Bồi dưỡng học sinh giỏi vật lý 11 tập 1

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Cty TNHH MTV DVVHKhnnn Vi?t LQI NOIDAU «B6I DlfONG HOC SINH GI61 VAT L I TRUNG HQC PHO THONG" la bo sach dung cho hoc sinh kha gioi, hoc sinh cac Idp chuyen Vat l i , cac thay c6 giao day Vat li d cac trUdng trung hoc thong Bo sach gom cuon: Boi dUdng hQC sinh gioi Vat U10, tap I (Donf^ hoc, Dong lUc hoc, TTnh hoc) Boi dUdng hpc sinh gioi Vqt li 10, tap I I (Cac dinh luat bcio loan, Nhiet hoc) Boi dUdng hQC sinh gioi Vat li 11, t|ip I (D/pn va Dien til) • Boi dUdng hgc sinh gioi Vat li 11, tap I I (Quang hinh) Boi dUdng hgc sinh gioi Vat li 12, tap I {Dao dong va Song hoc) Boi dUdng IIQC sinh gioi Vat li 12, tap I I {Dong dien xoay chieu va Dao don^ dien tCe) Boi dUdng hgc sinh gioi Vat li 12, tap I I I {Quang li Vat li hat nhdn) Ve cau true, moi cuon sach deu du'dc chia cac phan Idn, moi phan gom nhieu chuyen de, moi chuyen de la mot noi dung kien thiJc tron ven Moi chuyen de gom cac phan: A-T6m tat kien thrfc: Phan chiing toi trinh bay mot each c6 he thong nhi^ng kien thiJc tam cua chuyen de tiif cd ban den nang cao chiing toi chu dao sau nhffng kien thiJc nang cao de lam cd sd cho viec giai cac bai tap cua chuyen de B-Nhi?ng chu y giai bai tap: Trong phan chiing toi neu len nhu'ng chii y can thiet ve kien thiJc va ki nang giai bai tap Do la nhu'ng lufu y quan trpng giiip dinh hu'dng va tranh nhu'ng sai sot giai cac bai tap cua chuyen de C-Cac bai tap cua chuyen de: He tho'ng bai tap d day kha da dang du'dc s^p xep ttf de den kho, tCf ddn gian den phiJc tap va di/dc giai kha chi tiet nen rat phii hdp vdi nhieu do'i tU'dng ban doc Trong qua trinh bien soan chiing toi tham khao rat nhieu nguon tai lieu va ngoai niTdc, dac biet la cdc bo sach G/a/ loan Vat U thay Biii Quang Han lam chu bien - Nha xuat ban Giao due 1998, bo sach Bai tap va Un gidi Vat li OS Yung Kuo Lim lam chu bien - Nha xuat ban Giao due Viet Nam 2010, bo sach Ca sd Vat li David Halliday lam chu bien - Nha xuat ban Giao due 2002 de lam phong phU them phan kien thiJc cung nhiTphan Idi giai cac bai tap bo sich Vdi SLf gop siJc cua cac thay c6 giao da va dang cong tac tai cdc tnTdng chuyen, cac thay c6 giao da tijfng tham gia boi difdng hoc sinh gioi Vat l i cua cac tinh ca ni/dc, hi vong bo sach se la tai lieu tham khao thie't thifc, bo ich cho nhieu doi tifdng ban doc yeu thich bo mon Vat l i Mac dil da dau tiT bien soan kha kl ludng nhiftig nhu'ng han che, sai sdt la dieu khong the tranh khoi Rat mong nhan difdc sif dong gop, chia se cua cac thay c6 giao va cac em hoc sinh tren ca nifdc; Moi y kien dong gop xin gufi ve dia chi ngphudong@gmail.com hoac khang vietbookstore@vahoo.com.vn Xin tran gidi thi^u bo sach den quy thay c6 giao va cic em hoc sinh! Chu bi6n ThS Nguyin Phii Dong thvrnhat mdn TfNH N» LlTC TlJfdNG TAC TINH DIEN Chuxendil: A-TOMTAxKliNTHtrC •^^mt^.^ag^ I Dien tich - S\i tifdng tac giffa cac di^n tich Di^n tich: Cd hai loai dien tich: dien tich du'dng va dien tich am Cac dien tich cung loai thi day nhau, cac dien tich khac loai thi hut Djnh luat Culong: LiTc ti/dng tac giufa hai dien tich diem diJng yen ti le thuan vdi tich dp Idn ciia hai dien tich va ti le nghjch vdi khoang each giiJa Chung + k lq£2| e' r^ xjflq •'• e la h^ng so' dien moi ciia moi triTdng ( = : chan khong hoac khong khi) + r la khoang each giffa hai dien tich qi, q2 / " ^ j Chii y : Dinh luat Culong du'dc ap dung cho: - hai dien tich diem ^f'^ ^ \ ^ - hai qua cau tich dien phan bo deu 11 Djnh luat bao toan di^n tich " ^1 i< t '•'''^^O Trong mot he CO lap ve dien, tdng cac dien tich dtfdc bao toan: q, + q2 + = const j „ ^t^, ^^,(^-,3 B NHONG C H O t KHI GIAI B A I T A F - Khi dp dung djnh luat Culong ve siT tU'dng tac giffa cdc dien tich dffng yen can chu y: + dieu kien ap dung: hai dien tich diem hoac hai qua cau tich dien phan bo deu + cac hien tU'dng thiTc te" thffdng gap: • cho hai qua cau nho dan dien nhiT da nhiem dien tiep xiic hoac no'i vdi bKng doan day dan roi tdch rdi thi tdng dien tfch se chia deu cho hai qua cau: q'l = q'2 = • ' ' cham tay vao mot qua cau nho dan dien da tich dien thi qua cau se mat dien tich va trd trung hoa Bdi diiOng hgc sinh gi6i Vat ly 11, t$p - Nguyin Phu D6ng - Cty TNHH MTV DVVHUhang Vi?t Khi mot dien tich diem q chju tac dung ctia nhieu life tac dung Fp F j , c C A C B A I T A P vi; Lye T U O N G T A C TITOI D I E N Tl/CfNG T A C G I A CAC D I E N T I C H D I E M DlfNG YfeN cac dien tich diem qi, q2, gay thi hcJp life tac dung len q la: 1.1 Hai dien tich diem bang dat chan khong, each doan R = 4cm Li/c day tTnh dien giffa chiing 1^ F = 10'^N -f De xac djnh Idn cua hdp luTc F ta c6 the diTa vao: ** a) Tim Idn moi dien tich + djnh l i ham cosin: F^ - Fj^ + F2 + 2FjF2Cosa (a la goc hdp bdi Fj va ) b) Tim khoang each R, giffa chiing de liTc day tTnh dien la F, = 2,5 lO^^N Bai giai • F, va F2 cung chieu thi: F = F, + F2 (a = 0, cosa = 1) • F, va F2 ngiTdc chieu thi: F = IF, - F2I (a = n, cosa = -1) ^ a) Do Idn mSi dien tich _ Vi: + Hai dien tich day nen q, va q2 cung dau + Hai dien tich bang nen: qi = q2 • F, va F2 vuong goc thi: F= ,JF^ + F^ • Fj va F2 cung Idn (Fi = F2) thi: F = 2Fi cos y (a = 90°, cosa = 0) - Theo dinh luat Cu-16ng: -5 F =k = RJ^ R^ + phiTdng phap hinh chieu: F = ^jF[+F^ (F, = Fu + F2x + - Fy = F,y + F2y + F2 + R' -f Cac life tac dung len dien tich q thi/dng gap la: Vdi khoang each R: F = k - ' ^ R^ (1) - Vdi khoang each R,: F' = k - - (2) + liTc cSng day T R: ne'u q, va q2 trai dau; \\ic day ne'u q, • va q2 Cling dau) , 1,3.10"'C ^2 - + life: P = mg (luon hu'dng xuong) .SiSl Q^^Q 1,3.10 ' C b) Khoang each R, giffa chung de life day tTnh dien la F, = 2,5.10"^'N .) = + life tTnh dien: F = =4.10-1 j i ^ 9.10^ Vay: Do Idn cua moi dien tich la Khi mot dien tich q du'ng yen thi help luTc tac dung len q se bang 0: F = F, + '1 - 10r5 Suy ra: R, = R — = = 8cm y 2,5.10"^ , Vay: De life day tTnh dien giffa hai dien tich la F, = 2,5.10 ''N thi khoang ; u + lircdanh6icual6xo:F = k A / = k ( / - / o ) •I fi each giffa chiing la R| = 8cm FM 1.2 Hat bui khong d each mot doan R = 3cm, moi hat mang dien tichq =-9,6.lO-'^C _ H : a) Tinh life tTnh dien giffa hai hat 'iff'' b) Tinh so electron dirtrong moi hat bui, biet dien tich moi electron la e = 1,6.10-"C *" y-• Bai giai a) Lffc tTnh dien giffa hai hat Vuong goc Ciang Idn Ta cd: F = k = k^=9.10' R' R^ - ^ r , 1'\ ,-13x2 (-9,6.10-'-') = 9,216.10'^C ' (3.10-^)2 Vay: Life tTnh dien giffa hai hat la F = 9,216.10-'^C A\ Cty TIMHH MTV UWH khang V i ^ B6i diiBng hpc sinh gi6i Vjt ly 11, t?p - IMguygn Phu B6ng Bai giai b) So electron diT moi hat bui -9,6.10" Ta c6: ne = — e = ^,, , a) Dp Idn life hU'dng tarn dat len electron Vi life hU'dng tam chuyen dong tron cua electron quanh hat nhan chinh = 6.10' -19 1,6.10 Smi la life tTnh dien nen: v'c,fy ::r"!,; I Vay: So' electron d\X moi hat bui la ne = 6.10^ ^-19 1.3 Moi proton c6 khoi liTdng m = l,67.10""kg, dien tich q = 1,6.10""C Hoi life FM =k ^1^2 (-1,6.10~'^).1,6.10 = 9.10" = 9,2.10-* N R^ day Culong giiya hai proton Idn hdn li/c hap dan giffa chiing bao nhieu Ian? (5.10"")2 Vay: Do Idn life hU'dng tam dat len electron la: Fh, = 9,2.10"* N Bai giai *"- ^ b) Van toe va tan so chuyen dong cua electron - L\ic day Cu-16ng giffa hai proton la: F = k = kTa c6: Fh, = - Lire hap dan giifa hai proton la: F ' = G m,m2 = Gm R^ R^ - F' G m Suy ra: — = — F k Vay: 1,67.10 Vay: 1,6.10 9.10^ ' ' Life day Cu-16ng giffa hai proton Idn hdn life hap dan giCfa chung « 0,71.10"/s Van to'c va tan so' chuyen dong cija electron la Fh, « 2,25.lO' m/s va bang life F = 1,8N Dien tich to'ng cong cua hai vat la Q = 3.10"^C Tinh dien tich moi vat Life tmh dien giiJa hai vat la: F = k 11^2 R^ / - Life hap dan giifa hai vat la: F' = G R^ FR2 ^1^2 -G m R^ =1,6.10-'^ kinhR = 5.10""m a) Tinh Idn life hifdng tarn dat len electron b) Tinh van toe va tan so'chuyen dong cua electron Coi electron va hat nhan nguyen tur hidro tUdng tac theo djnh luat tTnh dien (1) 9.10'^ •;t, - VT hai dien tich day nen qi va q2 cung dau va ciing du'dng (suy tif de bai) Do do: 1,86.10-kg 1.5 Electron quay quanh hat nhan nguyen tuT hidro theo quy dao tron vdi ban = 2.10-10 Matkhac: 6,67.10"" 1,86.10"^ kg 1,8.1^ - qiq2 = Vay: De life tTnh dien b^ng life hap dan thi khoi lifdng cua moi vat phai la m= ^1^2 R^ D e F = F'thi: J^ Theo dinh luat Cu-16ng, taed: F = k = kR^ mjmj m = -.1 :v ^ ' Bai giai Bai giai k ^ = G i ^ R^ R^ , M , 2,25.10'm/s 2.3,14.5.10'" de life tlnh dien bang life hap dan - « 1.6 Hai vat nho mang dien tich dat khong each doan R = Im, day 1.4 Hai vat nho giong nhau, moi vat thifa mot electron Tim kho'l lu'dng m6i vat - 9,1.10 -31 n « 0,71.10"/s 1,35.10^'' Ian - 1-11 9,2.10"'.5.10" i m 2,25.10^ 27tR = 1,35.10,36 -19 ,2 va n = -27 6,67.10 mv R , , ^1+^2 - Q = 3.10"^ ,-10 2.10 q , + q = 3.10-' - - (2) d') ^ (2') /, - > Giai he (1') va (2') ta difdc: r " ® ^ ^ k r - - ^ ' q, = 2.10' C va q2 = l O ' C hoac q, = 10"' C va q2 = 2.10-' C Vay: Dien tich moi vat la: q, = 2.10-' C va q2 = l O ' C hoac q, = 10 C v^ q2 = 2.10 •' ' C 1.7 Hai qua cau kim loai nho nhu mang cac dien tich qi, q2 dat khong each R = 2cm, day bang life F = 2,7.10^N Cho hai qua cau Cty TNHH MTV DWHJ F' = k (q,+q2)= R^ -4 ±2RJ|^ = ±2.2.10"' 3,6.10 V 9.10^ H ; G TONG HglP TAG DyNG LEN MOT D l t N TIGH 1.8 Ba dien tich diem q, = -10"'C, q2 = 5.10"'C, = 4.10"'C Ian lu-dt dat tai A, B, C khong khi, AB = Scm, AC = 4cm, BC = 1cm Tinh life tac dung len moi dien tich , , , Bai giai Ta c6: AB = 5cm, AC = 4cm, BC = 1cm => AB = AC + CB C nkm doan AB c B e- Life tac dung len qi: =>F, =k 1211 AB' +k F, = , " ' N •" "" q3 q2 Fj = F j + F =^ Fi = F21 + F31 (F^^pPsi I3I1 AC^ 5.10"V-10"'') = 9.10'.( ( " ' ) ' (10"')2 '^""g'^hilu) 4.10-'.(-10"^) ( -2x2 "') => F3 = F13 + F23 = k I l l s + k ^ ' ' ' ' = 9.10'.( AC^ (-10"^).4.10" (4.10 ' ) ' (F,3;F23 + cung chieu) 5.10 ^4.10" (10"')' 1.9 Ba dien tich diem q, = 4.10"^C, q2 = -4.10"^C, q3 = 5.10"*C dat khong tai ba dinh ABC cua mot tarn giac deu, canh a = 2cm Xac dinh vectd life tac dung len q3 , ; „,,:•< is^jj , Bai giai =^(q,+q2)= ±8.10-^ (2) -v-9 - Giai he (1) va (2) ta di^dc: q, = 6.10"' C va qz = 2.10 ' C; q, = -6.10"' C va q2 = -2.10"' C hoac q, = 2.10"' C va qz = 6.10"' C; q, = -2.10"' C va qz = -6.10"' C Vay: Dien tich cua cac qua cau chU'a tiep xiic la: qi = 6.10"'C va q2 = 2.10"'C; q, = -6.10"'C va qs = -2.10"'C hoac q, = 2.10"'C va q2 = 6.10"'C; qi=-2.10"'Cvaq2 = -6.10"'C qi 4.10"^5.10- F3 = , " ' N q ; = q ^ = ^ ^1+^2 qiq2 ^ = 9.10' ( - " ' ) " (5.10-^)' AB= BC^ F2= 16,2.1 " ' N - Khi cho hai qua cau tiep xiic roi tach xa thi: F' = k vai: =k (Fj2;F32 ngiTdcchieu) F12-F32 ) Ta c6: Vi ll F3 = ^^3 + =12 F23, F,3 vdi F,3 = ; F23 a" =k a = F23Va a = (F,3,F23) 13'*23 = 120° 4.10"'.5.10 = 45.10-^N (2.10"')' Vay: Vectd life tdc dung len q3 c6: + diem dat: tai C + phi/dng: song song vdi AB + chieu: tiTAdenB + doldtn:F3 = 45.10"^N _i i 1.10 Ba dien tich diem qi = qj = q3 = q = 1,6.10""C dat chan khong tai ba dinh tarn giac deu canh a = 16cm Xac djnh lire tac dung len dien tich q3 Bai giai Taco: F3 = F,, + F23, vdi =>F3 = F,3 = F23 = 9.10' I1I3 Fi3 =k F23 = k I2I3 a a B6i duBng hoc sinh gi6i V$t 1^ 11, tjp - NguySn PhO Dflng F,3 = F23 C t y T N H H MTV DVVti |-,lunu UiAt va a = (F,3,F23) = 60° => F = 2F,3Cos-^ = k \0 ^ F = 2.9.10-/''^-'^7f.^ = 15,6.10-N (i6.io"2)2 I r 64.10"^(-10"'') = 9.10" = 36.10^N F23 = k (4.10"')^ >/F^TF^ = V(27.10-^)^+(36.10"^)^ =45.10'^N h2% Vay: Vectd liTc tac dung len q^ cd: + diem dat: tai C + phiTdng: CO (O la trung diem AB) _ 13 _ AC ) (tan OCB = F23 BC + chieu: tiT C den O + Idn: F3 = 45.10"'N \: - Fio = k——; vdi F20 = F30 ( V I qi Vay: Vectcf liTc tac dung len q3 c6: + diem dat: tai C + phu'dng; vuong gdc vdi AB + chieu: xa AB + l d n : F = 15,6.10-^'N 1.11 Ba dien tich diem qj = 27.10'^C, qj = 64.10"^C, q3 = -10"'C dat khong tai ba dinh tam giac ABC vuong goc tai C Cho AC = 30cm, BC = 40cm Xac dinh vectd liTc tac dung len q3 Bai giai Taco: ^ = + , vdi: a = 27.10"".(-10"'') (F,3,F23) = 90° 111.! F„ = k = 9.10^ = 27.10^N (3.10"')^ AC^ =>F3= vdi q i % 1.12 Tai ba dinh tam giac deu canh a = 6cm khong cd dat ba dien tich q, = 6.10'"C, q2 = q3 = - 8.10"'C Xac dinh liTc tac dung len qo = 8.10~'C tai tam tam giac Bai giai , T a c d : ^ = F , , + E , o - f = F,o+F23, 1,! ^ => F23 = 2F20COS va F23 = 9.10 F,o =k =>F,o = 9.10" F20 -k = q3); b 12% ;F3o =k = |h = =^ va a = {F^^'^o) = J20° - = 2k ^ % cos60° = '2F0 6.10^8.10"^ e.io-^Vi = 3,6.10^N 92 „.:d3f:! f|.:>f& 'O'ff! f'V iMs sill • Ann =^ Fo = 3,6.10^ + 4,8.10"^ = 8,4.10"'N Vay: Vectd life tac dung len qo cd: , + diem dat: tai O + phiTdng: vuong gdc vdi BC \ + chieu: tij" A den BC + doldn:Fo = 8,4.10-^N " ^ 1.13 Hai dien tich q, = 4.10'^C, q2 = -12,5.10"*C dat tai A, B khong khi, AB = 4cm Xac dinh lire tac dung len qj = 2.10"'C dat tai C vdi CA AB va F ' CA = 3cm Bai giai Tacd: F = F , + F = ^ F3 = J F ,X' + F,^y ; Ox n^m ngang, Oy thdng diJng Fn =k 11% = 9.10'^ 4.10^210"^ ,-2x2 (3.10-^) !)':' AC = 8.10^N B B6i clL0ng hpc sinh gi6i Vjt ly 11, tgp - Nguygn Phd Dfing F23 =k 1213 Cty TNHH MTV DWH Khang Vi?t Vay: LiTc tac dung len m i dien tich c6: (-12,5.10"^).210"^ = 9.10^ = 9.10-^N (5.10-2)2 BC^ Fx = F , ( x , + F23(x, = + F C O S B = F ^ = 9.10^ ^ = 7,2.10-^N BC • + chieu: ttr tarn luc giac + Idn: F = k- + phU'cfng: hdp vdi A C mot goc P: cosP = dung len m o i dien tich - j (8.10^'*)^ +(7,65.10"*)" tich tai D tren hinh ve „2 -(9.10~^)2 T a c o : F = F , + F + F = F , + F , v d i : F, = F2 = F = k ^ « 0,34 => p « 70° 2.8.10"^7,65.10~^ dp l d n : F = 7,65.1 O ^ N ^'-^ ' ' C - vty,, V''"' 1.14 C6 dien tich q b^ng dat khong k h i tai dinh luc giac deu canh a T i m lire tac dung len m o i dien tich D o tinh doi xiJng nen ta chi can khao sat mot dien tich ba't k i , ch^ng han dien R '23 \r „ AD^+HD^-AH^ cosp = • 2.AD.HD a2 + Ta c6: F = F, + F3 + F4 + F5 + F,, v d i : ,2 120° aV3 1V3 V 2a , =>F,3 = F, = F3 = kf =>F^ = F = k = k - ^ = k - i (c = 2a) D 2^ + _ w5 r t 2V B a a J 4a2 Q2 F4 = Ffi = k \ k - - ; b ' = ( a ) ' - a ' = a ^ p = 60° b^ 3a2 F = 2F4Cos30° = 2k 3a2 F =F , F F =k 12 = ^ / i k ^ n^m tren diTdng cao H D tich tai B tren hinh ve (2a)2 r V i F2 = F ; B D C = 60° =^ F = 2F2Cos30° = k ^ — 2 va F^ = F^ + F23 + F F C O S P , v d i : »| B a i giai c^ B a i giai Do tinh doi xu'ng nen ta chi can khao sat mot dien tich ba't k i , ch^ng han dien 2F13F3 F, = F = k - ; a = 12 ^ ' d i e m dat: tai C tSm luc giac (15 + ^ ) q2 c6: + + phU'cfng: AvtUng thang noi dien tich 1.15 Bon dien tich q giong dat d dinh tu" dien deu canh a T i m life tac = > F = V(7,2.10~'*)2+(2,6.10-^)2 = 7,65.10-^•N => cosP = d i e m dat: tai cac dien tich + AC Fy = F,3(y, + F23(y, = F , - F23.sinB = F , - F ^ = 8.10"^ - 9.10^ - = 2,6.10^N BC Vay: Vectd life tac dung len + 4.k4.k^ 4a2'"3a2 V a y : Life tdc dung len m o i dien tich c6: + d i e m dat: tai cac dien tich (3) k4/'^"^^ '" a^ ' 12 ' '•u > + phiTcfng: hdp v d i mat tur dien mot g6c a: cosa ^ — F E23 — ^3 13 Cty TNHH MTV DVVH Khang ViSt B6i du8ng hpc sinh gi6i V?t ly 11, tjp - Nguygn Phu B6ng f cosa = I 2> 2 > ( — - J a' ( TiTdng tir doi v d i cac d i e n tich q2, qs va q4 2\- I Vay: D o Idn liTc tac dung len m o i dien tich la F « 0,45.10"'N 2V2 ^ J a = 160°30' 2V^k^.Vik%+ \dn:F= Do'i v d i q,: Fi - F^, + V6k^ + F^j + F,,, + F2,i + Vy, + V^., v d i : F2, = F , = F r i = k \ ; F , = k (aVi)' 1.16 ffinh lap phiTdng A B C D , A ' B ' C ' D ' canh a = 6.10"'°m dat chan khong, Xac djnh life tac dung len m o i dien tich, ne'u: k a) Co dien tich q , = q2 = 1,6.10-"C tai A, C; dien tich qa = q4 = - , - " C t a i B ' va D ' b) Co d i e n tich q = 1,6.10""C va dien tich - q dat xen ke d dinh cua hinh lap phiTdng F21(x) - + F3, + F^,, Do'ivdiqi: F, = F31(z) vdi: F21 = F31 = F41 2a^ F , = k \ ; F , ( y ) = 0;F2,(z) = •\2'_ = F41(x) „2 : 0; F4i(y) = F41 = k \ ; F i ( z ) = 2i = k (aV2)^ •= k- 2a^ Fri(x) = 0; Fn(y) = 0; Fn(z) = F n - k - F21(x) = F21(y) = - F l C S ° = -k- F^r.(x) j-Uxl = —.F2.„z) = -F2-,cos45° = - k - ^ ^ — =-—• '2a2'2 F2.,(y) = k \ a^ „2 F3UX, = F , ( , = F3,cos45° = F4i(y) = F4i(z, = F4iCos45° = - = > F i x = F2i(x) + F3i(x) = — k F ,ly v -= r2l(y) F2HV, + + F4UV) r4i(y), = - 2a2 2a2 ^ +• a^ — a 2 k = Fruy) = Fruz) = F r c o s A ' A C = k • 4-l(x) = ' 0; F4-i(y) = F4'i(z) = - F ' , c o s ° = => F u = F2l(x) + F3i(x) + F4i(x) + Fn(x) a- ^ a2 F3'i(x) ^k^' k ^ 4~2k ^ + — ^ K — = k if r | ( ) + ^41(2) = /I ;v' 72 q^ 2a^ 14 (aV2)' = -k2a2' a) Ta c6: riz - • = k- F j K x ) = F31(y) = - F l C O S ° B a i giai - = k3a^ Fri = F i = F i = • q'4 ^2 = q2 = I " I Taco: ^ a^ '23^ ' a^ a' + F2-i(x) + FS-KX) + F4-l(x) 4 a^ a^ = a- '"-2 9.10\ -k • =0 + Sa^'aVi a^ /iSIO&snU:- => F,y = F21(y) + F31(y) + F4|(y) + Fi'Ky) + F2-l(y) + Fs'Ky) + F4'l(y) '— « 0,45.10"'N (6.10-'0)2 B6i duSng hpc sinh gioi Vat ly 11, tgp - IMguygn Phu D6ng TCr do: + C nam tren du'dng thang A B , ngoai doan A B , ve phia A F l z = F2I(z) + F3i(z) + F4i(z) + Fri(z) + F2-l(z) + FS-KZ) + F4-i(z) ' > * M + BC = 3AC = ( B C - Vay: Phai dat " a - a a- b) Dau va dp Idn cua q3 de qi, q2 cung can bang C - De qi va q2 cung can bang thi: AB^ a- ^.12 = 4cm A B F|2 + F32 AC ^2 3' va F12 = F32 -7 1,8.10 AB = 0,45.10"'C _ V i q , < ; q > ^ q > : qj = 0,45.10"'C F,=v^.t(,-:^.:^)k4]=(V^-Vi:?4)ki a F21 = F , =0 1i'l2 , 1312 , ^3^1 =k va k = k AB' AC^ BC' 13 = I A C = H ^2^1 | = 12cm va -Q- a- BC = | A B = tai C , vdi A C = 4cm; B C = 12cm thi q3 se nam can bang, F2, + F31 = va AB) ,^ , Vay: De q, va qa cung can bang thi qj = +0,45.lO'^C 1.18 Tai ba dinh tarn giac deu, ngu'di ta dat dien tich giong qi = q2 = q3 = F, = ( ^ / - ^ / ^ + l ) • ^ ^ i ^ ^ : l ^ « 0,54.10-^N (6.10-'°)2 - TiTdng tiT cho cac dien tich khac • q = 6.10~^C Phai dat dien tich thuf tUqo d dau, la bao nhieu de he can bang? " ' i.' Bai giai > - VSy: Do Idn cua life dien tac dung len moi dien tich la F « 0,54.1 O - ' N •fW •-'"n SlJ C A N B A N G C U A D I E N T I C H • , - ,1,/ ,|i ^''^ Cac lire dien tac dung vao qo: FJQ , FJQ va FJQ De qo can b^ng thi: • F,Q + F2Q + FJQ = Vi qi = q2 = q3 = q = lO^C => qo n^m d tarn tarn giac ABC 1.17 Hai dien tich q, = -2.10"^C, q2 = 1,8.10"^C dat khong tai A va B, - AB = / = 8cm Mot dien tich qa dat tai C Hoi: V i tinh doi xiJng cua he nen de he can bang ta a) C ct dau de q3 n^m can bhng? Ichi can xet them dieu kien can bang cua mot b) Da'u va Idn cua qs de qi, q2 cung can bang Itrong ba dien tich kia, chang han q3 De q3 can * * Ib^ng thi: Fo3 + Fj3 + F23 = B^igiai a) V i tri cua C de qs nhm can b^ng r ^ F o = F'3 = 2F,3Cos30° = 2k - Cac life dien tac dung len qs: F j j F j j ' - De q3 nkm can bing thi: F^J + F23 = => F j j = - F j j => F j j F j j cung phu'dng, 3k I0 ^2 A 18 t- = V3k 1113 B jVi I1I3I 73 (Fo3 = k = Vik q,, q2, q3 > •Il = nen I1I3 (F,3 = F = k Ills ) I0I3 a BC^ AC^ [BCJ I0I3 a' ngifdc chieu va c&ng Idn: Fo = F23 k fAcV ^ 3 6.10-''= 3,46.10-^C qo < I Vay: De he can bang tW ph; j.io-'c 17 16 Bfii dugng hpc sinh gi6i V^t ly 11, t^p - NguySn PhCi B6ng 1.19 d moi dinh hinh vuong canh a c6 dat dien tich Q = lO'^C Xac dinh dau, dp Idn dien tich q dat d tarn hinh vuong de ca he dien tich can bang? Bai giai - Vi dien tich d cac dinh hinh vuong nh\S nen dien tich q dat d tarn hinh vuong luon can bhng - Vi he CO tinh doi xufng nen chi can xet dieu kien can b^ng cua mot cac dien tich lai, chdng han dien tich dat d D - De dien tich dat d D nam can bang thi: Fj4 + F24+F34+Fq= =:>F'4 + F24 = Fq ( F , + F - F ) CtyTNHH MW'DWHJ ; q ' , ? =T Goi q, m la dien tich ban dau va khoi liTcJng cua moi qua cau - (2]sin-1)2 Trirdc cham tay vao mot qua cau, dieu kien can bang cua mot qua cau cho: 2 tana = - « — P 21 a ~— a^mg Trong dien moi E: (F = k ^ ; P = mg) a => a + Cac lire tac dung vao mot qua cau: lire P, li/c cSng day ^ 2kq^l F2 va lire day Ac-si-met F^ (1) mg 21 + Dieu kien can bang cua mot qua cau cho: a F2 = (P-FA)tan- Khi cham tay vao mot qua cau, qua cau se ma't he't dien tich, life dien giiJa hai qua cau khong nffa, hai qua cau se cham vao va dien tich lai du'cfc phan bo deu cho hai qua cau (q' = ~ ) ' hai qua cau lai day va = (D,-D2)Vg.tan cau lijc ta suy ra: - 2kq^ — • -1 q sin a, tan—*- «2 a, 2«1 n _ D,-D, • D, tan ' sm ^ Ot, -J-tan-i sm^-^tan-^ "4 •w 3,15cm => a = ^ TiJ(l) va (2)suyra: (2) mg (2) a •2 \2 e(2/sin ?) khoang each giiJa chiing la a', lu'dng tiT, tCf dieu kien can bang ciia mot qua a , lire dien Vay: Gia tri cua £ theo D,, D2, a,, a2 la = ? , ^ "f , 20 Trong khong khi: 1-24 Hai dien tich q, = 2.10'^C va q2 = -8.10"'C dat tai A va B khong khi, A B = 8cm Mot dien tich qa dat d C Hoi: ^) C dau de q., can bang? Khi qj can bang, qj phai cd dau nhu" the nao de can a) Tinh e cua dien moi theo Di, D2, tti, a2 - ^^2 E ^ ' • bang la can bang ben? khong ben? CtyTNHH MTV D W H Khang Vi§t i duSng hpc sinh gi6i Vjt ly 11, tjp - Nguygn PhCi B6ng B NHIJNQ CHIJ Y K H I GIAI BAI Dung dinh luat L e n x d xac djnh chieu dong dien cam iJng khung day T A P ~- K h i ap dung dinh luat Lenxcf de xac djnh chieu dong dien can chii y „ ' J,, triTcJng hcJp cu the: Thanh nam cham rdi den gan khung day, sau di qua khung day va rdi xa + Ne'u O tang, dong dien cam uTng mach Ic se tao ttr trudng ngiTdc chieu vdi tiT triTdng ban dau B de chong lai sif tang cua + N e u giam, dong dien cam iJug mach Ic se tao tCf trudng g cung chieu v d i tH tri/dng ban dau B de chong lai s\i giam cua : o n chay cua bien trd R di chuyen sang phai ^,«, , igit khoa K (ban dau dang dong) S chOrnhat cang d e t d i •• • Xac dinh chieu cua B : De bai cho, dac d i e m tif trifdng cua nam cham, cac I Ichung day Chung day tiT tri/cfng ban dau hinh vuong, sau duTdc k^o hinh O Nhu vay, each xac djnh chieu ciia Ic nhiT sau: ' >< = ; iTa khung day xa dong dien ' a m cirdng dong dien xolenoit quy t^c " C a i dinh o'c" xac dinh chieu cua B I I n cac tru-cJng hdp sau: • Xac dinh xem O tSng hay giam: DiTa vao bieu thiJc O = BScosa • Xic dinh chieu cua B^: DiTa vao sir tang, giam cua O ' j • Xac djnh chieu cua Ic: Theo quy t^c " C a i dinh oc" (hoac quy tac "Nam tay phai") - K h i xac djnh sua't dien dong cam ilng, dong dien cam ifng can chu y : K a- + Dung cdc cong thiJc tinh suat dien dong cam ufng mach k i n va doan day chuyen dong -V- (c) + K e t hdp v d i cac cong thlJc ve djnh luat m de xac djnh cac dai liTdng dien n h i f l , r, + K e t hdp v d i cdc djnh luat N i u - t d n de xac dinh cac dai lu'dng cd hoc nhif v, D a, s, c cAc BAI T A P V £ D O N G DI|:N CAM C A M C N Q D I $ N TIT ITNG M o t nam cham di/dc di/a lai gan mot vong day dan nhiT hinh ve H o i dong dien cam hanh nam cham rdi xuong tfug — ] i nam cham rdi de'n v6ng c6 chieu n^o ? V o n g day se di in chuyen ve phia nao ? • - hong tang, • B a i g i a i K h i diTa nam cham lai gan thi tif thong tang nen BQ ngi/dc chieu v d i B Theo quy t^c " N ^ m tay p h a i " thi Ic c6 chieu nhiT hmh ve - phai ben B^ thi tiJf ngi/dc chieu vdi B , dong dien B S _ N y Vi mat ben trai cua vong day la mat B^c ( N ) nen vong day se bi day, di chuyen ve khung day ^0 -r- am uTng cd chieu: A-^D-^C->B->A ^ K h i nam cham di qua khung day va rdi xa day thi tif thong giam, B, vdi B, dong dien cam uTng ciing chieu c6 chieu A-^B->C->D^A 404 405 Cty TNHH W T V D W I T K n a n g V i e i i dii8ng hgc sinh gi6i V j t ly 11, t i p - Nguygn Phu e n g b) Con chay cua bi6n trd R di chuyen sang phai Hai vong day dan tron ciing ban kinh dat dong Ta cd: TCr triTdng B cua dong dien I cd m, vuong goc nhau, each dien vdi V n g mot dong dien I di qua K h i g i a m I , vong hai cd chieu ttf ngoai K h i chay cua 6ng dien cam i?ng khong ? N e u cd, hay xae djnh bien ltd R di chuyen sang phai = > dien tret h i e u dong dien cam iJng tren hinh ve tang, nen cU'cJng dong dien I giam, tuf Bai giai thong qua khung giam, BQ ciing chieu v d i B, dong A B - > dien cam C-> D A lifng c6 'ir trirdng eua dong dien I vong day tron ed phU'dng vuong goc vdi chieu: ^ a t phang vong day 1, nghTa la song song v d i mat phang vong day Do vay hi I bien thien thi tiT tru'dng I gay bien thien nhiTng cac du'dng siJe dien c) Khi ngat khoa K (ban dau K dong): ^ - Ban dau K dong, B c6 chieu hU'dng len - Trong thdi gian ngat K, dong dien ong song v d i m a t ' p h a n g vong dSy nen tiT thong qua vong day b^ng khong nen khong cd dong dien cam iifng xuat hien vong day l4.4 Cupn day cd N = 100 vong, dien tich moi vong S = 300cm^ cd true song cuon day giam nen cam (Jng tif qua khung song vdi B day A B C D giam => ttf triTdng cam iJng vuong cd dien tich Idn hdn hinh chu" )6 Idn cua suat dien dong cam tfng: E = :, , nhat Do do, qua trinh keo thi D • ' /> 0,5 A tru'dng cam i^ng B^^ ciing chieu vdi chieu A - > B C - > D (Jng Ic A c6 AB [Smm^ dat vuong gdc vdi B cua ttr triJdng deu T i n h dp bien thien — A cam ijfng tiT dong dien cam ufng vong day la I = 2A e) DiCa khung day xa dong dien K h i du'a khung day xa dong dien thi tuf thong giam, Bat © chieu vdi B , dong dien cam ilng Ic c6 chieu: A - > B ^ C ^ D - > A Be D E = K h i giam ciTdng dp d6ng dien chieu v d i B , 406 B^, ciing dong dien cam iJug c6 A^D->C->B->A •••^v- Bai giai dien dong cam iJng xuat hien vong day cd dp Idn: AO A(BS) At At f) Giam ci/dng dong dien xolenoit chieu = 1,2V 1.5 V o n g day dong ( p = l,75.10"*Q.m) di/dng kinh d = 20cm, tiet dien So = x o l e n o i t thi tiT thong giam, At At V a y : Suat dien dong cam uTng trung binh cupn day la E = 1,2V den itr thong qua khung giam => ttf => dong dien cam NBS.Ccosttj - c o s a j ) ,-4 100.0,2.300.10 B dien tich cua khung giam dan, dan Cling sau A->B->C->D->A K h i hai hinh c6 ciing chu vi thi hinh B(, Quay deu cupn day de iinh cupn day d) K e o khung day hinh chiJ nhat cang det d i B cua tir tru'dng deu, B = 0,2T At = 0,5s, true cua nd vuong gdc v d i B Tinh suat dien dong cam ilng trung Bp cDng chieu vdi B => dong dien cam drng Ic CO chieu B = S AB 7id^ AB;; At At" / 7td S D i e n trd ciia vong day: R = p - = p — D / / A B S HiV I AB _ dS AB = — Ttd 4p • At Tcd^ E Cirdng dp dong dien cam ilng qua vong day: I = — cua i duBng hpc sinh gidi vat ly 11, tjp - Nguygn Phil D6ng Cty TMHH MTV DVVH Khang Viet 4.8 Vong day dan dien tich S = 100cm^ dien trd R = 0,01 Q quay deu tir At dS 0,2.5.10-^ tru'dng deu B = 0,05T, true quay la mot du'dng kinh cua vong day va vuong goc vdi B Tim cirdng dp trung binh cua dong dien vong va dien liTpng qua AR Vay: Do bien thien cam u^ng tiT mot ddn vj thdi gian la = 0,14T/s At 14.6 Cuon day N = 1000 vong, dien tich moi vong S = 20cm^ c6 true song song vdi B cua tCr trirdng deu Tinh bien thien AB cua cam u^ng tif thdj - gian At = iO'^s c6 suat dien dong cam iJug Ec = lOV cuon day Bai giai Sua't dien dong cam uTng xua't hien cuon day c6 dp Idn: E= AO At = NS AB At >AB = E.At NS 10.10"^ = 0,05T 1000.20.10"'* 14.7 Cuon day kim loai (p = 2.10"^fi.m ), N = 1000 vong, diTcfng kinh d = 10cm, tiet dien day S = 0,2mm^ c6 true song song vdi B cua tuf triTdng deu Tdc AB bien thien — = 0,2T/s Cho TI « 3,2 At a) Noi hai dau cuon day vdi mot tu dien C = ^ Tinh dien tich cQa tu dien b) No'i hai dau cuon day vdi Tinh ci/dng dp dong cam ifng v^ cong suat nhiet cuon day Ta c6: Sua't dien dong cam li'ng xua't hien cuon day c6 dp Idn: E= At = NS At = N Tcd^ AB 1000.71.0, r At -.0,2= 1,6V b) Cu'dng dp dong cam iJng va cong sua't nhiet cuon day S ~ S Sua't dien dong cam li'ng xua't hien vong day: E= AO BS(cos90°-cos60°) 0,05.100.10"^cos60" At At 0,5 = 5.10-V Cu'dng dp trung binh cua dong dien vong day: I = — = 5.10 -4 = 0,05A 0,01 Dien liTdng qua tiet dien vong day: q = It = 0,05.0,5 = 0,025C Vay: Cu'dng dp trung binh cua dong dien vong day va dien lu'dng qua tiet dien vong day la 0,05A va 0,025C 4.9 Vong day dan dong cha't dat tCf tru^dng bie'n thien deu c6 B vuong goc vdi mat phdng vong day ) Tinh hieu dien the' giQa hai diem bat ki tren vong ; ) Mac vao hai diem ba't ki cua vong mot von ke dien tiT, kim von ke c6 lech khong ? Bai giai Xet doan day ACB, ta c6: EACB = - ^ E R (E ti le vdi chieu dai day hay ti le vdi dien trd day) Gia sur dong dien c6 chieu nhiT hinh ve, theo djnh luat 6m ta cd: a) Dien tich cua tu dien: Q = CU = CE = 1.1,6 = 1,6 ^C Dien trd cua cuon day: R = p - = p Bai giai ) Hieu dien the giffa hai diem bat ki tren vong Bai giai AB den 90° R Vay: Dp bien thien AB cua cam (Jng tuf thdi gian At = 10"^s la AB = 0,05T AO tiet dien vong day neu thdi gian At = 0,5s, goc a = (n, B) thay ddi tCif 60° = 2.10"^ TT-O 1-1000 ^ 0,2.10'^ E Cirdng dp dong cam iJng qua cuon day: I = — = — = 0,05A R 32 Cong sua't nhiet cua cuon day: P = RI^ = 32.0,05^ = 0,08W Vay: Cu'dng dp dong cam iJng va cong sua't nhiet cuon day la 0,05A 0,08W R, R, UAB = I R A C B - E A C B = - ^ E - ^ E R K =0 Vay: Hieu dien thegiffa hai diem ba't ki tren vong la U = ) Kim von ke c6 lech khong? Mac du UAB = nhu-ng mach van cd dong dien diTpc tri bdi triTdng lire la Tren doan mach AB ta cd: Uv = E Do mac von ke vao hai diem A va B von ke se bj lech 409 Cty TNHH MTV D W H Khang Vi$t BfiidiJSng hoc sinh gi6i Vjt ly 11, tjp - Nguygn Phu e6ng Khung day dan tiet dien deu c6 dang hai nuTa du'dng 14.10 tron nh\i hinh ve, du'dng kinh d = 40cm, dien trd cua mot ddn vi chieu dai day Ro = 0,5Q/m Khung day dat AO, AB At At a ® E, + Chieu dong dien cam uTng I , : B tang ttr triTcJng deu c6 B vuong goc vdi mat phang B a/2 F Sj =kS, =ka2(V) ® B B - ® , RBe nen B„ ngiTPc chieu vdi B , dong I i ° ^ • D C E di ttr A d e n D + Vdi dong dien I i , Ei tiTdng diTdng vdi nguon cd eye am n6'i vdi A, circ khung Mot ampe ke' (RA = 0) du'dc m^c no'i tie'p mach nh\i hinh ve Tinh so chi cua ampe ke neu B thay doi theo thdi gian theo quy luat B = Kt, K = 2T/s du'dng noi vdi D Baigiai j, Xet khung day BCEF: Dien trd Ri la dien trd difdng kinh ciia khung: 0Bc R, = dRo = 0,4.0,5 = 0,2a Dien trd R2, R3 la dien trd nuTa du'dng tron: li R^ = R3 = y 0,5 = - ^ ^ , = 0,l7t(Q) I3 ^ + Suaft dien dong cam uTng E2: = AO, AB At At ka^ Si — R.S'i — -(V) f + Chieu ddng dien cam tfng I2: B tSng nen Bg ngiTdc chieu vdi B , dong I2 di ttr E den F Dien trd toan mach: R = R , + R - 1^+iR: 3^ = ', l r + 0,2 + 0,l7c = 0,436Q + Vdi dong dien I2, E2 tiTdng diTdng vdi nguon c6 circ am noi vdi E, circ I % Sua't dien dong cam uTng xuat hien khung: E = AO ABS At At = 2S = 7td^ = Ap dung djnh luat Om cho cac doan mach BC, ta c6: 3,14.0,4^ Cirdng dp dong dien qua R2: I , = = R AB + UBC = - E l + Ii.3ar = - Ijar ^ -Ka^ + Ii.3ar = - Isar Ka^ - I2.2ar = - har + UBC = E2 - l2-2ar = - Isar 25 0,436 Hieudienthe d a u R i : U , = E - R l = f + Il=l2+l3 = 0,288A Lay (4) cpng (5): larli = 3,5Ka' => Ii = « 0,1 A 0,17t Khung day dan kich thifdc nhiT hinh ve, dat vuong goc vdi B ciia ttr trirdng deu, B = Kt, dien trd cua mot ddn vj chieu dai ciia khung (5) o a r I i - arl2 = Ka^ j khung day Baigiai + Suat dien dong cam lirng El: 410 ^ 7Ka ^ Tinh cirdng dp dong dien qua tirng ph^n cua Xet khung day ABCD: :V; / 22r dayiar - ' •;i •••• 7Ka 7Ka l,5Ka2-3ar— Vay: So chi cua ampe ke la 0,1 A 14.11 (4) , RT (2) The (3) vao (1): 3arli - Ka^ = - (I, - l2).ar 0,l7i.O,288 = 0,035V = — = (1) (3) ' Lay (1) trtf (2): 3arli + 2arl2 = l,5Ka^ "2/5 Cirdng dong dien qua R3: difdng noi vdi F ay: +Cifdng dp dong dien qua nhanh trai: I i = IBAC = +Cifdng dp dong dien qua nhdnh giuTa: I3 = ICB = 22r Ka 22r" 3Ka +Cifdng dp dong dien qua nhanh phai: I2 = ICEB = U r 411 D W H Khang B6i dugng hpc sinh gi6i V$t ly 11, tap - NguySn Phu Dfing D i e n tich tren m o i t u : 14.12 M o t k i m loai M N nKm ngang c6 TcR^KC khd'i li/dng m c6 the triTOt khong ma sat Q, = C i U , = C , E = doc theo hai ray song song, cac ray hdp v d i mat phang ngang, goc d\id\a a hu'dng len Khoang thang each giffa ray la / Bo qua dien trcl cua Theo djnh luat bao toan dien tich: Q j + mach M a t khae: U j = U K h i chuyen dong, sua't dien dong cam iJng Ec bang: = - Qi • o D i e n tich tren tu d i e n : q = Cuc = CB/v.cos a _ Q2 _ Q'I+Q2 ^-77777^ ;Q2= Qi = Q, = d Cu'dng dong dien xuat hien mach: i = Q; _ Q2-Q1 _ ^ R ' K ( C , - C , ) 2 C1+C2 • C,+ C2 V a y : D i e n tieh tren cac ban tu sau lay dan d i \h Ec = B l v s i n ( ^ - a ) = Blv.eosa = U(^ - '1 Bai giai - ' hai Tinh gia toe chuyen dong cua M N - ' ' tu CO dien tieh khae da'u vdi nhau, dien tich cua tu bay g i d la Q p Q hai ray noi vdi mot tu dien C diJng - " TtR^KC = K h i lay dan di r o i sau giiJ cho ttr tru'dng khong doi tiJc la ta noi ban Dau He thong dat mot ttr trufdng B i ^ ; Q = C2U2 = C2E — = CBla.cosa d, TtR^KC, C2 - C , _ ;cR^KC2 C - C C1+C2 C1+C2 4.14 M o t eai vong c6 dirdng kinh d, khoi liTdng m v ^ d i e n trd R rdi vao mot tijf triTdng ttr dp cao kha Idn M a t phang vong luon n ^ m ngang va vuong goc vdi - Lire tijf tac dung len thanh: F = B i / = CB^/^.cos a B T i m van toe r d i deu cua vong ne'u B thay doi theo dp cao h theo quy luat - Tuf djnh luat I I N i u - t d n , ta c6: Psin a - Fcos a = ma B = Bo(l + a h) Coi gia toe trpng triTdng g la khong d o i va bo qua siJc can Omg.sina cua m o i triTdng => a = -CB¥a.cos^" = ma a(m + C B ¥ C O S ^ " ) = mg.sina Bai giai mgsma m+CB^/^cos^a K h i vong rdi d e u , dong nang cua vong khong d o i nen dp g i a m the ning V a y : Gia toe chuyen dong ciia M N la a = mgsma m + CB^/^cos^a 14.13 M o t vong day dan tron ban kinh R c6 mot dan vong bang nhiet li/dng vong toa AO Sua't d i e n dong cam ufng xuat hien vong: Ec = At dat doe theo mot di/dng kinh ehia doi vong day d giiJa A(BS) m o i nijfa vong day c6 mot tu dien, dien dung C i , C2 At V o n g day dat tilf tru'dng deu c6 B vuong goc v d i At -.B.a Ah At Ah K la mot hang so T a i mot thdi d i e m nao ngu'di ta At = V => Ec = — B n t t v (v m van t6c rdi deu ciia vong) T i m d i e n tich tren cac tu sau Bai giai - A(Bo(H-ah)-^)_^^ mat phang vong day, B thay doi theo quy luat B(t) = K t , lay dan d i r o i sau gii? cho tiT triTcfng khong d o i Suaft d i e n dong cam lifng xuat hien vong day: E = At E, Ttd^Bgav Ci/6ng dp dong d i $ n vong: I = - r ^ = — ^ — R 4R h Theo dinh luat bao toan nang liTdng, ta c6: mgh = R I t, v d i ^ = ^ • nd^B^av , AO At cua = -lis—1:= n^d^'B^a^v^ 16mgR 413 BSTduang hpc sinh giSi vat ly 11, tjp - NguySn Phu B6ng V a y : V a n toe rdi deu cua vong la v = Cty TNHH MTV DWH Khang Uigl 16mgR ngin chay qua dien ke xung kich, dien ke chi mot dp lech D p lech ti le TT^d'^B^a^ v d i dien lu^png dong dien chuyen qua dien k e , neu thcJi gian dong dien 14.15 M o t khung day dan hinh vuong canh a, khoi liTdng m , dien t r d R duo chay qua la nho so vdi chu k i dao dpng rieng cua bp phan dpng dien ke truyen mot van toe ban dau theo phi/dng ngang Khung chuyen dpng tron D a i liTpng xac djnh bKng ti le giffa dien li/png chuyen qua dien ke va dp lech mat ph^ng thang diJng mot tiT triTdng vuong g6c v d i mat khung cua dien ke gpi la h i n g so xung kich cua dien k e Cam iJng tijf B thay d d i theo quy luat B(y) = D d cam u^ng tif, ta dat cupn day vao khu viTc can do, eho mat phing Bo + kv, k = const Sau mot thdi gian khung i ^^ dat van toe khong doi v T i m van to'e ban dai Sau ta keo nhanh cupn day khoi tCr triTdng, k h i e n eho tCf thong qua dau truyen eho khung C o i gia toe cupn day g i a m den khong Trong cupn day xuaft hien sua't dien dpng cam iJng triTcJng g la khong d d i va bo qua life can cua (J) g day ra, dp bien thien tiT thong cang Idn va dien li/png chuyen qua dien ke Bai giai Chuyen dong cua khung day la tdng hdp cua chuyen dong deu v d i van toe di/dc truyen v^ theo phu^cfng nam ngang (theo true x ) va chuyen dpng theo phiTdng t h i n g duTng (doe theo true z) j,^ v l mach eua cupn day va dien ke eo mot dong d i e n ngin, chuyen qua dien ke mot dien liTdng cam ufng TiT triTdng cang manh, thi k h i ta keo cupn m o i trirdng - eua cupn day vuong gdc vdi tiT tri^dng K h i tiT thong qua cupn day la ciTe Theo phu'Png thang diJng, khung chju tac dung eua life trpng triTdng va life tir xung kich cang Idn V i vay, bang each xac dinh dp lech cua dien k e , ta diTdc cam i^ng tiT Trong thiTc te, ngiTdi ta rat hay dCing phiTdng phap de cam iJng tiJf T i r thong qua n vong eua cupn day no n^m tir tru-dng la: = BSn giiTa dong dien cam ij-ng khung va tiT triTcfng Luc dau, khung rdi nhanh K h i ta k6o cupn day k h o i tif triTdng, tir thong (!?2 qua nd bSng khong, do dan, sau dat van toe khong ddi nen: mg = BIl dp bien thien tir thong la: A O = O2 - O , = - B S n AB.S ka^ K h i tir thong qua cupn day bien thien, cupn day xuat hien suat dien R.At R Cirdng dp dong dien khung: I = = R m g = ka ka^ R a V = dong cam iTng: Cc = dO " ' dt ^ e ' kV V a n toe toan phan v cua khung chuyen dpng deu: Trong mach cua cupn day va dien ke c6 dong dien I = • D i e n lirdng R chuyen qua mach dien ke khoang thdi gian dt la: V 14.16 D e cam iJng tiT giffa hai ciTc cua mot nam cham dien, ngiTdi ta dat vao mot cupn day nho g o m N = 50 vong, noi v d i mot dien ke xung kich, mat p h i n g cupn day vuong gdc vdi B , dien tieh vong day S = 2cm^ dien trd cupn day raft nho, dien trd dien ke R = 2.10^Q K h i keo nhanh cupn day khoi tCr trirdng cua nam cham thi dien ke lech 50 dp chia B i e t ed mot dien liTdng 2.10"^C di qua dien ke thi k i m dien ke lech mot dp chia T i n h cam iJng tijT cua nam cham dien Bai giai - D i e n k e xung kich la mot loai dien ke nhay, m l bp phan dpng (khung day) c6 quin tinh Idn, nen c6 chu k i dao dpng rieng Idn K h i c6 mot xung dong dien 414 dq = I d t = ^ d t = K H ^ R -—do R K h i tir thong bien thien mot lirdng A O thi dien lirpng chuyen qua dien ke l a Aq = R D o do, k h i ta keo cupn day k h o i tir triTdng, dien liTdng chuyen qua dien ke l a : Aq = -AO BSn D i e n luTdng Aq chuyen qua dien ke" xung kich chi mot dp lech p V i the Aq = pC Blng xac dinh diTdc cam uTng tir B : B each dp lech p, ta c6 the _ R ^ _ RCP ^ l " ^ ^ ^ Sn bn V a y : C a m iTng tiJf cua nam cham dien I I B = 0,2T 2.10-^.50 B6i duang hpc sinh gidi Vjt ly 11 t$p - Mguyin Phu D6ng Cty TNHH MTV D W H Khang Vi^t 14.17 M o t o n g d a y c h i e u d a i / - c m , t i e t d i e n S = l , c m ^ c l o i sat tijf Trg,^ t h u p c m o t e a c h p h i f c t a p v a o c a m i f n g t i f Bo d a t v a o v a t U e u , tuTc l a v a o cU'dng C u o n diTOc n o i v d i m o t d i e n k e ' x u n g k i c h ( k i m d i e n k e ' l e c h m o t d o c h i a d d o n g d i e n c h a y q u a x o l e n o i t D o d o , b a n g phUdng p h a p d o n e u t r o n g b a i , C O d i e n li/dng 1,2.10"^C d i q u a ) , c u o n v a d i e n ke' c6 d i e n t r d R = Q Cho v d i n h f f n g d o n g d i e n q u a x o l e n o i t t i f n h o d e n I d n , ta c t h e n g h i e n ciJu difoc d o n g d i e n 0,5A qua c u o n day I r o i diing m o t dao d i e n d e d o i c h i e u d o n g dien sir b i e n d o i c u a |j, t h e o BQ n a y K h i d o k i m d i e n k e l e c h d o c h i a T i n h d o t i f t h a m c u a l o i s^t dieu kien thi nghiem tren ,., B a i giai A' ( • ; ( ) 18 V o n g d a y d a n b a n k i n h R d a t v u o n g g o c v d i B c u a t i f t r i f d n g d e u B t h a y d o i t h e o t h d i g i a n t h e o q u y l u a t B = k t , k = const T i n h cu-dng d p d i e n t r i f d n g -.-u ' • :!,*- X o l e n o i t c6 c h i e u d a i I d n h d n b a n k i n h t i e t d i e n n e n b e n t r o n g x o l e n o i t , tir ;;, t r i r d n g l a d e u Ne'u l o i sat tCr c d o t t f t h a m n c h i e m d a y k h o n g g i a n ben t r o n g x o l e n o i t , t h i c a m ij-ng tCr b e n t r o n g x o l e n o i t I d n h d n k h i k h o n g c l o i sat |i, I a n : B = ^IBQ = ^.^Qnl xody E tren vong Sua't d i e n d o n g c a m i f n g xua't h i e n t r o n g v o n g d a y : E N ( t r o n g d o n = — - l a so' v o n g d a y t r e n m o t d d n v j c h i e u d a i c u a x o l e n o i t ) - C h u y r K n g d p t i f t h a m )x c u a v a t sjft tCf k h o n g p h a i l a m o t h h n g s o , m a p h u o n g d a y c h a i c u o n d a y : c u o n c N , = 0 v o n g , c u o n c N = 100 v o n g D o n g d i e n c h a y t r o n g c u o n d a y N i c u a x o l e n o i t g a y r a t i f t r U d n g B va tir t h o n g E = k7cR^ _ _ q _ F.271R q (2) q T i r ( l ) v a (2) ta c : -;tR2=f:2^=Eo.27rR q ,.:•;:#,„,, (1) thifc h i e n k h i d i c h c h u y e n m o t d d n v i d i e n t i c h du'Png d p c theo v n g d a y k i n : nS'i v d i d i e n k e ' x u n g k i c h , n e n k h i t i f t h o n g q u a c u o n n a y b i e n t h i e n A O , t r o n g m a c h c u a d i e n k e x u n g k i c h c6 A' M a t k h a c : sua't d i e n d o n g c h i n h l a c o n g c u a d i e n t r i f d n g x o a y (tiJc t r i f d n g life l a ) x o l e n o i t , tiT triTcJng d o i c h i e u v a tiT t h o n g d o i d a u D p b i e n t h i e n tuf t h o n g qua cuon day N2 la A O = = kS ( E o = ^ ) = > E o = ^ q ,(1 V a y : C i r d n g d p d i e n t r i f d n g x o d y E t r e n v o n g d a y l a EQ = - D i e n k e xung kich chi mot lech a = — DOAN D A Y D A N C H U Y E N >?Sv,' C _ _ N , B S ^ 2N3^^tonIS R ^ g] CaR/ 2^oN,N2SI R ^ V a y : D o t i r t h a m c u a l o i s^t l a ,j B a i giai ~ = 1517 v a t l i e u s^t tif B a n d o c c t h e so s a n h p h e p d o | i v d i p h e p d o c a m tfng k h d c , dSc b i e t c h u y de'n e a c h g a y bie'n t h i e n tCf t h o n g T r o n g phi/dng p h a p d o M, , t a c t h e g a y n e n m o t d p b i e n t h i e n t i r t h o n g ^ " ( A O = ) b^ng cdch d o i chieu dong dien cuon day Suat d i e n d o n g xuat h i e n cuon day: ,, E ^ B/vsin a = 0,2.1.0,5.sin 30° = , V V a y : E = 0,05V , M a y b a y c c h i e u d a i / = m b a y theo p h i f d n g n g a n g v d i v a n t o e v = k m / h B i e t t h ^ n h p h a n t h i n g di^ng c u a c a m drng t i f T r a i Da't B = I O ^ ' T T i m h i e u d i e n t h e xua't h i e n d h a i d a u e d n h i t h e d u n g v o n k e t r e n m a y b a y d o h i e u d i ^ n t h e n a y d e suy r a v a n toe m d y b a y d i f d c k h o n g ? V I 416 „ • I.'- hien day _ ^^^^ Chu y : P h i f d n g p h a p n e u t r o n g b a i ra't h a y di/dc d u n g d e d o d o t i f t h a m c u a cac - TRONG T i f TRl/CfNG h d p v d i B c u a t i f triTdng d e u g o c a = 30°, B = 0,2T T i n h suat d i e n d o n g xua't Rl 2.47t - ^ 0 0 , " ^ , kR D o a n d a y d a n / = I m c h u y e n d o n g v d i v a n t o e v = 0,5m/s t h e o p h i f d n g ^ 2N,^^oN,IS 1,2.10-^256.12.0,6 D O N G l\»')b i^U'llit!' .^^.^ ' „:,„•,;, 417 B6i du8ng hgc sinh gidi vat ly 11 tjp - Nguygn Phu B6n9 Cty TNHH MTV D W H Khang Viet Bai giai Bai giai Ta c6: v = 720 km/h = 200 m/s •• Suat dien dpng cam iJng xuat hien tren thanh: E = B/vsin a = 0,4.0,2.6 = 0,48V a) Hieu dien the d hai dau canh - May bay chuyen dong giong nhif mot kim loai chuyen d6ng Cirdng dp d6ng dien cam liTng qua R: I = — = R triTcfng Trai Dat Vay: CiTdng dp d6ng dien dm uTng qua R la I = 0,32A Hieu diSn the d hai dau cdnh bang sua't dien dpng cam iJng: 14.23 Cho mach dien tCf tru'dng giong nhiT bai tren Van toe chuyen dpng U = Ec = B/vsina = 5.10-^50.200.1 = 0,5V cua AB la v = lOm/s, dien trd R = 150Q, cMbng dp dong dien cam iJng b) Co the dung von ke tren may bay hieu dien the d hai dau canh khong? I = 0,2A Bo qua ma sat Tim life keo tac dung len AB Khi noi hai dau cdnh vdi mot von ke ta c6 m6t mach kin Khi may bay chuyen dpng, tiT thong qua mach khong doi nen Ec = nen khong the van Bai giai B = 14.21 Thanh kim loai A B diTdc keo triTdt deu tren hai ray mat phang nam ngang vdi van toe tir tru'dng deu thang du'ng, cam iJng tuf B C2=r = 15T vdi van toe v = lOm/s Bo qua dien trd cac ray va cac npi tiep xiic ) Tinh dp Idn va chieu dong dien mach, Suat dien dpng xuat hien tren AB: E = B/vsina = B.0,5.10.1 = 5B he so' ma sat giuTa AB v^ ray Q C, 1) Muo'n dong dien AB chay tuf B den A, cirdng dp 1,8A phai keo AB tri/dt ! theo chieu nao, van toe va life keo bao = — ^ = - = 0,5 C2 1,5C, 1,5 nhieu ? Bai giai ^ => U, = 0,75V va U = 0,5 + 0,75 = 1,25V Dirdi tac dung cua life tff, AB se chuyen dpng sang phai, tren AB Vay: Dp Idn cam ifng tuf B = 0,25T se xuat hien suat dien dpng cam ffng: Ec = B/v = 0,1.0,2.10 = 0,2V 14.22 Thanh kim loai AB = / = 20cm diTdc loai nkm ngang nhiT hinh ve Cac ray n6'i vdi bang dien trd R = l,5Q Van t6c A B la v = 6m/s He thong dat mot tCf triTdng deu B th^ng du'ng (B = 0,4T) Bo qua dien trd ray va AB ^'^ ) Dp Idn va chieu dong dien mach, he s6 ma sat giffa AB va ray Ta c6: E = U = 5B = 1,25 => B = 0,25T keo tru'dt deu tren hai ray kim ' I dien trd la E = 1,2V; r = 0,5Q Do life dien tuf va ma sat, AB triTPt deu Bai giai C2 0,2.10 lOg, B vuong goc vdi khung day dan (B = 0,1T) nguon eo suat dien dpng va 0,5V.TinhB = Iv 24 Cho he thong nhi/ hinh ve, kim loai AB = / = 20cm, khoi Itfdng m = vao dau hai ray Bie't hieu dien the hai dau tu C2 la =^ U2 = 150.0,2 Vay: Life keo tac dung len AB la 0,6N B M^c hai tu dien C,, C2 (vdi C2 = l,5Ci) noi tiep y V i Ci noi tiep C2 nen: U , + U2 = U, vdi U, = RI Lire keo tac dung len AB: Fk^o = F,cr = B I / = 15.0,2.0,2 = 0,6N ® V = lOm/s Hai ray each doan / = 0,5m va dat n Suat dien dpng cam ijfng xuat hien tren thanh: E = B/vsin a = RI toe may bay bang each hieu dien the giffa hai dau canh may bay ' = 0,32A 1,5 J1 / / B / Cufdng dp dong dien mach: I = I V i trffdt deu nen: F = BIl 0,1.2.0,2 mg 0,01.10 o E-Ep 1,2-0,2 BIl = |img = 0,4 Vay: Cirdng dp ddng di$n mach la I = 2A, he so' ma sat giffa AB va ray 1^ 0,4 Tim ci/dng dp dong dien cam tfng qua R 419 Cty TNHH IVITV DWH Khang Vi6t B6\g hgc sinh gi6i Vjt ly 11 tjp - Nguyjn Phu D6ng b) Chieu, van toe va Idn life keo De dong dien AB ehay tii B den A thi theo quy tS'c "B^n tay trap AB phai triTdt sang phai: 1.2-1,8.0,5 ^ ^ j ^ E - E , ^ E - B l v => V = E - I r 01.0,2 = 15m/s r r Bl Lure k6o tae dung len AB: Fk + F =0 =>Fk = F„„-F= ^img-BIl =0,4.0,01.10-0,1.1,8.0,2 = 4.10-^N Vay: Van toe cua la v = 15m/s, Idn cua life keo la Fk = 4.10^(^ 14.25 Thanh dong MN khoi lu^dng m = 2g trifdt deu khong ma sAt vdi v = 5m/s tren hai dong thang dufng song song each khoang ® B / = 50cm tif tru'dng B nam ngang nhu" hinh ve, B = 0,2T Bo qua dien trd ede va dien M trd tiep xiie Cho g = Om/sl a) Tinh suat dien dong cam Ung MN b) Tinh liTc dien tiT, chieu va Idn dong dien earn tfng c) TinhR Bai giai a) Suat dien dong cam tfug xuat hien tren MN Ta e6: Ec = B/vsina = 0,2.0,5.5.1 = 0,5V b) Life dien tiT, chieu va Idn dong dien cam iirng - Thanh MN trU'dt xuong tac dung cua lye Luc tiT thong qua mach tang, xua't hien suat dien dong cam ufng Ec va cU'dng dong dien cam iJng Ic Thanh AB c6 dong dien Ic di qua se chju life tir F cua tif tru'dng B Dc chong lai siT bie'n thien tiT thong qua mach, lufc tijf F se cd chieu hU'dng len - Khi rdi deu: F = P = mg = 2.10 \0 = 2.10^'N 4' D o Idn dong dien earn iJng: F 2.10"^ = 0,2A Bl 0,2.0,5 : Vay: Lire dien tirF = 2.10'^N, dong dien cam lirng Ic = 0,2A c) TinhR Sua't dien dong cam iifng xua't hien tren thanh: Ec = B/v = 0,2.0,5.5 = 0,5V CU'dng dong dien xua't hien mach: Ip = —^ R R= 0,5 = , ^ Vay:R = 2,5Q • :/•v'^'*"-* ^"z4.26 Mot he thong day dan dat nam ngang nhiT hinh Thanh Hz triTdt tren eac canh Ox, Oy va luon vuong gdc vdi phan giac OH, Hz tiep xuc vdi Ox, Oy tai M va N Gdc xOy = a Van toe chuyen dong cua Hz khong doi va bang v Cac day dan deu ciing lam bhng mot chat, ciing IV tiet dien va cd dien trd bang r cho moi ddn vi dai Bo qua dien trd tiep xiic tai M, N He thong dat mot tCr tru'dng deu thang difng, cd c a m ilng tir B Khi Hz trU'dt tren Ox, Oy, hay xac dinh chieu va cU'dng dp dong dien cam iifng chay qua MN Bai giai Suat dien dong earn i^ng xua't hien tren MN: Ec = B/v Dien trd cua toan mach: R = ( 20M + MN)r MN „ MN vdi sina = OM = 20M 2sina 2sina R = ( — + l)r = l( + l)r sma sma Cirdng dong dien chay day dan MN: ErBlv Bvsina ,^ + sina, R (1 + sina)r K—: )r sma Theo quy tac "Ban tay phai" ta xac dinh diTdc chieu dong dien qua MN tir M denN Vay: CiTdng dong dien cam ti'ng chay qua MN la I = (1 + s m a ) r 27 Khung day dan hinh chiT nhat ACCA dat th^ng diTng, mot phan khung nam tir triTdng cd dirdng cam ufng vuong gdc vdi mat phang khung TiT tru'dng coi la deu (B = IT) khoang MNPQ va bang ngoai khoang Cho AC = / = 10cm, khung cd dien trd R = 0,2Q, khoi lirdng m = 20g Khung dirdc di chuyen thang duTng di xuong vdi van toe v = m/s 421 B6i dLOng hgc sinh gi6i vat a) Tinh ciTcfng dp dong dien cam iiTng khung va nhiet lUdng khung toa djch chuyen doan 10cm b) Tinh liTc ngoai can tac dung de khung chuyen dong vdi van toe deu nhiT tren Bai giai a) Cirdng dong dien cam ilng khung va nhiet liTdng khung toa djch chuyen ^ - Suat dien dong cam ufng xua't hien khung: j,, AO A(BS) B.AS BlAx 1.0,1.0,1 At At At At At Thdi gian khung djch chuyen: , Ax 0,1 ^ 0,1.0,1 1' At= — = — = 0,05s = ^r-r^ = 0,2V 0,05 0,2 = l A , - CUdng dp dong dien cam dng: !(-, = R 0,2 Nhiet liTPng toa tren khung: Q = Rl^t = 0,2.1 lO,05 = 0,01 J Vay: Khi khung dich chuyen, cifdng dong dien khung la lA, nhiet lifdng toa tren khung la 0,01 J b) Life ngoai can tac dung Gia suf cam ufng tiT B c6 chieu tif triTdc sau mat phing hinh ve Khi khung chuyen dong xuong diTdi, tif thong qua khung giam, B^ ciing chieu vdi B , dong dien cam ilng Ic c6 chieu A -> C -» C -> A Life tijf tac dung len canh AC c6 chieu hu'dng len tren, life tii tac dung len cac canh AA va CC se can bang nhau: T a c : P = mg = 0,02.10 = 0,2N F = BI/sina = 1.1.0,1 =0,1N Q ^ De chuyen dong deu vdi van toe v = 2m/s can tac dung liTc ngoai: F = P - F = 0,2 - 0,1 = 0,1N theo chieu hiTdng len tren (do P > F) 14 28 Thanh kim loai / = 1,2m quay tif triTdng deu quanh true A , A vu6ng goc vdi va song song B , B = 0,05T Van toe quay cua 1^ co = 120 vong/phut Tim hieu dien the hai dau ne'u true quay: ^ a) Qua mot dau b) Qua mot diem tren each mot dau 10cm 422 Cty TNHH ivi IV UVyH_Khang Vi$t ly 11, t$p - Nguygn PhO Sfing Bai giai Khi quay v6ng thi se quet dien tich: S = 7t R^ Khi quay phiit thi se quet dien tich la: A S = co S = 1207t RI Hieu dien the dau se bang suat dien dong cam iJug: U = Ec = AO BAS B.1207IR' At At At i true quay qua mot dau thi R = I = 1,2m: U= 0,05.120.7t 1,2' = 0,45V iXt'V.:.':"' 60 Khi true quay qua mot diem tren each dau 10cm thi R = + 0,1 = 1,1m .- ,Jlif0 - -m « u = 0,05.120n.l,r = 0,38V 60 29 DTa kim loai ban kinh r = 10cm dat vuong goc vdi B cua tCf tru'dng deu, B = 0,1T nhU' hmh ve, ® , dia quay vdi tan so n = vong/s Cac tiep dilm tai O, A noi dla vdi ampe ke' Tinh suaft dien dong cam iJng giffa O, A va chieu dong dien cam tfng Bai giai Suat dien dong cam lirng xua't hien giSa O va A: BAS Ec = AO At At Khi dia tron quay thi dTa se quet mpt dien tich: AS = co^R => E^ = B.coTtR^ 0,1.3.7i.O,r = 9,42.10-^V t Khi dTa quay, tiT thong tSng, tiT tru'dng cam u'ng B^ ngu'dc chieu vdi B , theo quy t^c nam tay phai Ic cd chieu tii A den O , 30 Mpt vong tron bhng day dan ban kinh r = 10cm dat tif tru'dng deu vuong goc vdi mat phang vong, B = 10"^T Vong noi vdi tarn b^ng kim loai: OA co'dinh, OB quay quanh O vdi van toe goc 00 = 4rad/s khong doi Dien trd cua moi ddn vi chieu dai vong va Ro = IQ/m Tinh cirdng dp dong dien qua cac va cac cung cua vong tron theo thdi gian 423 Cty TNHH IVIIV DVVH Khang Vi^t B a i giai - 10' ^ l Khi OB quay, tren xua't hien sua't dien dong cam iJng Ee dien dong dUOc xac dinh nhiT sau: f n ui; + Do bien thien tuT thong thdi gian A t : ' l+2t- ;f M, mfHiU EQB R•AOB Ec = - At l+2t- 10"\2t 4t '271 I + 2t- 4t^ dung C, dien trd cac khong dang ke; ab la mot kim loai kho'i lu'dng m diTdc dat tiTa len •A2B M N va PQ nhiT hinh ve He noi tren nam anh hurdng cua tuf trUdng deu c6 vectd cam u'ng i\i RA2B = (27t - (p)rR() = (27t - a)t)rRo , ^ MrtR„.(27t-cot)rR„ ^AiB-^A2B -3 hai dau M N difdc no'i vdi qua tu dien dien Ta c6: RAOB = RQA+ROB = 2rRo; RAIB = 9rRo = cortRo ; =>RN = 10 song song vdi mat phang nhm ngang, + Sua't dien dong cam iJng tren OB: Bcor^ 4t2 cot 2n 4.31 M N va PQ la hai kim loai dai thang dat H Ac:>=BAS = B ^ = ^ : ^ ^ 2 Ad) = B hudng vuong goc vdi td giay, chieu tu" tren xuo'ng Tac dung mot \\ic F nam mat phang _ cort.(27t-cot)rRQ td giay cho ab c6 chuyen dong tinh tie'n 27ir vdi gia toe a khong doi .1 Jiff Suy ra: ; Hay tim Idn cua li/c F GiCTa ab va cdc M N , PQ c6 he so ma + Cu'dng dong dien qua cac la: sat la fi., khoang each giila M N va PQ la L Bcor^ B a i giai 1= 2rR ^^AOB+RN Gia silf ab chuyen dong xa tu dien, theo quy t^e "Ban tay phai" dong ^ T^''^ dien se ed chieu tuf b den a Tai thdi diem t, ab eo van toe v, gia toe a Bcor 10 42(2 2Ro(2 + cot "^>-) 2.1(2+4t-^) 27t + Suaft dien dong cam iJng tren ab la: E = BLv ,-3 10"^4.10"' l+2t- Hieu dien the giffa hai dau tu dien la: U = E = BLv 4V Cirdng dong dien qua mach la: i = ^ 27t CirdngdodongdienquanhanhAlBla: I , = I - ^ R AlB = 4t^ cortR, dt = ma => F = ma + mg + B ^ C L \ = > F = m(a + ^ g ) + B^CL^a 10,-3 In 1.2t-^ + Cu'dng dong dien qua nhdnhA2B la: cort.(2rt - (ot)r 10 ^ l+2t- dt Li/c tif tac dung len ab la: F, = BiL = B^CL^a va eo chieu theo quy t^c F - F, - F„« 2^-4t lit _ IO"^(7t-2t) 4t2 (l+2t-—)rt 7t R A2B dt "Ban tay trai" Phi/dng trinh chuyen dong cua ab la: 27cr (27t - rot) 4t^ - cort.(2rt - cot)rRQ -3 l+2t- 1-3 l+2t- 10 = C — = C — = B C L — = BCLa dt 4t^ 2m (27i-a)t)r Vay: Dp Idn cua liTc tac dung len ab la F = m(a + ^l g) + B^CL^a 14.32 Mot triTdt b^ng kim loai c6 khoi lifdng m, CO the triTdt khong ma sat doc theo hai diTdng ray bang kim loai dat song song, nghieng vdi phiTdng ngang mot gdc a va each mot doan la b Cac dUdng ray du'dc noi kin d ben du'di bang mot tu chifa tich dien, ed dien dung C • • 425 Cty TNHH MTV DVVH Khanq Vi§t B6i duSng hgc sinh gi6i vat ly 11 tap - Nguyen Phii flflng Toan the he tr6n day dxidc dat mot ttf triTdng deu c6 vectd cam tfng tiJf B thang diJng (hinh ve) Vao thcfi diem ban dau, triTdt diTdc giff d khoang each / den canh day Hoi sau bao lau tCr luc buong tru'dt thi no dat den canh day ? Tinh van toe cua no ? Bo qua dien trd day dan Bai giai Gia sijr tai thcfi diem t, tru'dt kim loai c6 van toe v, gia to'c a Suat dien dong cam vlng xuat hien tren la: E = Bbv.sinp = Bbv.cosa - Hieu dien the'hai dau tu dien la: U = E = Bbv.cosa - Cu'dng dong dien qua mach la: i = ^ = C ^ = C — = BCb.cos a — = BCba cos a dt dt dt dt - Lire tiJf tdc dung len triTdt la: F = Bbi = B^Cb^a cos a va c6 chieu diTcfc xac djnh theo quy tac "Ban tay trai" Phu'cJng trinh chuyen dong cua triTcft la: b P + F = ma => Psin a - Fcos a = ma ^ m mg.sina - B^Cb^a.cos^" = ma f => a = m+B^Cb^cos^a mgsina // - ThcJi gian tiT liic buong de'n luc cham tu dien la: /21(m+B^Cb^cos^a) ^ 2s 21 ' mgsina mgsina t = J — :=> t = m + B^Cb^cos^a - Van toe cua cham den tu dien la: v = yfzas = I •2mg/sina V m +B^Cb^cos^a ChuvendelS: A T M TAT HIEN Tl/dNG TU CAM K I E N TliCrc Djnh nghla; Hien tiTcJng tiT cam 1^ hien Wdng cam i^ng dien tif xay tu" thong qua mach kin bien thien chinh siT bie'n thien cua dong dien mach gay Tuf thong t\f cam: O = U (I la dong dien qua mach, L la tiT cam ciia mach Vdi ong day (xolenoit) thi L = 471.10"'' 426 H, la tijr tham cua loi s^t tCr; N, S, / la so vong, tiet dien va chieu dai o'ng day) SuS't di^n dOng W cam: E,e = = - L — At At Nang liTc/ng tiJf trifcfng cua 6ng day: I - Nang liTdng tCrtriTdng: W = -LI^ = -LI^ = ^ - ^ S l - Mat nang liTcJng tCr triTcJng: w = B^ 87r.lO"\ 87i.lO'^n NHtJWQ CHCI t KHI Q i A l BAI TAP Ap dung cac cong tMc ve hien tifdng tif cam: tuf thong tif cam, tu" cam, suat dien dong tif cam, ning lu'cfng tif trUcJng Coi suat dien dong tiT cam nhu" suat dien dong cam tfng binh thu'dng (mach c6 nguon dien) ke't hdp vdi cac dinh luat m de tinh toan cac dai liTdng dien nhirl, U, r J; CAC BAI TAP VE HIEN TUONG T V C A M ,1 X61en6it dai / = 31,4cm, c6 N = 1000 vong, dien tich moi vong S = 10cm^ CO dong I = 2A di qua Tinh tCr thong qua moi vong day Tinh suat dien dong tii cam xolenoit ngat dong dien thcli gian A t = 0,1s, suy dp tif cam cua cuon day * ' Giai lai bai toan xolenoit c6 loi, tiT tham cua loi la |i = 500 Bai giai Tir thong qua moi v6ng day -7 N Cam urng tCf B ong day: B = 471.10 y l TCr thong tir cam qua moi vong day: O' = BS = 471.10"''.y.SI -6 10.10"^2 =8.10''Wb 1000 A-2 31,4.10" Vay: TiT thong qua moi vong day la = 8.10'^Wb I) Sua't dien dong tir cam xolenoit tir cam„ cua AO vaA L = — = 1000 5.3 Vong day sieu dan tif cam L , ban kinh r dat vuong goc vdti B cua tCr = 0,004H :-.(':SV.,;;;;t- tru'dng deu, cam (Jng tiT tang deu ttr den BQ Tinh cUcJng dp dong dien cam Vay: Sua't dien dong tiT cam xolenoit va tiT cam cua cuon day la uTng vong ec = 0,08V va L = 0,004H • Bai giai c) TrU'dng hdp xolenoit c6 loi tCf tham cua loi la |j = 500 Ttr thong qua vong day: = BScosa = B^Trr" •V'i Tuf thong tiT cam qua moi vong day: O" = nO'= 500.8.10"'^ =4.10"^Wb CiTdng dp dong dien cam i^ng vong day: I = — - Tcr^B, Suatdien dong tir cam: e^ = N ^ ^ = 1000.4.10"-^ = 40V At ' Vay: Cu'dng dp dong dien cam iJng vong day la: I = ' T NO)" 4.10^ll000 ^„ Do lii cam: L = — = = = 2H I I 5.4 Cho mach dien nhirhinh ve, L = IH, E = 12V, r Vay: Khi xolenoit c6 loi lis tham cua loi la |x = 500 thi ke't qua d cac can = 0, R = lOQ Dieu chinh bien trd de 0,1 a, b deu tang len 500 Ian giay R giam 5Q Tinh cu'dng dp dong dien 15.2 Chiyng minh rang nang liTcfng tiT triTcfng xolenoit la: W^^^ = mach khoang thdi gian tren IS Gpi I la cu'dng dp dong dien nguon E sinh ra; Ic la cufdng dp dong dien tir , vdi B la cam cam (do Ec sinh ra) W-IQ Ta c6: ling til' xolenoit R,+ r NSng liTdng tir trirdng: W = Ec = L • * LI^ 12 10 + = 1,2A; Al At 12 l2 = 2,4-1,2 At ^ Rj+r 5+0 = 2,4A = 12V 0,1 Vi R giam nen I tang va theo djnh luat Len-xd, dong dien tiT cam L ngU'dc chieu vdi I Cu'dng dp dong dien mach thdi gian tren la: r = I - Ic = Cam lirng tu" ong day: B = nHonl => I = ^' i E Bai giai vdi V = Si the tich ong day => L = H ^ Q I I ^ V E,r Bai giai va mat nSng lu'cfng ttr triTdng xolenoit la: w^^^ = Do tiT cam cua ong day: L = y = — ^ OT^B,, ,^ E—E R + r' = ( v i E = Ec) Vay: CiTdng dp dong dien mach khoang thdi gian tren la F = 5,5 Xolenoit khong loi chieu dai /, tiet dien S va N vong day =^W = ^^^o"^^ B^ ^ _BH^ ^ B ^ '(n^^n)' 2HHO 2n^io" W B^ Mat nSng lu'cfng tiT trUdng: w = —2L = _ V 2n^o Vay: Nang liTdng tif triTdng va mat dp nang lu'cfng ttr triTcfng xolenoit la: „, B^/S B^ W„, = va w„ = - ) Dien trd xolenoit bang R, cu'dng dp qua xolenoit ti le vdi thdi gian I = kt Tinh hieu dien the' hai dau xolenoit Hai dau xolenoit tren noi vdi mot nguon dien c6 sua't dien dong E, dien trd r = 0, dien trd xolenoit R ra't nho Khi t = 0, ngiTdi ta dong mach cho ddng dien qua xolenoit Tinh cu'dng dp dong dien qua xolenoit Bai giai '•1 f\(r-: igh Hieu dren the hai dau xolenoit Cam tfng tiT xolenoit: B = 47t.l0'^nl = 471.10"''ykt 428 429 Cty TNHH MTV DVVH Khang Vi?t duBng hpc sinh gi6i Vjt ly 11, tjp - Nguyjn Phii B6ng - Vi B bie'n tiiien tiieo t nen xolenoit c6 mot sua't dien dong t\X cam: At = -47:.10" = -N- At T2 / kS V\c Be sinh ngifcJc chieu vdi I mach nen theo djnh luat 6m U = -Ec+RI= 47t.l0 -7 ta c6: kS + kRt 15.7 Cho mach dien nhU" hinh ve; cuon day c6 tiT cam L, dien trd thuan khong dang ke Cac tu cd dien dung Ci va C2 NgUdi ta dong khoa K Tim dong dien cUc dai qua cuon day Tim hieu dien the' cifc dai tren hai ban cua tu Ci Bai giai Tai thdi diem dong dien qua cuon day cifc dai (WL = WL(max); W2C = 0), sua't dien dong cam ufng b^ng 0, toan bo hieu dien the cua nguon dat len tu Ci, dien tich tu C, la: Q, = C|Uo n Theo dinh luat bao toan dien tich suy nguon da "cung ca'p" cho mach m6t b) CiTdng dong dien qua xolenoit Vi r = 0, R rat nho nen U = E = -Ec = 47r.l0"^ ^ k S Matkhac,Ec = - L — => AI = - ^ A t = - A t , v d i L = 471.10"^^^^ nen: At L L El AI = At => I = -7 47t.lO"^N^S 47t.lO dien tich: AQ = CiUo- C,C Uo = c / El + Nang liTdng dien triTctng c\ic I dai d tu dien la: Wc E = -CU^ = -CE^, '2/ + N5ng liTcJng tCf triTSng cifc dai d oiig day la: W L = ^LI^^ Theo dinh luat bao to^n n^ng lu'dng: Wc = W , o l c E = vay: Imax = iLI^^=>W = E Gid tri ciTc dai ciia E^ 0• —U -I 2 da thiTc = A Q.Uo = - nen Theonguon dinh luat bao hien toan mot nangcong: lifdng:A Wmrac = Ws, o - C U ^ + A = ic.U^ + - L I ^ 2 47I.10"^N2S 15.6 Mot pin c6 sua't dien dong khong doi E mac no'i tie'p vdi mot ong day c6 tu" cam L va mot tu c6 dien dung C thong qua mot khoa K Ban dau khoa K mcl, tu khong tich dien Xac dinh gia tri ciTc dai cua d6ng dien mach sau dong khoa K Bo qua dien trd thuan mach Bai giai C,C, - Trirdc dong khoa K, dien tich tren moi tu la: Q = CUo = Vay: Hieu dien the hai dau xolenoit la U = 47r.lO~^ ^ k S + kRt Vay: CiTdng dong dien qua xolenoit la I = u d6ng dien mach sau d6ng khda K la 4^ 2(Cj+C2) C,+C2 ° ^ ° Vay: Dong dien ciTc dai qua cuon day 1^ lo = ° •Io = CiUo VL(CI+C2) C.Uo VL(C,+C2) " c, (Ban doc tu* giai de tim ket qua cua Uimax = Uo(l + C1+C2 )) 15.8 Hai ong day gio'ng nhau, diTdc m^c vie nguon dien khong ddi, sua't dien dong E va dien trd r, thong qua hai khda Ki va K2 (hlnh ve) Ban dau hai khoa deu md Sau dong Ki trU'dc roi den K2 Xic djnh Idn cua dong chay qua Ki v^o thdi diem dong K2 neu biet r^ng sau dong K2, d6ng on dinh chay qua Ki Idn hdn dong 6n djnh chay qua K2 la Ian Bo qua dien trd thuan ciia hai ong day r i t y E,r I J B6i duSng hgc sinh gioi V$l ly 11, tjp - Nguygn Phu D6ng Ten Quo'c te' MVC LVC K ' v ivy hi^u Vivt Nam "hdn thii nhat TINHDIEN Chuyen de :USC TUfdNG T A G T I N H D I E N deci centi deci centi d 0,1 = 10-' c Chuyen de 2: D I E N TRUCJNG 25 Chuyen dS 3: DIEN THE VA HIEU DIEN THE 46 Chuyen de 4: TIJ DIEN 71 ; m (tBd nXni • • ; • 0,01 = 10-^ Phdnthithai mili mili m :i D6NG D I E N K H O N G D O I 0,001 = 10'^ C/iM^n micro micro nano nano pico pico 0,000 001 = 10-^ n P 0,000 000 001 = 10"' 0,000 000 000 001 = ' ^ ^ 5/DONG DIEN KHONG DOI - DIEN TR6 ^ DINH LUAT M C H O DO AN M A C H 125 Chuyen d^ 6.MACH CAU DIEN TRd 166 Chuyen de 7: DIEN TRCJ PHU TRONG CAC DUNG CU DO DIEN 185 Chuyen de 8: CONG VA CONG SUAT CUA DONG DIEN 199 Chuyen de 9: DINH LUAT OM CHO TOAN MACH DINH LUAT OM TONG QUAT femto femto f 0,000 000 000 000 001 = 10"'^ atto atto a 0,000 000 000 000 000 001 = 10"'* zepto zepto z 0,000 000 000 000 0 000 001 = 10-^' yocto yocto y 0,000 000 000 000 000 000 000 001 = 10-^* 217 Chuyen de 10: CONG VA CONG SUAT CUA NGUON DIEN VA MAY THU DIEN 311 Chuyen de 11: DONG DIEN TRONG CAC MOI TRUING 353 •*n'^." Phdnthiiba i D I E N TlJ ^ Chuyen de 12: TlJ TRUCfNG 364 Chuyen de 13: Ll/C TlJ 380 Chuyen de 14: CAM LfNG DIEN T\J 403 Chuyen di 75.-HIEN T U O N G T U CAM 0: 426 • • 1., ; ^
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