cơ sở vật lí tập 2

MUC LUC CHUONG 11 SU QUAY 11 - Hoat dOng dia van dOng vien trtidt bang 11 - Cac hien s6 quay 11 - Cac dai lacing gOc coi nhv cac vec td : N6i them 11 - Su quay vOi gia tdc g6c khOng dOi 11 - Cac Nen so dai va Nen s6 g6c 11 - DOng nang quay 11 - Tinh toan quan tinh quay 11 - MO men quay 11 - Dinh lust thU hai oh Newton cho sit quay 11 - 10 Cong COng suat va dinh li ye cong - dOng nang On tap va TOm tat Cau hOi Bai tap va bai toan Bai toan bo sung 11 14 18 20 25 26 29 33 36 38 48 CHUONG 12 SU LAN MOMEN QUAY VA MO MEN XUNG LUNG 12 - St1 lan 12 - Cai yo - yO 12 - Tro lai vat mO men quay 12 - MO men Ong lacing 12 - Dinh lust thU hai cua Newton du6i clang gOc 12 - MO men dOng 111Ong cua mOt he hat 12 - MO men Ong luring cua mOt vat ran quay quanh mOt trvc c6 dinh 12 -8 Sti bao toan mO men dOng luting 12 - Su ban loan rn6 men dOng long MOt s6 thi du 12 - 10 Tien dOng cita quay hoi chuyen (TV chon) 12 - 11 MOmen dOng Wong cludc luring tit h6a (Tv chon) On tap va Tom tat Cau hOi Bai tap va Bai toan Bai toan bO sung Tieu luan CO hoc dia cac dOng tac quay vu dao 51 59 61 64 65 67 68 70 71 80 81 82 84 87 95 96 CHUONG 13 CAN BANG VA DAN HOT 13 - Can bang 13 - Cac diet' kien can cita can bang 13 - Trong tam 13 - Vai thi du ye can bang tinh 13 - Cac cau trilc bat dinh 13 - Dan hoi On tap va Tom tat Cau hoi Bai tap va Bai toan Bai toan.bO sung 104 105 106 108 118 119 125 126 127 137 CHUONG 14 DAC) DONG 14 - Dao dOng 14 - Chuyen dOng dieu h6a dOn gian 14 - Chuyen 'Prig dieu h6a dOn gian : Dinh lust ye lac 14 - Chuyen &Ong dieu h6a dOn gian : Khao sat ve nang lUdng 14 - MOt dao dOng tit diet.' h6a g6c don gian 14 - Cac lac 14 - Chuyen dOng dieu haa don gian va chuyen dOng trOn deu 14 - Chuyen dOng dieu haa don gian tat clan (tv chon) 14 - Dao thing curing bitc va sv cong httong (tV chon) On tap va TOm tat Cau hoi Bai tap va Bai toan Bai toan b6 sung 140 140 144 149 151 152 159 160 162 164 166 168 177 CHUONG 15 SU HAP DAN 15 - The gi6i va lac hap dan 15 - Dinh lust hap clan oh Newton 15 - Su hap dan va nguyen Ii chong chap 180 180 182 390 ■ •■ 15 - SO hap clan On be mat Trai Wt 15 - Do hang s6 hap dan G 15 - SO hap dan ben Trai Dat 15 - The nang hap dAn 15 - Hanh tinh va ye tinh : Dinh luat Kepler 15 - ye tinh : quy dao va nang IttOng (41 chon) 15 - 10 Nghien cOu can ke hOn ye ski hap clan (tO chon) On tap va TOm tat Cau hal Bat tap va Bai toan BAi toan b6 sung Tieu luan Vat li hoc ye khOng lacing 184 188 189 191 196 201 206 208 210 212 222 224 CHLIGNG 16 CHAT LUU 16 - Chat Ittu va the gi6i quanh to 16 - Chat Wu IA gi 16 - Kh6i ltIdng rieng va ap sugt 16 - Chat lt.tu thai nghi 16 - Do ap sugt 16 - Nguyen Ii Pascal 16 - Nguyen li Archimede 16 - Chat Wu li Wang dang chuyen dOng 16 - Dilong dOng va phtIOng trinh lien tuc 16 - 10 PhtlOng trinh Bernoulli 16 - 11 Val ap dung cna pluIOng trinh Bernoulli 16 - 12 SO chay cna chat lou "thud (tO chon) On tap va Tom tat Cau hoi BAI tap N/A BM toan BM toan be sung Tieu luan Vat li va the thao Khi Ong luc hoc ye vat nem 229 230 230 234 237 239 241 244 245 248 251 254 256 258 260 271 272 CHLIONG 17 SONG - I 17 - SOng vb hat 17 - Song 17 - Song tren mOt day keo cang 17 - BO& song va tan s6 17 - T6c dO dia mOt song dang Ian truyen 17 - T6c dO song tren met day keo cang 17 - T6c anh sang 17 - Nang Wong va c6ng sugt mOt song Ian truyen (to chon) 17 - Nguyen li ch6ng chap 17 - 10 Si tan sac (to chon) 17 - 11 Giao thoa cua song 17 - 12 SOng Sing (song ding) 17 - 13 SOng dOng va so cong httong On tap va TOm Cat Cau hOi BAI tap va Bat toan Bai toan bet sung 279 279 280 282 284 288 291 292 294 295 297 300 302 305 307 309 316 CHUONG 18 SONG - II 18 - S6ng am 18 - Van the cUa am 18 - Sti truyen song am 18 - along dO am va mOc (Wang dO) am 18 - Cac nguOn nhac am 18 - Phach 18 - Hieu Ong Doppler 18 - Hieu Ong Doppler d6i vai song anh sang On tap va Tom tat Cali hoi Bat tap va Bai toan Tieu luan Am hoc ciia phong Ma nhac : Khoa hoc hay nghe thuat 318 319 324 327 332 335 337 344 346 348 349 362 PHU LUG , DAP SO CAC BAI TAP VA BAI TOAN SO LE 369 387 391 SC; QUAY I 11 Trong mon judo, mot van Ong vien yeti hdn vei nho hdn, ma nctm yang vat li có thi thdng inOt van Ong vien khOe hdn, to hdn, ma khong hien bier vat hi Ditt duoc chang minh dOn*g tac ca ban "hip throw" , do, van dOng vien xoay doi Hui quanh hong caa minh va - neu Ong tac cong - quat nga doi thu tren san Neu khong sa dung thich clang vat II hoc thi, cle (pat nga, phai có sac manh rat lon va co the de dang that bai Nhung uu the thu duoc nhO vat 11 hoc, la gi ? Nghia la, "quang qua Ming", (xem bai town mdu 11-12) 11-1 110AT BONG CUA VAN BONG VIEN TRISQT BANG DOng tac duyen clang cua mOt ngudi truot bang nghg thuat cd thd dung minh hoa, mOt each thil vi ye phuong dign them mi hai dang chuygn (Ring thuan khigt, hay khong pha trOn 1-11N11 11-1 a) Nghe si trot bang n6i tieng Yamaguchi, chuygn dOng tinh tien thuan tily (a) va chuygn dOng quay thuan tny (b) Trong trtiong hOp thit nhat, chuygn dOng dtiOc thitc hien theo mOt phaing c6 dinh, trueing hop thU hai - quanh mOt truc c6 dinh Hinh 11-la trinh bay mOt nglig si truot bang ludt tren mat bang, theo mOt dudng thang, vbi t6c khOng d6i Chuygn dOng cua co ta la chuygn &Ong tinh tin thuan thy Hinh 11-1.b trinh bay su quay cde co ta vdi mOt t6c (10 khong d6i, quanh mOt true thAng thing, mot chuygn dOng quay thuan thy Trong chuong nay, chhng ta se nghien cdu loci chuygn dOng thd hai Sit tinh tin la chuygn Ong theo mOt during thang, la chuygn Ong ma cho dgn day chting ta da nghien cdu chu ygu Su quay la chuygn dOng cue cac banh xe, banh rang, Ong co, kim d6ng 116, roto cite dOng co phan laic va canh quat may bay len thang DO la chuygn dOng cua electron quay va nguyen ttt quay, cua bao, va cua cac hanh tinh quay, cua cac sao, cac thien DO la chuygn (Ring cua dign vien nhao 10n, van dOng vien nhay va cua cac nha du hanh vu tru tren qug dao Chuygn Ong quay cO c1 moi noi, quanh ta 11-2 CAC BIEN SO QUAY Trong chueng nay, thong ta nghien eau su quay &la- mOt vat ran hay c6 the quanh mOt true c6 dinh Dieu han chg thti nhat cd nghia la chting '1:a se khOng xet sit quay oda nhfing vat nhu Mat Trbi, vi Mat Trbi la mOt qua cau khi, chti khong phai mOt vat ran Dieu han chg thtl hai cua chung ta loai ngoai nhting vat gi6ng nhu mOt qua ki dang lan xu6ng theo ban ki Qua cau ay dang chuygn Ong lan, la si quay quanh mOt true chuye'n dOng Hinh 11-2 trinh bay mOt vat ran hinh clang bat ki, chuye'n dOng quay thuan tay, quanh mOt true c6 dinh, goi la true quay MOi diem eita vat chuyen dOng tren mOt doting trop, co tam d tren true quay, va mOi diem chuyen Ong duoc cling mOt gdc, sau mOt khoang thei gian nhat dinh Chung ta d6i chigu dieu vOi mOt vat chuyen dOng tinh tien thuan tiny theo mOt phuong c6 dinh Trong si tinh tign thuan ttly mOi diem dia vat chuyen Ong theo mOt dueng thang va m6i diem chuygn citing throe ding mOt khocing cach sau mOt khoang thei gian nha't dinh Dudi day, se thuong xuyen dung ski so sanh gala chuyen &Ong thang va chuygn &Ong quay (chuyen Ong theo gdc) Sau day, chung ta se so sanh cac dai Wong gdc Wong &tang, vUi cac dai luong dai, ye vi tri, dO cloi, van t6c va gia t6c VI TRI THEO GOC Hinh 11-2 cung trinh bay mOt cluang mOc, c6 dinh tren vat, vuOng gdc voi true quay, va quay cling vcii vat, chting ta c6 the mo to chuygn dOng &la vat bang each chi rO vi tri theo goc eira clueing true la gdc ma diking lam vei mOt true co dinh 'Prong h 11-3, vi tri gdc dtioc dOi voi true x, va dtioc cho bai : (11-1) = - (tinh bang radian), r do, s la dO dai cua cung, tren bat ki dubng troll nao, cat boi true x va duting m6c, va r la ban kinh dtiOng trOn at HiNH 11-2 MOt vet ran hinh clang b Gcic dinh nghia theo each nen bang radian (rad), , chuyen Ong quay than toy quanh hen la Wang \Tong (vg) hay clO Radian, bhng ti s6 hai dai, trtic z cua he toa dO Vi tri cua du-bng la mOt s6 thuan toy, va do, khong co thti nguyen Vi dO mo'c doi vc3i vOt ran al), 5,, nhung no vuOng ,goc vOi trnc quay NO la c6 dai cfra mot &tong tem ban kinh r la 2.rr, nen ea vOng phai dinh d6i vdi vat va quay ding vdi vat troll co 2n radian = 2.7r r —= 2n rad ) r rad = 57,3° = 0,159 vg vg = 360° (11-2) (11-3) Sau mai \Tong quay tron ven cua &Ong m6c quanh truc quay, cluing ta khong cho tro Iai bang khong Ngu dtiong m6c quay duoc hai yang, thi B = zlit rad 'Prong chuy6n clang tinh tign theo mat &tang thang, thong ta bigt chicle moi thti can bigt ve vat chuygn clang ngu chUng ta bigt x(t), vi tri cua no, nhu mat ham cUa thi gian Cung thg, chuygn clang quay thuan tity, chimg ta bigt duoc moi thti can bigt ye su quay cita mat vat, ngu chting ta bigt 0(t), vi tri theo gcic &la &tang m6c, nhu mat ham cua thoi gian HiNH 11-3 Vat ran quay ctia h 11.2, tilt dien thang, nhin tit tren xu6ng Mat phang cua ti6t dien vuOng goc voi truc quay Trong vi tri nay, &tong m6c lam vdi truc x mOt goc B DO DOI GOC Ngu vat ran tren hinh 11-3 quay quanh truc quay nhu tren hinh 11-4, ma lam cho vi tri theo gcic cua &tong m6c thay d6i tit 01 dgn 02, thi vat thuc hiOn mat dtii goc cho bai : AO = 02 (11-4) Dinh nghia ye cloi g6c khong nhiing dung duoc cho vat ran, xet ye than ba, ma can dung &toe cho moi hqt ciia v4t Ngu mat vat chuy6n clang tinh tign theo mat true x, thi dcti Ox ciia no co th6 duong hoac am, thy theo vat chuygn clang theo chieu x tang, hoac giam Cung vay, clai goc 6.0 curia mat vat quay cung co th6 cluong hoac am, thy theo vat quay theo chieu tang (tren cac hinh 11.3 vä 11.4 la nguoc chieu kim clang ho) hoac HINH 11-4 Duong m6c cua vat ran tren hinh 11.2 va giam (theo chieu kim clang h6) 11.3, es vi tri gOc 01, vao thei diem ti va vi tri goc 02 vao thdi dim t2 Luong 4B (= 62 - 01) la dO ddi goc khoang thdi gian (= tz - ti) Tren hinh, khOng ve vat VAN TOC GOC Gia sit rang (xem h 11-4) vat quay dm too vi tri gdc 01 vao thai didm t1 va vi tri gdc 02, vao thdi didm t2 Chting ta dinh nghia van toc goc trung binh cua vat cti — B2 - 01 t2 -t1 08 At' (11-5) AB la dO cloi gdc khoang thoi gian At (chit w la chit Hy lap o-me-ga) V6n t6c goc (arc th6i) a), ma cirang ta se ndi den nhieu hon ca, la gioi han cua ti s6 p.t (11-5), At den tOi khong Nhu vay : AO = lim T = clO (11-6) Ngu cluing ta bigt 0(t), cluing ta co thd tim duoc van t6c goc a), bang cach lay dao ham Dinh nghia cAla van t6c goc khong nining dung duoc cho vat ran quay, xet ye Wan 130, ma dung duoc cho 772.6i hat cud v4t Don vi van t6c gdc thong tinging la radian tren giay, (rad/s) hoac yang tren giay (vg/s) Ngu mOt hat chuydn dOng tinh tign theo mOt true x thi van tdc dai v co thd duong hoac am, tity theo hat chuydn Ong theo chieu x tang, hoac x giam Cling vay, van t6c gdc co da mOt vat ran quay cung co thd ducing hoac am, theo vat quay theo chieu tang (nguoc chieu kim citing h6) hoac B giam (theo chieu kim deing h6) DO Ion dia van t6c goc goi la t6c d6 goc, cung duoc ki hidu la co GIA TOC GOC Ngu van t6c gdc cua mOt vat quay khOng phai la hang s6, thi vat co gia t6c gdc Goi co va co i Ian luot la van t6c gcic d thbi diem t2 va t1 Gia t6c goc trung binh cfm vat quay duoc dinh nghia la = 2- t2 — t1 CD Act) At (11-7) Acv la bign thien cila van t6c gdc khoang thbi gian At Gia t6c gOc (tic th6i) a ma cluing ta se ndi de'n nhieu hon ca, la giai han cim dai Wong nay, cho At tign den tOi khong Nhu vay Aw dco (11-8) a = lim — = — dt At at -> Dinh nghia ye gia t6c gdc khong nhang dung &foe cho vat ran quay, xet ye toan bi), ma dung duoc cho ca moi hat caa v4t Thong tinging, don vi gia t6c gdc la radian tren giay binh phuong (rad/s2) hoac \Tong tren giay binh pinging (vg/s2) Bai Wan mat! 11-1 Vi tri goc cua mOt duting mdc, tren mOt banh xe dang quay duoc cho boi : = t3 - 27t + 4, dO t &foe bang giay, va 0, bang radian : a) Tim co(t) va a(t) Giai Dd co cluoc co(t), eh-tang ta lay dao ham cda 0(t) theo t : co De' co &doe a(t), ta d0(t) - 3t2 dt - 27 (Dap s6) dao ham cda co(t) theo t : a= dw(t) dt d(3t2 -27) - 6t dt (Dap s6) b) Vao ldc nao thi co = ? Giai Cho co(t) = 0, ta &roc = 3t2 - 27, gidi ra, ta tim (Woe : t = ±3s (Dap s6) Nghia van t6c gcic tile thoi bang khOng, 3s trddc va 3s sau Tong 116 cda chting ta chi só khong c) M6 ta chuydn Ong cda banh xe, t Giai Dd tra loi, chiing ta xet cac bidu thdc cda 0(t), co(t) va a(t) Ltic t = 0, ddOng m6c cua banh xe cs = rad, va banh xe dang quay vdi van t6c goc - 27 rad/s (tic la, theo chiseu kim clsOng 116 vdi van t6c goc 27 rad/s) va vbi gia t6c gdc bang khong Vdi < t < 3s banh xe tidp tac quay theo chieu kim dong h6, nhung vdi van t6c gcic giam dan, vi bay gib no co gia t6c gOc deicing (ngtioc chieu kim d6ng h6) (tim co(t) va a(t), vdi t = 2s, chang han) Dic t = 3s, banh xe cldng lai ch6c lat (co = 0) va td trade den gib no van quay theo chieu kim d6ng 116 (during m6c bay giO a = -50 rad) Vdi t > 3s, gia t6c g6c cua banh xe tip tac tang Van t6c goc cda no, ma bay gib cling ngdoc chieu kim d6ng ho, se tang nhanh vi dau cua w va a phd hop vdi Bai town mfiu 11 -2 MOt quay quay tren san vdi gia t6c gOc a = 5t3 - 4t, cid cac he s6 co dan vi phi hop vdi giay va radian Luc t = 0, quay co van t6c g6c 5rad/s va mot cluOng in& tren no b vi tri goc = rad a) Tim bidu their cda van t6c gcic co(t) cda quay Giai Td p.t 11-8, ta ddoc : dco = a.dt Tich phan, ta chicle : = fa dt = (5t3 - 4t)dt = T5i t4 • - + C Dd tinh hang s6 tech phan C, ta chd y rang co = rad/s luc t = The- cac gia tri vao bidu thdc cda co cda ta, ta ddoc : rad/s = - + C, Va.y : C = rad/s Do do: co = 5- t4 — 2t2 + (Dap s6) b) Tim bigu fink cua vi tri gdc 0(t) cila quay Tit p.t 11-6, ta &doe : dO = cv.dt Tich phan, ta chicle : r = Scodt = j ( T t- — 2t2 + 5)dt = c - + 5t + C' = t5 - t3 + 5t + 2, (Dap s6) do, C' dtioc tinh, nhO chi' Yr rang = rad litc t = 11-3 CAC DAI LIJONG GOC COI NHIS CAC VECTO : NOI THEM Chung ta co thg ma ta vi tri, van t6c va gia t6c cua met hat rieng le bang cac vecto Ngu hat bi buOc phai o tren met &tong thang, thi ta khOng that can dgn tiu thg cua vecto Hat nhti vay chi co hai pinking danh cho no, va ta co thg tro hai phtiong ay bang cac da'u cOng va Cung nhti vay, mOt vat ran hay c6 thg quay xung quanh mOt truc co dinh chi co thg quay theo chieu hoac ngtioc chigu kim dong h6 quanh true dd, va chting ta lai co thg phan biet hai chieu ay, bang cac dau Ong va trit Nay cau hed : "Lieu ta co thg xit H dO dili gdc, van t6c goc va gia tgc g6c cita mOt vat ran quay, nhti cac vecto ?" Cau tra l i (voi sit z de dat ma ta se lam rO, dttai z Trueday) la : "Co" Hay xet van t6c gdc Hinh 11-5a trinh bay mOt dia hat quay quanh mOt true c6 dinh Dia co t6c de quay co khong dOi (= 33 1/3 vg/ph) va co mOt chigu quay c6 dinh (theo chigu kim d6ng h6, nau nhin tit tren xuang) Chung ta quy tide bigu din van toc gcic cua no bang (a) mOt vecto httang doc theo chigu true quay, nhti trail hinh 11-5b HINH 11-5 (a) MOt cat dia hat quay quanh mOt truc thang ding trung slot Chung ta chon dO dai cfia vecto truc cita may (b) Van t6c goc cua dia 05 the biL dien bang vectd co, tren truc quay, va chi xuong dUOi, nhu ta thgy tren h (c) Chung ta thi6t theo met thang thuan lap chieu &la vectd van t6c goc la chi& !Wong xu6ng, bang cach dung quy tien nao do, chang han, veil 10 tac ban tay phai Khi cac ngon tay cita ban tay phai chay tron quanh dia va chi &tong ma dia quay, thi ng6n tay cat choai ra, chi chi& ciaa w vg/ph bang 1cm Chung ta thigt lap met chidu cho vecto co, bang cach dung quy tac ban tay phai, nhu ta thay tren h 11-5c Khum ban tay phai cho cong theo dia quay, dd cac ngdn tay cda ban chi chiseu quay Khi do, ngdn cai cda ban choai se chi chieu cda vecto van t6c goc Ngu dia quay theo chieu nguuc 14i, thi quy tac ban tay phai se not cho ban bidt rang, vecto van t6c goc bay gib hoeing theo chidu ngticic 141 Khong de gi lam quen \Teri viec bidu din cac dal Wong gcic bang cac vecto Theo ban nang, chfing ta cho dal rang cd met vat nao chuydn creng theo chieu dm met vecto day, lai khong phai thg That vay, met vat (vat ran) lai quay quanh phuong cua vecto 'Prong linh vile sii quay thuan ttly, thi met vecto xac dinh met true quay, chit khong xac dinh chieu chuydn Ong cUa met vat nao dci Tuy nhien, vecto cling xac dinh chuydn deng Hon nita, no tuan theo moi quy tac vd phep tinh vecto, da not clan chuong Gia t6c goc a la mot vector' khac, va ne cling tuan theo cac quy Vac ay Bay gib clan su de dat da nhac ci tren Cac dai goc (trit phi cluing rat nho) khOng the coi dirge la vecto Tai lai khong ? Tat nhien chting ta co thd cho chting cd chidu Ian 16n, citing nhu cluing ta da lam dgi vOi vecto van t6c goc hinh 11-5 Thy nhien indi la (theo each ndi cda nha toan hoc) didu kign can, nhung chua du Dd co thd bidu din duct bang vecto, met dai Wong can phai tuan theo quy tac Ong vecto, ma met cac quy the not rang, ndu ban ceng hai vecto, thi thd tu theo de ban Ong chting se khOng coy nghia gi De cloi gee khong vuut qua duuc phep this De' thay diet' nay, hay dat met quydn sach det tren san, nhu hinh 11-6a Bay gib cho quydn sach thuc hien hai phep quay 90° lien tigp, 16n dau, quanh true (na.'m ngang) x va sau quanh true (thang citing) y, dung quy the ban tay phai cid xac dinh chidu cluong moi trubng hop Bay gib, voi quydn sach ci cling vi tri ban dal' (h 11-6b), hay thuc hign hai de dbi gOc ay theo thti tti ngdoc lai (ttic la, tan dau quanh true y, va sau do, quanh true x) Nhu hinh ye cho thay, quydn sach kat thilc u hai hudng rat khac Nhu vay, hai Ong tac giong lai sink kat qua khac nhau, tity theo thd tu ma anh thuc hign chting \Tay, phep Ong cac de deli khong co tinh giao hodn, tUc la de deli gee (c0 (b) 10 HiNH 11-6 (a) Tit met vi tri ban dgu d ben trai, cho guy& sach hai phep quay 90° lien tiep, phep this nhgt quanh true (nA'm ngang) x, rei quanh true (thang ditng)y (b) Quyen sach vAn nhgn dtldc hai phep quay ay, nhung theo the to ngtIdc 'al Neu de dai goc thing mot dai Wong vectd thi thU tit oh cac dai se khOng có anh hong Ta thgy ro van cI6 IA cac dO (Jai goc (len) kitting phai dal Wing vectd, du ta co the' gan cho chOng CA dO len IA'n chieu Nguyen t6 Kt hieu Nguyen a so Z kh6i luvng mol, &tot khoi (Leong rieng glcm 3d 20oC Diem ?tong cluty, °C Die'm sot, °C Nhiet dung nen& JI(g°C) ö 25°C Iridi Ir 77 192,2 22,5 2447 (5300) 0,130 Kali K 19 39,102 0,862 63,20 760 0,758 Kern Zn 30 65,37 7,133 419,58 906 0,389 Kripton Kr 36 83,80 3,488 x 10-3 -157,37 -152 0,247 0,195 - Lantan La 57 138,91 6,189 920 3470 Lorenxi Lr 103 (257) - - - Liti Li 6,939 0,534 180,55 1300 3,58 1663 1930 0,155 0,707 Lutexi Lu 71 174,97 9,849 Ulu ht4nh S 16 32,064 2,07 119,0 444,6 Magie Mg 12 24,312 1,738 650 1107 1,03 Mangan Mn 25 54,9380 7,44 1244 2150 0,481 - Mendelevi Md 101 (256) - - - Molipden Mo 42 95,94 10,22 2617 5560 0,251 Natri Na 11 22,9898 0,9712 97,85 892 1,23 Neodim Nd 60 144,24 7,007 1016 3180 0,188 1,03 Neon Ne 10 20,183 0,8387 x 103 -248,597 -246,0 Neptuni Np 93 (237) 20,25 637 - 1,26 NhOm Al 13 26,9815 2,699 660 2450 0,908 Niken Ni 28 58,71 8,902 1453 2730 0,444 Niobi Nb 41 92,906 8,57 2468 4927 0,264 Nitd N 14,0067 1,1649 x 10-3 -210 -195,8 1,03 Nobeli No 102 (255) - - - - Osimi Os 76 190,2 22,59 3027 5500 0,130 Oxi 15,9994 1,3318 x 10-3 -218,80 -183,0 0,913 Paladi Pd 46 106,4 12,02 1552 3980 0,243 Photpho P 15 30,9738 1,83 44,25 280 0,741 Platin Pt 78 195,09 21,45 1769 4530 0,134 Plutoni Pu 94 (244) 19,8 640 3235 0,130 Poloni Po 84 (210) 9,32 254 - - Prazeodim Pr 59 140,907 6,773 931 3020 0,197 - - Prometi Pm 61 (145) 7.22 (1027) Protactini Pa 91 (231) 15,37 tioc ItIOng (1230) - - Radi Ra 88 (226) 5,0 700 - - Radon Rn 86 (222) 9,96 x 10-3 (0°C) (-71) -61,8 0,092 Reni Re 75 186,2 21,02 3180 5900 0,134 Rodi Rh 45 102,905 12,41 1963 4500 0,243 Rubidi Rb 37 85,47 1,532 39,49 688 0,364 Ruteni Ru 44 101,107 12,37 2250 4900 0,239 375 Nguyen 16 KI hieu Nguyen ta so Z kh6i luong mol,glmol khoi lttowg rieng gicm3a 20°C Diem nOng chdy °C Diem soi, ° C Nhiet dung rieng 00°C)c) 25°C Samari Sm 62 150,35 7,52 1072 1630 0,197 SAt Fe 26 55,847 7,874 1536,5 3000 0,447 Scandi Sc 21 44,956 2,99 1539 2730 0,569 Selen Se 34 78,96 4,79 221 685 0,318 Silic Si 14 28,086 2,33 1412 2680 0,712 St ront i Sr 38 87,62 2,54 768 1380 0,737 Tali T1 81 204,37 11,85 304 1457 0,130 Tantan Ta 73 180,948 16,6 3014 5425 0,138 Tecnexi Tc 43 (99) 11,46 2200 - 0,209 6,24 449,5 990 0,201 Telu Te 52 127,60 Tebi Tb 65 158,924 8,229 1357 2530 0,180 Thiec Sn 50 118,69 7,2984 231,868 2270 0,226 (3850) 0,117 Thori Th 90 (232) 11,72 1755 Thiry ngan Hg 80 200,59 13,55 (long) -38,87 357 0,138 Titan Ti 22 47,90 4,54 1670 3260 0,523 Tuli Tm 69 168,934 9,32 1545 1720 0,159 Unipenti a) Unp 105 262 - - - - Uniquadi b) Unq 104 261 - - - - (238) 18,95 1132 3818 0,117 tJrani U 92 Vanadi V 23 50,942 6,11 1902 3400 0,490 Vang Au 79 196,967 19,32 1064,43 2970 0,131 Vonfam W 74 183,85 19,3 3380 5930 0,134 Xenon Xe 54 131,30 5,495 x 10-3 -111,79 -108 0,159 Xeri Ce 58 140,12 6,768 804 3470 0,188 Xesi Cs 55 132,905 1,873 28,4 690 0,243 0,155 Ytecbi Yb 70 173,04 6,965 824 1530 Ytri Y 39 88,905 4,469 1526 3030 0,297 Ziriconi Zr 40 91,22 6,506 1852 3580 0,276 + Cac tri gia cac ngoAc ddn is cOt kh6i luOng mol IA cac s6 kh6i hicing cua cac clong vi phOng xa cua cac nguyen t6 co thoi gian song clai nhgt Diem nong chiy va diem sOi cac ngoAc ddn kheing chAc chAn + Cac gia tri d6i v6i cac chat chi dung cac chat d trang thai phan ttl thOng thUang nhu Hz, He, 02, Ne v.v Nhiet dung rieng cua chgt gia tri ap sugt kh6ng cUSi Xuat xti : Theo Wehr, Richards, Adair, Physics of the Atom, mat bAn Ian thit to, Addison - Wesley Reading, M.A, 1984 va theo J.Emsley, The Elements, migt bun Ian thit hai NhA xugt bun Clarendon, Oxford 1991 a) Kusatovi, Ku b) Ninxbori, Ns 376 PHU LUC E BANG TUAN HORN CAC NGUYEN TO Chu Id Hang NhOm II Nhom I 2 3 4 10 Oxit cao nhat Xeri Nile:in) VI Fr 89 88 ** Radi Ac Franxi Ra 226,025 (223) R20 Nhom VIII Nhom VII Hidro 1,008 45 F Flo N Oxi B Cacbon C Nita Bed Bo Liti Be Li 18,998 15,999 14,007 12,01 9,01 10,81 6,94 17 16 15 14 12 13 11 CI Si Photpho P Luu huynh S Clo Al Silic Nat Mg Magie Nhorn Na 32,06 35,45 30,97 28,09 24,31 26,98 22,989 25 24 23 22 21 20 19 Vanadi Cr Crom Mn Mangan Fe Titan V Canxi Sc Scandi Ti Kali Ca K 54,94 51,996 50,94 47,90 44,96 40,08 39,10 35 34 33 32 31 30 29 Br As Selen Se Brom Ga Gemani Ge Men Zn Galt Cu Kern Clang 79,91 78,96 74,92 72,59 69,72 65,38 63,54 43 42 41 40 39 38 37 Niobi MoMolipden Tc Tecnexi Ru Ytri Zr Zidconi Nb Rb Rubidi Sr Strand Y (99) 95,94 92,91 91,22 88,91 87,62 85,47 53 52 Sb 51 50 49 48 47 I Te lot Telu Sn Antimon In Thi6c Ag Cadimi Cd Indi Bac 126,90 127,60 (Stibi) 118,69 114,82 112,41 107,87 121,75 75 74 73 72 57 56 55 Reni Os Bad La Lantan Hf Hafini Ta Tantan W Vonfram Re Xesi Ba Cs 186,2 183,85 180,95 178,49 138,91 137,31 132,91 85 84 83 82 Hg 81 80 79 Bi Poloni Po Atatin At Pb Bitmut TI Chi Tali Au Thiry:10 \tang (210) (209) 208,98 207,2 204,37 200,59 196,97 Hap chat khf voi hidro Ce Nheim V He H 87 Nhom IV H I Nhom III RO 104 105 106 107 Ne 27 Coban Ni 58,93 26 S6t Co 55,85 44 Ruteni Rh 101,07 76 Osimi Ir 190,2 45 Rodi Pd 102,91 77 Iridi Pt 192,2 Heli 4,003 10 Neon 20,18 Ar 18 Agon 39,95 Kr 36 Kripton 83,80 Xe 54 Xenon 131,30 Rn 86 Radon (222) 28 Niken 58,71 46 Paladi 106,4 78 Platin 195,09 109 108 Actini Ku Kusatori Ns Ninsbori (262) (261) (227) R203 R02 R205 RO3 R207 RH, RH3 RH2 RH RO„ 71 70 Lu 69 Yb 68 Tm 67 Er 66 Ho 65 Dy 64 Td 63 Gd 62 Eu 61 Sm 60 Pm 59 Nd 58 Pr 174,97 173,04 168,93 167,26 164,93 162,50 158,93 157,25 151,96 150,35 ('147) 144,24 140,91 140,12 Lutexi Ytecbi Tuli Eribi Honmi Diprozi Tebi GadOlini Europi Samari Prometi Prazeodim Neodim 99 Fm 100 Md 101 (No) 102 (Lr) 103 98 Es 97 Cf 94 Am 95 Cm 96 Bk 93 Pu 92 Np 91 U Th V MV 90 Pa (256) (255) (252) (253) (254) (251) (247) (247) (243) (244) (237) 238,03 (234) 232,04 Lorenxi Mendelevi Nobeli Fecmi Ensteni Califoni Beckeli Curl Amerixi Plutoni Neptuni Urani Protactini Thori 25-CO SO VAT L? T2 377 HE mu Luc F SO CHUYEN Doi HO s6 chuy6n d6i cd thd duoc doc trkic tip tii nhang bang Vi du dO = 2,778 x 10-3 yang, vay 16,7° = 16,7 x 2,778 x 10-3 yang Cac dai luting SI &toe vidt hoa 'loan toan MOt phan G Shortley va D Williams, Elements of Physics Prentice - Hall, Englewood Cliffs, NJ, 1971 GOC PHANG de) =1 phut = 1,667 x 10-2 giay = 2,778 x 10-4 RADIAN = 57,30 vOng = 360 60 1,667 x 10-2 3438 2.16 x 104 3600 60 2,063 x 105 1,296 x 106 RADIAN VOng 1,745 x 10-2 2,909 x 10-4 4,848 x 10-6 6,283 2,778 x 10-3 4.630 x 10-5 7,716 x 10-7 0,1592 GOC KHOI hinh cau = 4.7r steradians = 12,57 steradians DO DAI cm MET km in ft mi 0,3937 39,37 3,937 x 104 12 6,336 x 104 3,281 x 10 3,281 3281 8,333 X 10'2 5280 6,214 X 10-6 6,214 x 10-4 0,6214 1,578 x 10-5 1,894 X 10-4 1 centimet = 1 MET = 100 kilomet = 105 inch = 2,540 fut = 30,48 dam = 1,609 x 105 10-2 1000 2,540 x 10-2 0,3048 1609 angstrom = 10.10 m 1haili=1852m = 1,151 cram = 6076 ft fermi = 10-15 m nom anh sang = 9,460 x 1012 km parsec = 3,084 x 1013 km 10-5 10-3 2,540 x 10-5 3,048 x le 1,609 fathom = ft rod = 16.5 ft ban kinh Bohr = 5.292 x 10-11 m mil = 10-3 in yard = ft nm = 10-9 M DIEN TICH MET vuOng centimet vuOng fut vuOng inch vuOng MET2 cm2 ft2 =1 = 10-4 = 9,290 x 10-2 = 6,452 X 10-4 104 929.0 6,452 10,76 1,076 x 10-3 6,944 x 10-3 dam vuting = 2,788 x 107ft2 = 640 acres barn = 10.28 m2 378 acre = 43,560 ft2 hecta = 104 m2 = 2.471 acres int 1550 0,1550 144 THE TICH MET3 cm3 =1 -6 = 10 = 1,000 x 10-3 = 2,832 x 10-2 = 1,639 x 10-5 10 1000 2,832 x 104 16,39 MET kh6i centimet kh6i lit fut kh6i inch kh6i ft3 in.3 35.31 3,531 X 105 3,531 x 10-2 5.787 x 104 6,102 x 104 6,102 x 10-2 61,02 1728 1000 1,000 x 10-3 28,32 1,639 x 10-2 gallon chgt long U.S = quarts chgt long U.S = pints U.S = 128 aoxdchgt lOng U S = 231 in.3 gallon hoang gia Anh = 277,4 in.3 = 1,201 gallons chgt long U.S KH6I LONG Cac dai luong es ben phai hoac o phia dudi clubng cham cham khong phai la don vi kh6i Wong nhung thubng duoc dung nhu the" Vi du to vigt kg "=" 2,205 lb nghia la kilogam la met kh6i luong nang 2,205 pound tai nal ma g cd gia tri tieu chugn la 9,80665 m/s2 g gam =1 11(111:CAM = 1000 = 1,459 x 104 slug &In vi kh6i KILOGAM 0,001 14,59 u 6,852 x 10-5 6,022 x 1023 6,022 x 1026 3,527 x 10-3 35,27 2,205 x10-3 1,102 x le 2,205 1,102 x 10-3 8,786 x 1027 514,8 32,17 1,609 x 10-2 1,718 x 1025 5,857 x 10-26 3,662 x 10-27 6,250 2,732 x 1026 16 0,0005 5,463 x 1029 3,2 x 104 2000 6,852 X le lUOng nguyen tit = 1,661 x 10.24 1,661 x 10.27 1,138 x 10-28 2,835 x 10-2 1,943 x le = 28,35 aoxo 3,108 x le 0,4536 = 453,6 pao ton = 9,072 x 105 907,2 ton lb i oz slug 62,16 x le 1,830 x 10-3° 3,125 x le tgn he met = 1000 kg KHoI LONG RIENG Cac dai Wong o ben phai hoac a phia dual duong chain chain la Wong rieng, cd thti nguyen khac kh6i Wong rieng, xin xem chu thich ye bang kh6i luting KILOGAM I MET3 g/cm3 lb/ft3 lb/in =1 515,4 0,5154 32,17 1,862 x 10-2 = 1,940 x le = 1,940 = 3,108 x le = 53,71 1000 16,02 2,768 x 104 0,001 1,602 x 10-2 27,68 6,243 x 10-2 62,43 1728 3,613 x 10-5 3,613 x 10-2 5,787 x 10-4 slug/ft3 slug tren filt3 KILOGAM tren MET3 gam tren centimet3 pao tren fut3 pao tren inch3 379 THOI GIAN narn gio phtit GI AY netm gib phut GIAY =1 = 2,738 x 10-3 = 1,141 x 10-4 = 1,901 x 10-6 = 3,169 x le 365,25 4,167 x 10-2 6,944 x 10-4 1,157 x 10-5 8,766 x 103 24 1,667 x le 2,778 x 10-4 5,259 x 105 1440 60 1,667 x le 3,156 x 107 8,640 x 104 3600 60 mi/h cmls TOC DO fut tren giay kilomet tren gio MET tren GIAY mile tren gio centimet tren giay ft/s kinlh MET/GIAY =1 = 0,9113 = 3,281 = 1,467 = 3,281 x 10-2 1,097 3,6 1,609 3,6 x le 0,3048 0,2778 0,4470 0,01 nut = hai li/h = 1.688 ft/s , 0,6818 0,6214 2,237 2,237 x 10.2 30,48 27,78 100 44,70 imi/min = 88.00 ft/s = 60.00 mi/h Lilt Cac don vi lurc Zs ben phai hoac phia dudi duttng chdm chdm hien it dung Dd lam sang to : gam laic (1g1) la luc tac dung len met vat c6 kh6i lung gam tai dia diem ma g c6 gia tri Ceti chudn la 9,80665 m/s2 dyn dyne NIUTON pao paodal gram Iktc kilogram Iktc =1 = 105 = 4,448 x 105 = 1,383 x 104 = 980,7 = 9,807 x 105 _ NIUTON lb pol 10-5 4,448 01 1383 9,807 x 10-3 9,807 2,248 x 10.6 0,2248 3,108 x 10-2 2,205 x le 2,205 7,233 x 10-5 i 1,020 x 10- 7,233 102,0 32,17 453,6 14,10 7,093 X 10-2 70,93 1000 _ ghic kgliec j 1,020 x 10.6 0,1020 0,4536 1,410 x le 0,001 AP SUAT atm atmOtphe = 1 dyn tren centimet2 =9,869 x le inch 0.16c 64°C = 2,458 x 10-3 centimet th6y ngan 0°C a) = 1,316 x 10-2 PAXCAN = 9,869 x le pao tren inch2 = 6,805 x le pao tren fate = 4,725 x le dyn/cm2 inch of water cm Hg PAXCAN 1,013 x 106 406,8 76 1,013 x 105 14,70 2116 4,015 x le 7,501 x 10-5 0,1 1,405x10-5 2,089 x 10-3 2491 0,1868 249,1 3,613 x le 5,202 1,333 x 104 5,353 4,015 x le 1333 10 7,501 x i0-4 0,1934 1,450 x le 27,85 2,089 x 10-2 6,895 x 104 27,68 5,171 6,895 x 103 144 478,8 0,1922 3,591 x 10-2 47,88 6,944 x le a) Tai ndi ma gia tdc twang c6 gia tri tieu chuan la 9,80665 m/s2 bar = 106 dyn/cm2 = 0.1 MPa , millibar = 103 dyn/cm` = 102 Pa , 380 Iblin for = mm Hg • lb/fie NANG LONG, CONG, NIIItT Nhiing dai lugng es ben phai hoac phia duoi duang chgm chgm kitting thuc su la don vi nang Wong nhung dua vao cho tien Chimg pita sinh tit cOng tit& Wong duong - kh6i luong - nang Wong Wong d61 tinh E = mc2 va bigu din nang luting tOa ngu mot kg hoac mOt don vi kh6i lugng nguyen tit hgp nhgt (u) hoan toan chuygn nang ltigng (hai hang cu6i) hoac kh6i Wong dugc chuygn hoan toan mot don vi nang lugng (hai cot cu6i ben phai) erg Btu 1 British thermal unit (d.vi nhiet cua Anh) 9,481 erg x 1041 1,285 flit- pao x10-3 2545 ma lktc -gio 1JUN calo kiloat-gia elect ron-vOrt mega electron-vOn gai1 klio7 c/Onvi Ichoi Wong nguyen tU hOp nhgt 1,055 x 1010 ft.lb hp.h 777,9 3,929 X 10-4 1055 kWh eV 252,0 2,930 6,585 x le 1e 3,725 x 10-14 1,356 5,051 1,356 x10-7 x107 2,685 1,980 2,685 x 106 x 1013 x 106 0,7376 3,725 9,481 10 x 10-7 x 10-4 4,186 3,088 1,560 4,186 3,969 x10"6 x10-3 x107 3,600 1,341 2,655 3,600 3413 x106 x 1013 x106 1,602 5,967 1,182 1,602 1,519 x 10-22 x 1042 x 10-19 x 1046 x 10.19 1,602 5,967 1,182 1,602 1,519 x 1046 x 10-6 x 1043 x 10-2° x 1043 58,87 6,6.29 3,348 i,9g7 8,Zi x 10 16 x 1010 x 1016 x 1013 x 1023 1,492 5,559 1,101 1,492 1,415 x 1043 x 10-3 x 10-10 x 1047 x 104° cal JUN 7,376 x 10-8 2,389 x 10-8 0,3238 6,413 X 105 0,2389 8,600 x105 3,827 x 10-20 3,827 x 1044 2,146 x 1016 3,564 x 1041 6,585 x le x 1015 6,242 6,242 2,778 11 x 105 x 10-14 X 10 8,464 I 8,464 3,766 12 x10-7 X1018 X 10 1,676 i 0,7457 1,676 19 X 1025 X 10 6,242 i 6,242 2,778 18 x 1012I x le x 10 2,613 2,613 1,163 X 1019 x1013 I x10 2,247 2,247 19 x1025 X 10 -6 10 4,450 I x 10-26 10-6 4,450 x 10-2° 61-010- -5,2,497 - - -5,6x 1010 x 1035 x 1029 932,0 9,320 4,146 x10-17 x 108 u kg MeV il 7,070 1,174 12 X 10.14 x 10 1,113 x 10-24 1,509 x10"17 2,988 x 10-11 1,113 x 10-17 4,660 x10-17 4,007 X10"11 1,783 x 10-36 670,2 9,037 x109 1,799 x 1016 6,702 x 109 2,806 x1010 2,413 x1016 1,074 X 10-9 1,074 1,783 x 10-30 x lo-3 6,022 x 1026 1,661 x 10-27 CON G SUA'T Btulh ft.lbls hp ddnvi nhiOt cila Anh tren gio =1 0,2161 3,929 x flit- pao tren gig)/ = 4,628 1,818 x 10-3 ma 14c = 2545 550 le calls kW OAT 6,998 x 10"2 2,930 x 0,2930 0,3239 le 1,356 x le 1,356 178,1 0,7457 745,7 4,186 calo trEn gigy = 14,29 3,088 5,615 x 10-3 4,186 x 10-3 kilOat = 3413 737,6 1,341 238,9 1000 0,2389 0,001 1 OAT = 3,413 0,7376 1,341 x 10-3 381 Tif THONG macxoen macxoen =1 VEBE 10-8 Nn3E = 108 gaoxa =1 TESLA 10-4 miligaoxa = 104 = 0,001 10-7 107 TU' TRU'ONG gaoxo TESLA miligaoxo testa 382 = vebe/m2 1000 PHU LUC G CONG THUC TOAN HiNH HOC Dili ng trim ban ldnh r ; chu vi 27rr ; dign tich 7rr2 fah cau ban ldnh r ; di ;.1 tic), 47r2 CI A4 cao h.; dign tich thd tich = yrr3 Hinh tru trim xoay, thAng dung ban kinh r, = 2.7-cr2 + 2.7rrh ; thg tich = nr2h ah • Tam gide day a va chigu cao h : dign tich = — NGHIEM CUA PHU'ONG TRINH BAC HAI Ngu axe + bx + c = thi x = —b ± Vb2 4ac • 2a HAM LU'ONG GIAC CI_J'A GOC d sinO = — cos9 = —r r; tgO = y x • cotgO = — x' y r r secO = — ; csc9 = — x y DINH LY- PITAGO Trong tam giac vuOng a2 b2 = c2 TAM GIAC Cac gdc la' A, B, C Cac canh dgi la a, b, c Cac gdc A + B + C = 180° sinA sinB sinC a 383 c2 = a2 b2 - 2abcosC • gdc ngoai D = A + C DAU VA KI HIEU TOAN HOC = bang P-•-• xap xi bang Ion cling 'bac # khac vali • Wong duang vOi, (long nhat veil • > iiln han (> lOn han nhieu) • < nil?) hon ( 500 Hz (a) 100N/m (b) 0,45s 11 (a) 6,28 x 105 rad/s (b) 1,59mm 13 (a) 1,0mm (b) 0,75m/s (c) 570m/s2 15 (a) 1,29 x 105N/m (b) 2,68Hz 17 (a) 4,0s (b) yr/2 rad/s (c) 0,37cm (d) (0,37cm) cos (n12)1 (e) (-0,58cm/s) sin(r/2)t (f) 0,58cm/s (g) 0,91cm/s2 (h) s6 khOng (1) 0,58cm/s 19 (b) 12,47kg (c) 54,43kg 21 1,6kg 23 (a) 1,6Hz (b) 1,0m/s, (c) 10m/s2, ± 10cm (d) - (10N/m)x 25 22cm 27 (a) 25cm (b) 2,2 Hz 29 (a) 0,500m (b) -0,251m (c) 3,06m/s 31 (a) 0,183A (b) ding mot hitting 37 (a) k1 = (n + 1)k/n ; k = (n + 1)k (b) fl = +1)Inf ; f2 = + lf 39 3,7 10-2J 41 (a) 130N/m (b) 0,62s (c) 1,6Hz (d) 5,0cm (e) 0,17J (f) 0,51m/s 43 (a) 7,25 x 106N/m (b) 49,400 45 (a) mu/(m + M) (b) mu/ \lk(m +M 47 (a) -(80N) cos [(2000 rad/s)t - rad] (b) 3,lms (c) 4,0m/s (d) 0,080J 49 (a) 16,7cm (b) 1,23% 51 (a) 0,735kgm2 (b) 0,024Nm (c) 0,181 rad/s 53 0,079kgm2 55 9,79 in 57 99cm 61 Ta 63 5,6cm 65 (a) 0,869s (b) r = R/2 69 (a) L2 + 12x2 27r (b) 0,289 71 (a) 0,35Hz (b) 0,39Hz (c) s6 khong 73 14,0° 75 1x 2g 274m/3k 77 (a) 2,0s (b) 19,8 Nm/rad 79 0,29L 81 0,39 83 (a) 0,102kg/s (b) 0,137J 85 k = 490N/cm ; b = 1100kg/s 87 1,9 in Chu-ung 15 19m 2,16 1/2 3,4 x 105km 3,7 x 10-5N y tang 11 M = m 13 3,2 x GmM 10-7N 15 (1 ,) 17 (a) 1,62m/s2 (b) 4,9s 19 0,0161b 21 3,4 x 10-3g d2 8(1 -R/2dy/ (b) 6,1 x 10-4g (c) 1,4 x 10-11g 23 9,78m/s2 25 (b) 1,9h 27 (b) 3,2m 31 (a) G(M,+ M2)m/a2 (b) GMmlb` (c) 35.(b) 2,0 x 108N/m2 (c) 360km 37 (a) -4,4 x 10-11J (b) -2,9 x 10-11J (c1) 2,9 x 10-11J 39 1/2 41 220km/s 44 -Gm(ME/R + Mm/r) 49 2,6 x GMmx 104km 51 (a) 82km/s (b) 1,8 x 104 km/s 53 (a) (x2 +R2)3/2 (b) V2 = 2GM -7 55 1,87y 57 5,93 x 1024kg 59 0,35 thang am lich 61 3,9y \R yR2 +x- 63 5,01 x 109m hoac 7,20 ban kinh Mat Trbi 65 3,58 x 104km 67 810 73 (a) 42,1km/s (b) 12,3km/s (c) 16,6km/s 75 1,6cm/s ve phia (long theo xich dao 77 (a) -GMEm/r (b) -2GMEm/r (c) Nd roi huOng ye tam Trai Dat 81 (a) KhOng (b) Cung nhu vay (c) Cd 83 (a) Tar3/2 (b) Kar-1 (c) Lar1/2 (d) vur-1/2 (a) (b) 1,8 x 1032J (c) 1,8 x 1032J (d) 0,99 km/s Chuang 16 1000kg/m3 1,1 x 105 Pa hoac 1,1 atm 2,9 x 104N 6,0 lb/int 1,90 x 104 Pa (143mmHg) 11 5,4 x 104 Pa 13 0,52m 15 (a) 6,06 x 109N (b) 20 atm 17 0,412cm 19 2,0 21 44km 23 (a) pgWD2/2 (b) J3gWD3/6 (c) D/3 27 -3,9 x 10-3 atm 29 (a) 388 740kg/m3 39 fAla (b) 201b 31 1070g 33 1,5g/cm3 35 600kg/m3 37 (a) 670kg/m3 (b) 390kg 41 (a) 1,2kg (b) 1300kg/m3 43 0,126m3 45 Nam 47 (a) 1,80m (b) 4,76m3 49 2,79g/cm3 51 (b) 3,17s 53 4,0m 55 28ft/s 57 43cm/s 59 (a) 2,40m/s (b) 245Pa 61 (a) 12ft/s (b) 131b/int 63 0,72ft lb/ft3 65 (a) (b) R1/ R2 = 1/2 (c) Than nueic den h , = h1/4 67 116m/s 71 110m/s 73 1,11 x 104N 75 pv-A, Jo la khoi Wong rieng cua khong 77 1,4cm 79 (a) 74N (b) 150m3 83 (a) v = 4,1m/s, v' = 21m/s (b) 8,0 x 10-3m3/s 85 (a) 830W (b) 1100W Chuang 17 (a) 75Hz (b) 13ms (a) 1,7s (b) 2,0m/s (c) 3,3m (d) 15cm (a) 0,68s (b) 1,47Hz (c) 2,06m/s (c) 200cm/s ; phtiong -x (a) 5cm/s (b) Ve phia x tang 11 (a) 2,0mm ; 96Hz ; 30m/s ; 31cm (b) 1,2m/s 13 (a) 6,0cm (b) 100cm (c) 2,0Hz (d) 200cm/s (e) phuong -x (f) 75cm/s (g) -2,0cm 17 129m/s 19 135N 23 (a) 15m/s (b) 0,036N 25 y = (0,12mm) sin [(141m-1)x + (628s-1)t] 27 (a) 5,0cm (b) 40cm (c) 12m/s (d) 0,033s (e) 9,4m/s (0 5,0sin (16x + 190t + 0,79), voi x tinh bang m, y bang cm, t bang s 29 (a) v1 = 28,6m/s ; v2 = 22,1m/s (b) M1 = 188g ; m2 = 313g 31 (a) iik(A0(/ + AO/m 33 (a) = 2P1 (b) P = P114 35 (a) 3,65m/s (b) 12,2N (c) s6 kh6ng (d) 44,3W (e) s6 khong (f) s6 kh6ng (g) 0,50cm 37 82,8°, 1,45 rad 41 5,0cm 43 10cm 45 (a) 82,0m/s (b) 16,8m (c) 4,88Hz 47 (a) -0,0390m (b) y = 0,15 sin (0,79x + 13t) (c) -0,14m 49 (a) 66,1m/s (b) 26,4Hz 51 (a) 144m/s (b) 3,00m ; 150m (c) 48,01z ; 96,0Hz 53 Hoa ba thtY nhat va thil nhi dm A lan lttgt sanh visi hoa ba thtt tit va thil tam ciia B 55 (a) 0,25cm, 120cm/s (b) 3,0cm (c) s6 khong 61 (a) 1,3m (b) y = (0,002) sin(9,4x) cos(3800t), vOi x va y m, t s Chuang 18 6% D6i voi nglibi nghe dai, vao khoang 0,85s 7,9 x 101°Pa Neu chi (a) rieng dai la khong chinh xac, no phai biet ro gidi han 10-4cm Neu chi rieng thi i gian la khong chinh xac thi sai s6 khOng &Lige qua mot phan mittli van (10-5) 43,5m 11 40,7m 13 100kHz 15 (a) 2,29 ; 0,229 ; 22,9kHz (b) 1,14 ; 0,114 ; 11,4kHz 17 (a) 6,0m/s (b) y = 0,30sin(grx/12 + 507a) voi x va y cm va t s 19 4,12 rad 21 (a) 343 (1 + 2m) Hz, vOi m la mot s6 nguyen tit den 28 (b) 686mHz, \TIM m la mot s6 nguyen tit den 29 23 (a) Tam (b) Tam 25 64,7Hz ; 129Hz 27 (a) 0,080W/m2 (b) 0,013W/m2 29 35,7nm 31 (a) 1000 (b) 32 33 (a) 39,7,uW/m2 (b) 166nm (c) 0,923Pa 35 (a) 59,7 (b) 2,81 x 10-4 37 (a) lar-1 (b) smar-112 39 (a) 5000 (b) 71 (c) 71 41 171m 43 3,16km 45 (a) 5200Hz (b) Bien dOsAD / Bien dQsBD = 47 350m 51 (a) 833Hz (b) 0,418m 53 Nhan vOi thila s6 55 Nit6c day den dO cao 7/8 ; 5/8 ; 3/8 ; 1/8 m 57 (a) L ( - -) (b) 13cm (c) 5/6 59 12,4m 61 (a) 71,5Hz (b) 64,8N 63 45,3N 65 r 2,25ms 67 0,02 69 3,8Hz 71 (a) 380 dam/h, di xa ngtibi chti (b) 77 dam/h di xa ngitoi chit 73 15,1ft/s 75 3,1m/s 77 2,6 x 108m/s 79 (a) 77,6Hz (b) 77,0Hz 81 (a) 42° (b) lls 83 0,189MHz 85 (a) 970Hz (b) 1030Hz (c) 60Hz KhOng 87 (a) 1,02kHz (b) 1,04kHz 89 1540m/s 91 (a) 8,29Hz (b) 13,9Hz 93 (a) 598Hz (b) 608Hz (c) 589Hz 95 0,073 97 (a) 1,94 x 104km/s (b) Lui xa dan 99 ± 3,78pm 101 49,5m/s 389 [...]... 11 -24 , to co x = +L /2 I = f x2dm = f x2 ( dx = — [x3111 12 -L /2 — \ L/ 3L x = -L /2 M = [ L 3 2) ( )3 — 2 = 2 12 (Dap s6) Digu nay phi hop vai kgt qua cho trong bang 11 -2( e) b) Quan tinh quay dia thanh quanh mot true vuong goo vOi thanh, di qua mot da"u thanh, la bao nhieu ? Giai Ta ph6i hop ke't qua trong pha'n (a) voi dinh 11 true song song (p.t 11 -25 ), va dtioc : = /kh.t + Mk- = 2 12 ML + (M) 2 2... &fee trong bai toan mau 11-11, ta duec : w = co + at = 0 + ( -24 rad/s2) (2, 5s) = -60 rad/s (Dap s6) c) DOng nang cua dia llic t =2, 5s la bao nhieu ? Giai Theo p.t 11 -23 , thing nang cua 1 1 dia la - kr- trong do / = - MR2 \Tay, 2 , 2 dung gia tri dia w tim dude trong (b) : 1 1 1 2 K = - /co2 = 2 2 MR ) w2 = ( 4) (2, 5 kg)(0 ,2 m )2 (-60 rad/s )2 = = 90J (Dap s6) Mot cach khac de' giai bai toan nay, la tinh... kinh R = 25 cm Mu banh quay voi 85000 vg/ph, thi no trO dugc met Ong nang quay la bao nhieu ? Giai Quan tinh quay &Ia banh da hinh tru, theo bang 11 -2( c) la : 1 1 I = MR2 = () (75kg)(0 ,25 m )2 = 2, 34 kg/m2 Van t6c gdc cua banh da la w = (85000 vg/ph)(2x rad/vg)(1 ph/60s) = 8900 rad/s Theo p.t 11 -25 , Ong nang quay cua banh da la : 1 1 K= = (2, 34kg m2)(8900rad/s )2 = 9,3.107 J = 26 kWh (Dap s6) 2 \2 / 24 Lacing... Quan tinh quay cita vat, quanh truc di qua P, theo p.t 11 -24 , la I = f r2 dm = f vx - a )2 + (y - b )2] dm Ta co thg sap xep lai thanh : I = f (x2 + y2) dm - 2a f xdm - 2b f ydm + f (a2 + b2) dm (11 -26 ) Theo dinh nghia kh6i tam (p.t 9-9), hai tich phan u giiia p.t 11 -26 cho ta toa de cita kh6i tam vat (nhan yea met hang s6) Vi (x2 + y2) bang R2, trong do, R la khoang cach tit 0 dgn dm, nen tich phan... cluing co van t6c goc ban dau 320 vg/ph Giai Giai p.t 11-9 (co = coo + at) d6i yeti t, ta doge : co 0 - 320 vg/ph t - a -63,3 vg/ph2 — = 5,1 phdt (Dap s6) c) Kg tit Mc co van t6c gcic ban dau 320 vg/ph, canh quat con quay dugc bao nhieu yang, mdi cliing ? GULL Gidi p.t 11-11 (co2 = a) 02 + 2a0) d6i vdi 0, ta chigc : 0 - co 2 - wo2 2a 0 - ( 320 vg/ph )2 = (2) ( -63,3 vg/ph2) = 809 yang 11-5 CAC BIN (Dap... /kh.t trong phan (a), va khoang cach h giita hai true song song, thi bang nita de dai cua thanh Nhtt vay, theo p.t 11 -25 : I 22 2 Mh 1 2 1 \ 2 ± (2m) ( L) = 2 (Dap s6) Ta có thg nghi6m lai kel qua nay, bang each tinh tr‘ic tigp, theo p.t 11 -22 (Dap s6) I = Infi = (m)(0) (m)(1- )2 = mL2 True quay C/77 Bai town mfiu 11-8 Hinh 11-15 trinh bay mot thanh ming, d6ng tinh, kh6i Wong M va do dai L (al a) Quan... ta khOng bigt Fay gi lam v 2 , Thay vao dO,_ chting ta se coi dia ctia (va bat ki vat ran quay nao khac) nhu met tap hop nhieu hat co van tot khac nhau, sau do chung ta co thd citing clang nang cita moi hat cid lai, dd tim duoc dong nang cua than be vat Bang cach do, chting ta thu duoc clang nang am mot vat quay : 1 , 1 1 2 K = 2 m + 2 m2v 22 + — 2 m3V3 K = L 2 m.v2 (11 -20 ) / trong do mi la kh6i... mCI + n2, H -X 47/ CY (11 -27 ) Theo p.t 11 -22 , quail tinh quay quanh met truc di qua khol tam la I= n = m(d - x )2 + ma x2 /77,, C/7,, J HMI 11-16 Bai man matt 11-9 SO do mot phan tit axit clohidric MOt true quay di qua kh6i tam va vuOng g6c vOi dUong n6i tam cua hai nguyen The x ti p.t 11 -27 , sau vai phep bign cldi dai s6, ta 172H •M CI 2 (1,01u)(35,0u) dugc : = - ( 127 pm) 35,0u +1,01u - 15800 upm2 mci... (2 - 9) v= 0 + at 1 x = v 1 + 2a? 0 v2 = v 02 + 2ax 1 x = - (v + v)t 2 ° 1 x = vt - - at2 2 (2 - 13) (2 - 14) (2 - 15) (2 - 16) Bien sa Ong n-4t x 9 C6ng thlic g6c PhUdng trinh s6 w = a + at (11-9) 1 2 at = wot + - a a vo 0 2 co2 = wo + 2a0 1 + co)t 0 = -2( w° 1 ca2 0 = tot - 2 (11- 10) (11-11) (11- 12) (11-13) trudng hop nay Chung tOi se khong thigt lap cluing, ma chi don gian vigt chting ra tii cac... bang 2- 2, chting t6i trinh trong su quay thudn ttly, trubng hop gia bay mOt boat phuong trinh cua chuydn dOng cung quan trong, va mOt boat song song cac p.t cung ap dung dugc cho t6c goc khong doi Bang 11-1 PHUONG TRINH CAC CHUYEN DONG VLSI GIA TOC DAI VA GIA TOC GOC KHONG DOI Phuang trinh só Cong thitc dai (2 - 9) v= 0 + at 1 x = v 1 + 2a? 0 v2 = v 02 + 2ax 1 x = - (v + v)t 2 ° 1 x = vt - - at2 2 (2 - ... song 17 - 12 SOng Sing (song ding) 17 - 13 SOng dOng va so cong httong On tap va TOm Cat Cau hOi BAI tap va Bat toan Bai toan bet sung 27 9 27 9 28 0 28 2 28 4 28 8 29 1 29 2 29 4 29 5 29 7 300 3 02 305 307... ta duoc : (2) (2 1, kg) 2m (Dap s6) - 4,8 m/s2 g M + 2m = - (9'8m/s2) 2, 5 kg + (2) (1 ,2 kg) = a Tigp theo, dung p.t 11-36 dd tim T : 1 (Dap so) T = - Ma = - (2, 5 kg)(-4,8m/s2) = 6,0N 27 Nhu ta dot... Bai toan BAi toan b6 sung Tieu luan Vat li hoc ye khOng lacing 184 188 189 191 196 20 1 20 6 20 8 21 0 21 2 22 2 22 4 CHLIGNG 16 CHAT LUU 16 - Chat Ittu va the gi6i quanh to 16 - Chat Wu IA gi 16 -