nang lng dao ong cua mach (nang lng ien t)211 t = = = = = 2 =20LI CU constW W W Qomax max 2C022Mch dao ng c in tr thun R 0 th dao ng s tt dn e mach dao ong duy tr th phai bu phan nang lng mat i di dang nhiet nangQ = I 2 Rt duy tr dao ng cn cung cp cho mch mt nng lng c cng sut:2 2 2 22 I R C U R U RC0 0P = = =2 2LNeu trong mach co ien tr thuan R cang nho th xay ra cong hng ro hn (nhon hn)Chu y: * Trong dao ong song ien t th ien trng va t trng dao ong cung pha vi nhau vachung tao vi phng truyen song thanh mot tam dien thuan (tng oi mot vuong goc).* Neu mach dao ong vi chu ky la T, tan so f th nang lng ien trng va nang lng ttrng dao ong vi chu ky T/2 tan so 2f.* Nang lng ien trng va nang lng t trng dao ong ngc pha nhau* Sng in t mang nng lng, nng lng ca sng in t t l vi lu tha bc bn catn s( W f 4), nh vy tn s ca sng in t cng cao th nng lng sng cng ln. Sng in t c y cc tnh cht ca sng c hc nh: Tun theo cc quy lut truyn thng,phn x, khc x, nhiu x.Pht thu sng in tTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 20. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 20IEN XOAY CHIEUI. Nguyen tac tao dong ien xoay chieu1. T thong: T thong gi qua mot khung day co dien tch S gom N vong day quay eu vi vantoc goc quanh truc quay trong mot t trng eu B cos( ) cos( ) 0 = NBS t + = t + n v : Wb(ve be)Vi: = NBS 0 r r = khi t = 0t thong cc ai ; (n B)2. Suat ien ong cam ng do may phat tao ra:cos( ) cos( )( ) 0 e NBS t E t V e e = = + = +0 0 E =NBS = : suat ien ong cc ai = e : pha ban au23. Tan so cua suat ien ong cam ng cung nh cua dong ien: f = n pn (vong/s) toc o quay cua roto.p so cap ccCh : Mt my pht in c 1 cp cc t mun pht ra vi tn s 50Hz th phi quay vi tc n = 50 vong/s; c 10 cp cc t mun pht ra vi tn s 50Hz th phi quay vi tc n = 5 vong/s .S cp cc tng ln bao nhiu ln th tc quay gim i by nhiu ln.4. Hieu ien the cung cap cho mach ngoai:cos( ) 0 u u =U t + e u =u : la hieu ien the tc thi ; U0 : la hieu ien the cc aiNeu bo qua ien tr trong cua may phat th : u = e5. Cng o dong ien mach ngoai:cos( ) 0 i i = I t +i: la cng o dong ien tc thi; I0 :cng o dong ien cc ai6. Cac gia tr hieu dung:UoE = E 0 U = I = Io(V)2;2;27. Nhiet lng toa ra tren ien tr R: Q = RI2t =P.t (J)II.oan mach ch co mot phan t:1. oan mach ch co ien tro thuan R* u =U cos t R 0 * i =I cost 0 * nh luat Om: I0=U0 hay I=RA R BU (A)R* ghep ien tr:1 1 1 ... 1// 1 2rrO I= + + + va nt n R = R + R + ... + R 1 2n R R R R* Gian o vect: oan mach ch co R u va i cung pha : = 0 R 2. oan mach ch co cuon day thuan cam L:* u =U cos t L 0 * )i = I cos( t 02* nh luat Om: I0=A BU0 hay I=ZLrU0LU vi Z L L = cam khang ;ZLURrI0+TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 21. GV. TRNG NH HUNG T: 0908.346.838 Trang 21* ghep cuon day: nt n L = L + L + ... + L 1 2 va1 = 1 + 1 + ... +1// 1 2n L L L L* Gian o vect: oan mach ch co L th u luon nhanh pha hn i goc . Suy ra2I U00 = hayCA BI = U vi= 1 dung khangZC 1 = 1 + 1 + ... +1r . Suy rar r r rtg U U U UZ Z0 L 0C L CL CA R L M C BrULr r+UL UCI =U max ;2rOP Umax = ; cos =1rrTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )2 = L3. oan mach ch co tu ien co ien dung C:* u U t C cos 0 =* )2cos( 0i = I t +* nh luat Om:C ZC ZC* ghep tu ien n C = C + C + ... + C // 1 2 vaC C C Cnt 1 2n * Gian o vect: oan mach ch co C th u luon cham pha hn i goc22 = CIII. Mach R,L,C noi tiep:u = u + u + u U = U + U +UR L c R L C T gian o vect:U2 =UR2 + (UL UC )2 vi U = IZ;vi Z = R2 + (ZL ZC )2 goi la tong tr macho lech pha cua u so vi icos( ) 0 u u =U t + va cos( ) 0 i i = I t + =u iVi:RUURR===0* Neu tg > 0 > 0 Z Z LC L > C >1/mach co tnh cam khang th u sm pha hn i* Neu tg < 0 < 0 Z Z LC L < C Z Z ;* Neu L C > / 4 R < Z Z* Neu = / 2 mach khong cha R;* Neu / 2 mach phai cha R;I0U0C+U ABUR IUCwww.MATHVN.comWWW.MATHVN.COM 22. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 22Cong suat: P =UI cos = I 2 (R + r) Vi he so cong suat la:R r U +UR r U+Z=cos =UUUUI U* Chu y : = = = = = C= ......CR LLMNMNABABZZRZZNeu cuon day co r th: ( R r )2 ( L C )2 U = U +U + U U va ( )2 ( L C )2 Z = R + r + Z Ztg U U Z ZL CR rU UL CU U 0 0L CU U+R r+R r+===0 0** Cac dau hieu nhan biet cong hng ien thng gap:ieu kien cong hng1. ieu kien can : Cho L hoac C hoac hoac f thay oi e ieu kien u xay ra.2. ieu kien u :+LC= = 1 = 1Z ZfL C LC2+P U2RZ R I Umin max max = = =R+ R LC L C U =U U = 0U =U max+ = 0 tan = 0cos =1 ( u va i cung pha ).+ u cung pha vi uR ; u cham pha / 2 vi uL ; u nhanh pha / 2 so vi uC* * Neu R,U la hang so. Thay oi L hoac C, hoac hoac f:2P RI R U2 22L C R Z Z( ).+ = =P Z Z P U L C2Rmax max = =cong hng cos =1* * Neu L,C, ,U= const. Thay oi R e cong suat at cc ai.P R r Z Z2( ) ( ) L C R + r = Z Z + + L C CauChy max ( )R +rmin2P U = =>max R r2( +)R L,r CA BR LCA BZ = (R + r) 2 Cos = 2 va tan = 12** Cho R thay oi e cong suat tren bien tr R at cc ai.2Khi o: R = r 2 + ( Z Z )2 va P =UL C max R r2( +)* * Neu L,C, ,U= const. Khi cho R thay oi ta thay co hai giatr R1 va R2 co cung cong suat P 2)= v 2 2R12R2tg tg tgtg tgC 1 2 = 1 21 2 1= +Trng hp c bit = /2 (vung pha nhau) th tg1tg2 = -1.r r** Cho U Uhoac = / 2 tan .tan = 1 1 2 1 2 1 2 + =. 0/ 2 ** Cho 1 2 >1 2tan .tan 1 1 2 =IV. May phat ien xoay chieu mot pha:1. Nguyen tac hoat ong : Da tren hien tng cam ng ien t2. Cau tao:* Phan cam: La phan tao ra t trng, thng la nam cham vnh cu hay nam cham ien.* Phan ng: La phan tao ra dong ien, gom khung day vi nhieu vong day dan quanquanh.* Bo gop: La phan a ien ra mach ngoai, gom hai vanh khuyen va hai choiquet.V. May phat ien xoay chieu ba pha:1 . nh ngha dong ien xoay chieu ba pha.La mot he thong gom ba dong ien xoay chieu co cung tan so, cung bien onhng lech pha nhau2 hay 120o tc ve thi gian la 1/3 chu ky T.3e Ec t1 0e Ec t2 0e Ec t3 0os( )os( 2 )3os( 2 )3TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )== = + trong trng hp ti i xng th1 02 03 0os( )os( 2 )3os( 2 )3i Ic ti Ic ti Ic t== = + 2. Nguyen tac hoat ong: Da tren hien tng cam ng ien tCau tao: Gom hai phan chnh:+ Phan cam: la Roto, thng la nam cham ien+ Phan ng : la stato, gom ba cuon day giong het nhau quan quanh loi thep at lech nhau1/3 vong tron tren than stato.3.Cach mac ien ba pha: 2 cach* Mac hnh sao: 4 day gom 3 day pha(day nong) va mot day trung hoa (day nguoi). Taitieu thu khong can oi xng. d p d p U = 3U ; I = I* Mac hnh tam giac: mac 3 day. Tai tieu thu phai mac oi xng d P d p U =U ; I = 3I4. u iem cua dong xoay chieu ba pha:* Tiet kiem c day dan tren ng truyen tai t ni san xuat en ni tieu dung.* Tao t trng quay rat manh ma khong can phai quay nam cham ien.VI. ong c khong ong bo ba pha:WWW.MATHVN.COM 25. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 251. nh ngha: La thiet b ien bien ien nang cua dong ien xoay chieu thanh c nang2. Nguyen tac: Da tren hien tng cam ng ien t va t trng quay, t trng tong hptai tam quay luon la 1,5B0Lu y: khung day quay vi toc o goc0 nho hn toc o quay cua t trng quay (cua dongien)roto tu _ truong dong _ ien < =3. Cach tao t trng quay: 2 cach* Cho nam cham quay* Tao bang dong xoay chieu 3 pha.4. Cau tao cua ong c khong ong bo ba pha: 2 phan* Stato: giong stato cua may phat xoay chieu 3 pha* Roto: hnh tru co tac dung nh mot cuon day quan quanh loi thep.VII. May bien the truyen tai ien nang:1. nh ngha: La thiet b bien oi mot hieu ien the xoay chieu nay thanh mot hieu ien thexoay chieu khac co cung tan so nhng co gia tr khac nhau.2. Cau tao: 2 phan* Mot loi thep gom nhieu la thep ky thuat mong ghep cach ien e tranh dong ien phuco.* Hai cuon day ong quan quanh loi thep vi so vong day khac nhau. Cuon s cap N1 vongday noi vi mang ien xoay chieu, cuon day th cap N2 vong day noi vi tai tieu thu.3. Nguyen tac hoat ong: Da tren hien tng cam ng ien t.S bien oi hieu ien the ve cng o dong ien trong may bien theGoi 1 1 1 1... U , I ,N ,P Hieu ien the, cng o, so vong day, cong suat, cua cuon s cap.Goi , , , ... 2 2 2 1 2 U I N P Hieu ien the, cng o, so vong day, cong suat, cua cuon th cap.Hieu suat cua may bien the . He so may bien thecosU I2 2 2cosU I1 1 1H P= 2= ThuCap =P1PPSoCapK = N1N2Neu H = 100% thNso = = 1= 2=1N212Neu Ns < Nth may tang the (N1 Nth may ha the (N1>N2 )IIUUNNIthuIUUsothusothuVIII.Truyen tai ien nang:N1 N2U1 U2R/2Pphat PTThuUphat UTthuLa s truyen tai ien nang t ni san xuat ti ni tieu thuGoi Pphat: cong suat ien can truyen tai t ni san xuat en ni tieu thuUphat: Hieu ien the ra may phat ienI: Cng o dong ien tren ng day1. Cong suat hao ph tren ng day:2P = RI = R PPhatR/22 22Phat cosU2. o giam the tren day: Phat Tieu Thu U IR U U _ = = TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 26. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 263. Hieu suat truyen tai ien nang:P P PPhatPPhatTieu Thu = _ =PPhat4. ien tr day dan:R = lSvi: l la chieu dai cua day dan=2lan khoang cach t ni phat en ni tieu thu (.m) la ien tr suatS(m2) la tiet dien day dan.IX. Cach tao dong ien mot chieu1. Cach tao:* Dung pin va ac quy => cong suat rat nho, gia thanh cao* Dung may phat ien mot chieu => Cong suat cao hn pin, ac quy. Gia thanh cao hn sovi viec tao dong ien xoay chieu co cung cong suat.* Chnh lu dong xoay chieu => kinh te nhat va pho bien nhat.2. May phat ien mot chieu* Nguyen tac hoat ong : Da tren hien tng cam ng ien t* Nguyen tac cau tao:+ Phan cam va phan ng giong may phat ien xoay chieu mot pha+ Bo gop ien gom hai vanh ban khuyen va hai choi quet.3. Chnh lu dong ien xoay chieu bang iot ban dan* Chnh lu na chu ky: mac diot ban dan vao mach co tac dung cho dong ien qua taitieu thu trong chu ky theo mot chieu xac nh => dong chnh lu la dong ien nhap nhay dunge nap ac quy.* Chnh lu hai na chu ky: Mac 4 iot ban dan vao mach mot cach thch hp, dong ienqua tai tieu thu trong ca hai na chu ky eu theo mot chieu xac nh.TNH CHAT SONG CUA ANH SANG1. nh ngha tan sac: Hien tng mot chum anh sang trang sau khi qua lang knh khong nhng bkhuc xa ve pha ay cua lang knh, ma con b tach ra thanh nhieu chum anh sang co mau sackhac nhau goi la hien tng tan sac anh sang.Nguyen nhan tan sac: Do chiet suat cua mot moi trng trong suat oi vi cac anh sang n sackhac nhau la khac nhau (no tan sac anhsang.2. Anh sang n sac: Anh sang n sac la anh sang khong b tan sac khi qua lang knh. Moi anhsang n sac co mot mau sac xac nh goi la mau n sac.3. Anh sang trang: Anh sang trang la anh sang c tong hp t vo so anh sang n sac khacnhau co mau sac bien thien lien tuc t o en tm. (0,38m 0,76m)4. Giao thoa anh sang:+ Bang hnh hoc ta co hieu quang trnh ( hieu ng i)d d = ax 1 2DS1d1MxI d2 ODS2aTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 27. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 27+ ieu kien e M la v tr van sangd d = k 1 2 , vi k Zx k D S = = ( k = 0;1;2...)V tr van sang: kiaV tr van sang trung tam (bac 0) ng vi k=0V tr van sang bac 1 ng vi k = 1V tr van sang bac 2 ng vi k = 2V tr van sang bac n ng vi k = n+ ieu kien e M la v tr van toi:x +S3S2S1S0S1S2S3T3T2T1T1T2T3iO Be day bd d = (2 k + 1) , vi k i = 2b1 2Z 2V tr van toi: ( lu y khong co van toi bac 0 )x k D T ) k = 0;1;2...) ( 12k ik D= (2 +1) = + = +aa2( 12Van toi th nhat ( van toi bac 1) ng vi k=0 va k=-1Van toi th hai (van toi bac 2) ng vi k=1 va k=-2Van toi th hai (van toi bac n) ng vi k=n-1 va k=-nKhoang van: Khoang van la khoang cach giahai van sang lien tiep hay hai van toi lien tiep.= = S k + S k t k + t k i x x x x , 1 , , 1 ,i D a=Ta co:ckk = ,fvn = vafn = c suy ra:v = kkvanni ikkn = ;nBe day b ic = 299792458 3.108m/ sChu y: Khi i t moi trng nay sang moi trng khac th tan so f luon khong oi nennang lng pho ton cung khong oiKhoang cach t van nay en van kia:* cung ben van trung tam: 1 2 x = x x* hai ben van trung tam: 1 2 x = x + xV tr hai van trung nhau:k D 2ax x k D k k= 1= a21 , 1 2 , 2 1o rong quang pho bac n: la khoang cach t van sang o bac n en tm bac nx = x x = n D ( ) ttnn n aQuang pho bac n bang n lan quang pho bac 1: 1 x n x n = * o rong phan trung nhau (giao nhau) cua hai quang pho lien tuc:_ _ +1 = o n tim n l x x lu y: Neu l 0 th khong giao nhau* Tm so van sang ,ti tren vung giao thoa co be rong L:L ,2= vi n la phan nguyen; p la ch so thap phan au tien.n piVd: 3,45 th n=3 va p=4; 5,78 th n=5 va p=7;So van sang trong vung giao thoa: N = 2n +1 SiTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 28. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 28So van toi trong vung giao thoa: + Neu p 5 th: N = 2n + 2 T+ Neu p 0 tc anot noi vi cc dng va catot noi vi cc am. (UAK = U+ )- Neu UAK < 0 tc anot noi vi cc am va catot noi vi cc dng (UAK = U +). Luc nay UAKong vai tro can tr dong quang ien. Neu dong quang ien triet trieu th |UAK |= Uh cxac nh bi cong thc: 2eU 1 m v h e =2 0max11. ien the cc ai cua kim loai b co lap ve ien:eV = 1 m v 2vi Vmax la ien the cc aie max 2 0max1 1212. nh l ong nang: mv 2 mv =e.UAnot AK 220max13. Ban knh electron khi bay vao t trng eu theo phng vuong goc:R mv0maxe .Bmax =14. Tia Rnghen:eU mv hf hc= = = e=1.6.1019 (C)minmax21AK X2XVi : UAK la hieu ien the gi hai au anot va catot cua ong RnghenfXmax la tan so ln nhat cua tia Rnghen ma ong co the phat ra.X min la bc song nho nhat cua tia Rnghen ma ong co the phat ra.W = 1 mv 2ong nang cua electron khi ti c oi am cc 2Khi cac electron ap vao oi am cc (oi catot) se lam nong oi am cc . Nhiet lng cungcap lam tang nhiet o cua oi am cc len t 0C la: Q = mct0m la khoi lng cua oi am cc (khoi lng cua chat lam nguoi oi am cc)C la nhiet dung rieng cua oi am cc(cua chat lam nguoi oi am cc)t 0 la o tang nhiet oNeu toan bo nang lng electron ap vao eu lam nong oi am cc th Q nW t e =e n So electron ap vao trong 1s; t la thi gian electron ap vao oi am ccTIEN E BOHR QUANG PHO VACH NGUYEN T HYRO1. Tien e ve cac trang thai dng:Nguyen t ch ton tai nhng trang thai co mc nang lng xac nh goi la trang thaidng.Trong cac trang thai dng nguyen t khong bc xa nang lng.2. Tien e ve s bc xa hay hap thu nang lng cua nguyen t :Khi nguyen t trang thai dng co nang lng Em sang trang thai dng co nang lng En (vi Em> En) th nguyen t phat ra mot photon co nang lng ung bang hieu m n E E :mn = hf = hc = E Em nmnVi fmn va la tan so va bc song ng vi bc xa phat ramn Ngc lai neu nguyen t trang thai dng co mc nang lng thap En ma hap thu mot photon conang lng hfmn th chuyen len trang thai dng co mc nang lng cao hn Em3. He qua cua tien e Bo:Trong cac trang thai dng cua nguyen t electron ch chuyen ong quanh hat nhan theo nhng quyao co ban knh hoan toan xac nh goi la cac quy ao dng. quy co R cang ln th nang lngcang caoTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 33. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 334.Pho nguyen t hyro: oi vi nguyen t hiro, ban knh co quy ao dng tang ty le vi bnhphng cac so nguyen lien tiep:Ten quy ao: K L M N O PBan knh: ro 4ro 9ro 16ro 25ro 36roMc nang lng: E 1 E 2 E 3 E 4 E 5 E 6r n2 r n = 0ro = 5,3.10 -11 m la ban knh BoE E 0 nnnvi Eo = 13,6 eV= ; =1,2,3..., 2* Bc song cua day Laiman: 1 n P 54 3n = 6O432N321M21L1H H H HKLaiman Banme Pasenvi max 21 = L va min 1 = L* Bc song cua day Banme: 2 n vi max 32 = B va min 2 = B* Bc song cua day Pasen: 1 n vi max 43 = P va min 3 = Pn = 5n = 4n = 3n = 2n = 1Emhf Hap thu Bc xa hfmn mnEnDay Laiman (LyMan):Phat ra cac vach trong mien t ngoai, cac electron mc nang lng cao (n= 2,3,4 , ng vi cac quy ao tng ng L,M,N ) nhay ve mc c ban( mc 1, ng vi quy aok)Day Banme: Phat ra cac vach pho mot phan trong mien t ngoai va 4 vach pho trong mien khakien o H ,lamH , cham H va tm H . Cac electron mc nang lng cao ( n = 3,4,5 ng vicac quy ao tng ng M,N,O) nhay ve mc th hai(ng vi quy ao L)Day Pasen: Phat ra cac vach pho trong vung hong ngoai. Cac electron cac mc nang lngcao ( n=4,5,6, ng vi cac quy ao tng ng N,O,P, ) nhay ve mc th 3( ng vi quy ao M)HAP THU VA PHAN XA LOC LA CUA ANH SANG1. Hap thu anh sang la hien tng mot moi trng vat chat lam giam cng o chum sang truyenqua no2. Cng o I cua chum sang n sactruyen qua moi trng hap thu, giam theo quy luat ham somu cua o dai ng i d cua tia sang. I = I e d 0 I0 la cng o chum sang ti moi trng la he so hap thu cua moi trng ( phu thuoc vao bc song )3. Nhng vat hau nh khong hap thu anh sang trong mien nao cua quang pho c goi la gan nhtrong suot vi moi trng o. Nhng vat khong hap thu anh sang trong mien nhn thay cua quangpho c goi la trong suot khong mau. Nhng vat hap thu loc la anh sang trong mien nhn thay thgoi la vat trong suot co mau.TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 34. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 34HIEN TNG QUANG PHAT QUANG- LAZE1. Huynh quang: la s phat quang di anh sang kch thch, nhng khi ngng kch thch th haunh anh sang phat quang tat ngay (di 108s). No thng xay ra vi chat long va chat kh.2. Lan quang: la s phat quang di anh sang kch thch, nhng khi ngng kch thch th anh sangphat quang van con keo dai (108 s tr len). No thng xay ra vi chat ran. Cac chat nay goi la chatlan quang.3. nh luat Xtoc ve s phat quang.Anh sang phat quang co bc song dai hn bc song cua anh sang kch thch : > 4. LaZe:la mot nguon sang phat ra chum sang song song, ket hp, co tnh n sac cao va co cngo ln.* Nguyen tac phat quang cua laze da viec ng dung cua phat xa cam ng.THUYET TNG OI HEP CUA ANHXTANH ( Einstein)1. Tien e I cua AnhxTanh: Cac nh luat vat ly (c hoc, ien hoc) co cung mot dang nh nhautrong moi he quy chieu quan tnh.2. Tien e II cua AnhxTanh: Toc o anh sang trong chan khong co cung o ln bangc 3.108m/ s trong moi he quy chieu quan tnh, khong phu thuoc vao phng truyen va vao toc onguon sang hay may thu.3. o co chieu dai :l0 la chieu dai trong he ng yen2v l chieu dai cua thanh khi chuyen ong vi toc o v0 l = l 1 < l2 0c4. S cham lai cua ong ho khi chuyen ong vi toc o v. = t la thi gian o theo ong ho chuyen ong;00 t t > 2201tvct la thi gian o theo ong ho ng yen.6. Khoi lng tng oi tnh.= mm0 la khoi lng ngh (ng yen); m la khoi khi vat chuyen ong vi toc o v0m m 2201vc7. He thc gia nang lng va khoi lng; Nang lng toan phanW m c + 1 m v= = 22c2c2E mc m2 01v020 2TRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM 35. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 35VAT LY HAT NHAN NGUYEN TI. PHONG XA HAT NHAN1. Cau tao hat nhan nguyen t: Hat nhan co ky hieu AXZ gom co :A: nuclon (so khoi) ; Z: so proton (ien tch hay so th t trong bang tuan hoan); N = A Z: so11 = ; cua ntron: 1n1u = MeVttT tN t N N t N N etT t ln 2 0,693 hang so phong xaT = chu ky ban ra ( thi gian e so hat nhan cua chat phong xa b phan ra)No, mo la so nguyen t, khoi lng cua chat phong xa thi iem ban au .Nt , mt la so nguyen t, khoi lng cua chat phong xa thi iem t (con lai sau thi gian t ).N,m la so nguyen t b phan ra, khoi lng b phan ra cua chat phong xa sau thi gian t .m N0A0 = ;N mtNAt = ;N mNA tT X ym AX ytm m Am = 0 (1 2 ) = (2 1)Y AT X zX zZ ATRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )ntronKy hieu: cua proton: P 1H10* Ban knh hat nhan: R = 1,2.10 15 A 3 ( m)2. ong v:Cac nguyen t ma hat nhan cha cung so Z proton, nhng co so ntron N khac nhau goi la ongv.3. n v khoi lng nguyen t (n v cacbon) u1u = 1/12 khoi lng cua ong v nguyen t cacbon 12C61u = 1,66055.10 -27 kg; mp = 1,0073 u; mn = 1,00867 u ; 2 1 931,5c4. Phong xa:la hien tng mot hat nhan khong ben t phat ra tia phong xa va chuyen thanh hat nhan khaca. nh luat phong xa:tso nguyen t con lai sau thi gian t: T tN = N 2= N et 0 0 Khoi lng con lai sau thi gian t: T tm = m = m et .2 . 0 0so nguyen t b phan ra sau thi gian t: ( ) = ( ) = (1 2 ) = (1 ) 0 0 0Khoi lng t b phan ra sau thi gian t: m = m m ( t ) = m (1 2 ) = m (1 e) t 0 0= = =T TA(gam) cua mot chat cha NA = 6,023. 10 23 nguyen t (hay phan t).mo(gam) No nguyen t (hay phan t).m(t) (gam) .. N(t) nguyen t (hay phan t).m(gam) .. N nguyen t (hay phan t).A NAA =Chu y: oi vi phng trnh phong xa: AxXAyY +AzZ th khoi lng chat Y, Z tao thanh sauthi gian t la:= 0 (1 2 ) = (2 T1)xtxm AATxtxm AAm0X ,mX : l khi lng ban u v cn li ca X sau thi gian t.mY , mZ : l khi lng sinh ra ca Y v Z sau thi gian t.WWW.MATHVN.COM 36. www.MATHVN.comGV. TRNG NH HUNG T: 0908.346.838 Trang 36o phong xa H : ai lng ac trng cho tnh phong xa manh hay yeu cua chat phong xa co bang so phan ra( hay so phong xa) trong mot n v thi gian = so phan ra /s.tH(t) = dN(t) T tdtt H H H e= = 0 0 2 ; 0 0 H = N ; t t H = Nn v: 1Bq = 1 phan ra/s; 1Ci = 3,7.10 10 Bq5. o hut khoi va nang lng lien ket:a. o hut khoi: 0 0 m = m m = Zm + Nm m > p nmo = tong khoi lng cua cac nuclon rieng re ng yen ( trc khi tao thanh hat nhan)m = khoi lng hat nhan mo > mmp = khoi lng proton; mn = khoi lng ntronb. He thc Anhxtanh: E = mc2m = khoi lng cua vat; c = 3.10 8 m/sE = nang lng ngh cua vatc. Nang lng lien ket hat nhan AX: W = (m m )c 2 = [ Z.m + (A Z).m m ] .c 2Z lk 0 x P n X La nang lng toa ra khi cac nuclon lien ket thanh hat nhan( nang lng can thiet e pha vhat nhan thanh cac nuclon rieng le)d. Nang lng lien ket rieng AXZ :W WlkAlkR =*** Nang lng lk rieng cang ln nguyen t cang ben vng. ***6. ng dung cua cac ong v phong xa:* Phng phap nguyen t anh dau: dung 31P15 la phan lan thng tron lan mot t phong xa ra boncho cay. Theo doi s phong xa cua ta se c qua trnh van chuyen chat trong cay.* Dung phong xa : Tm khuyet tat cua cac san pham uc, bao quan thc pham, cha benh ung th.* Phng phap xac nh tuoi cua vat: o o phong xa cua 14C6 se xac nh c tuoi cua cac co vat.PHAN NG HAT NHANI. PHAN NG HAT NHAN:1. nh ngha: La s tng tac gia hai hat nhan dan en s bien oi cua chung thanh cac hatnhan khac.A+ B C + DTrong so A,B,C,D co the la cac hat s cap electron, p, nS phong xa A B +CPhong xa la trng hp ac biet cua phan ng hat nhan toa nang lng.A la hat nhan me, B hat nhan con va C la hat , ...2. Cac nh luat bao toan trong phan ng hat nhan: A B C A DZAZAZAZ441+ 2 3+1 23Bao toan nuclon(so khoi A): A1 + A2 = A3 + A4Bao toan ien tch( Nguyen t so Z): Z1 + Z2 = Z3+ Z4Bao toan ong lng: 1 2 3 4 P + P = P + P Hay: 1 1 2 2 3 3 4 4 m .v m .v m .v m .vr r r r + = +Vi : x x x p = m v r ong lng cua hat nhanong nang:W m.v2 =2Moi lien he gia ong lng va ong nang: P2 = 2mWTRUNG TAM LUYEN THI AI HOC AI VIET ( NGUYEN LA TTLT AI HOC S PHAM TP.HCM )WWW.MATHVN.COM