Sách Giáo Khoa Vật Lí Lớp 10 Cơ Bản

" Sách Giáo Khoa Vật Lí Lớp 10 Cơ Bản 🔙 Quay lại trang tải sách pdf ebook Sách Giáo Khoa Vật Lí Lớp 10 Cơ Bản Ebooks Nhóm Zalo BO GIAO DUC VA DAO TAO BO GIAO DUC VA OAO TAO LLiONG t)UYEN BINH (long Chu bicn kicniChu hicn i NGUYEN XUAN CHI - CO ClANG TR.4N CHI MINH - vu OUANG - BUI GIA THINH Z7^ (Tdi bdn ldn thu tu) NHA XUAT BAN GIAO DUC VIST NAM CAU TRUC CAC T^i^iCi SACH GIAO KHOA 1. Ph^n noi dung bai hoc gom cac trang in thanh hai cot : mot cot la noi clung chinh cua bai hoc, cot con lai chCr nho, trmh bay cac hmh ve, tranh, anh, bieu bang, do thi, cac cau hoi (ki hieuS * ) de giao vien va hoc sinh cimg tham gia xay dung bai hoc... Tuy nhien, vai cac hmh, do the... co kich thuoc lan thi in tran trang. 2. Sau phan noi dung bai hoc la (Dhan tom tat bai hoc, dugc in dam. Cuoi moi bai hoc la phan cau hoi (ki hieu ''•) va bai tap (ki hieu"^ l de hoc sinh lam a nha. Phan dap an va dap so bai tap dugc in a cuoi cuon sach. .3. Sau mpt so bai hoc co nhung bai dgc them ghi la "Em co biet ?" Chiu tracti nhiem xuat ban : Chu tich HDQT kiem Tong Giam doc NGO IRAN Al Pho Tong Giam doc kiem Tong bien tap NGUViN QUY THAO Bien tap lan dau Bien tap tai ban Bien tap kT thuat Trinh bay bia va minh hoa SUa ban in Che ban NGUYEN VAN THUAN - VU THj THANH MAI PHUNG THANH HUYEN TA THANH TUNG TA THANH TUNG PHONG SL/A BAN IN (NXB GIAO DUC TAI HA NOI) CONG TY CO PHAN Ml THUAT VA TRUYEN THONG Trong sach nay co sCr dung moi so anh tu lieu cua Thong tan xa Viet Nam Ban quyen thuoc Nha xuat ban Giao diJC Viet Nam - Bp Giao due va Oao tao VAT Ll 10 Ma so : CH005T0 In 100.000 ban (ST), kho 17x24 cm. IntaiCongtyCPI n Nghe An. 216-Tran Phu -TP Vinh - Nghe An. S6in:08GK.S6 xuat ban: 01-2010/CXB/552-1485/GD. • In xong va nop luu chieu thang 01 nam 2010. 1. Vat ll hoc nghien ciiu cac dang chuygn dong, cac qua trinh bien doi... va cau tao ciia cac vat thd. Do la mot trong cac mon khoa hoc tu nhien quan trong nhat ciia chuong trinh Trung hoc pho thong. Cac em hoc sinh da bat dau hoc mon Vat If tir cac ldp Trung hoc co so. Nhung tir ldp 10 Trung hoc phd thdng. mdn Vat If mdi dugc trinh bay mdt each he thdng, sau sdc va day dii hon. Trong chuong trinh Trung hoc phd thdng, mdn Vat If chii yeu diing phuong phap thuc nghiem : h^u het cac khai niem, dinh luat, cdng thuc... deu dugc rut ra ttr cac quan sat, thf nghiem... trong thuc te. 2. Chuong trinh mdn Vat If ldp 10 Trung hgc phd thdng gdm hai phan : • Phan mdt - Co hgc : nghien cuu cac dang chuydn dgng co, cac djnh luat co ban ciia chuyen dgng co. • Phan hai - Nhiet hgc : nghien ciru cac trang thai ciia cac vat the cau tao bdi cac phan tii'; nghien cuu su trao ddi nang lugng giua cac vat the trong qua trinh bien ddi. 3. Cac tfnh chat vat If khae nhau ciia mdt vat the dugc bieu didn bang cac dai lugng vat If khae nhau. Trong chuong trinh Trung hgc phd thdng. ta chi gap hai loai dai lugng vat If: - Dai lugng vd hudng ; - Dai lugng vecto. a) Dqi luang vo huang : Dai lugng vd hudng chi cd mdt gia tri : hoac khdng am (khd'i lugng. the tfch...), hoac cd dau duong hay am (dien tfch, cdng, hieu dien the...). N --,\a CJ» b) Dqi luang vecta: dugc didn ta bang mdt vecto xac dinh bdi die'm gdc, die'm nggn, gia, chidu va do ldn. Vi du : Vecto luc F = ~MN : - Didm gd'c M ; - Didm nggn N ; M - Chieu cua vecto la chidu ttr diem gdc de'n diem nggn ; - Do ldn vecto bang F = \MN\. 4 Thli nguydn cua mdt dai lugng vat If. Khi do mdt dai lugng, ngudi ta phai chgn mot dai lugng ciing loai lam chuan dd so sanh ggi la dan vi. Ngudi ta thay rang, chi can xac dinh don vi ciia mdt sd dai lugng co ban, cac don vi ciia cac dai lugng khae cd thd tir dd suy ra. Vi du : Don vi co ban : \ do dai : met (m) . thdi gian : giay (s) khd'i lugng : kildgam (kg) Tir dd suy ra don vi : i van td'c : m/s hay m.s~' j gia td'c : m/s- hay m.s"- luc : kg.m/s- hay kg.m.s"^ (ggi la niuton) Cdng thiic xac dinh su phu thugc ciia don vi mot dai lugng nao dd vao cac don vi co ban dugc ggi la thli nguyen ciia don vi dd. De kf hidu thii nguydn ciia mdt don vi, ngudi ta diing hai dau ngoac vudng. \'i dit : [cdng] = [luc.do dai] = kg.m.s~-.m = kg.m^.s"-^ [ddng lugng] = [khdi lugng.van td'c] = kg.m.s"' [ap suat] = [luc] kg.m.s [dien tfch] = kg.m"' .s m PHAN MOT CO HOC a hoc nghien CLTU cac dinh luat chi phoi sir chuyen dong va di;ng yen cua cac vat. Phao ho^f Of" hd Hoan Kie<. ka hoc cho phep xac dinh duac vi tri ciia vat a bat ki thoi diem nao. No cho ta kha nang thay tri;ac 'dLfOC dirdng di va van tdc cua vat, tim ra dugc nhung ke't ca'u ben vQng. CO HO * 5 s f^G CHl/ONG I Dpng hoc chat diem Ddng hoc la mdt phan cija Ca hoc, trong dd ngirdi ta nghien cau each xac dinh vj tri cua cac vat trong khong gian tai nhOrng thdi diem khae nhau va md ta cac tinh chat cua chuyen ddng cua cac vat bang cac phuang trinh toan hoc, nhung chira xet den nguyen nhan chuydn ddng. Cac khai niem : chat diem, quy dao, he quy chieu, van tdc, tdc do trung binh, van td'c tire thdi, td'c do gdc, gia td'c cua chuyen ddng Cac dac diem ve quy dao, van td'c va gia td'c cua cac chuyen ddng thing deu, thing bie'n ddi deu, rai ti; do va trdn deu <. Cdng thirc cdng van td'c O to aang ler d<\o Ma Phuc. iCao Br^ CHUYDN OONG CO I - CHUY6N DONG CO. CHAT DICM 1. Chuyen dong co Chuyen dong co ciia mot vqt (goi tdt Id chuyen dong) Id su thay doi vi tri cua vqt do so vai cdc vqt khdc theo thoi gian. 2. Chait diem Mdt d td tai dai 4 m dang chay tren dudng Ha Ndi - Hai Phdng, dai 105 km. Nd'u phai chi vi trf cua d td H I Cho bie't (mpt each gan diing): - Dudng kinh cua Mat Trdi: 1 400 000 km. - Dudng kinh ciia Trai Da't : 12 000 km. - Khoang each tCr Trai Oat de'n Mat Trdi; 150 000 000 km. a) Ne'u ve dudng di eua Trai Dat quanh Mat Trdi la mot dudng tron, dudng kinh 15 cm thi hinh ve Trai Oat va Mat Trdi se la nhung hinh tron e6 dudng kinh bao nhieu xentimet ? b) C6 the coi Trai Da't nhu mpt chat diem trong he Mat Trdi dupe khdng ? tren dudng di trong mgt ban dd thi ta chi cd the ve dugc bang mdt cham (mdt diem). Dd la vi chieu dai ciia d td chua bang bd'n phan mudi van chieu dai con dudng. 6 td dugc coi la mdt chdt diem trdn dudng Ha Ndi - Hai Phdng. laU Mot vqt chuyen dqng duoc coi Id mot chdt diem neu kich thuoc cua no rdt nho so voi do ddi duirng di (hodc so vdi nhirng khodng cdch md ta de cap den). Khi mgt vat dugc coi la chat diem thi khd'i lugng ciia vat coi nhu tap trung tai chat didm dd. Cac vat ma ta ndi ddn trong chuong nay ddu coi la nhirng chat didm. 3. Quy dao Tap hgp tat ca cac vi trf ciia mdt chat didm chuydn ddng tao ra mdt dudng nha't dinh. Dudng dd ggi la c/uy dgo ciia chuyen dpng. II - CACH XAC OINH VI TRI CUA VAT TRONG KHON G GIAN 1. Vat lam moc va thuoc do Cdt cay so trdn Hinh 1.1 cho bidt ta dang each Phii Ly 49 km. Trong trudng hgp nay ta da lay mdt cdt cay so d Phti Ly la vqt lam mdc. Khoang each tir cdt cay so den vat lam mdc da dugc do trudc. Vat lam mdc dugc coi la diing yen. [ S Vay, neu dd hiet dudng di (cpiy dqo) cita vqt, ta chi cdn chon mqt veil ldm moc vd mqt chieu duang tren difdng do la co the .xdc dinh duac chinh .xdc vi tri cua vqt hdng cdch diing mqt cdi thudc do chieu ddi doqn dudng tit vat ldm mdc den vqt (Hinh 1.2). 2. He toa do Mud'n chi rd cho ngudi thg biet chfnh xac mdt didm M can khoan trdn tudng dd ddng dinh, cfin ndi rd didm dd nam tren mat tudng nao, each mep san va mep tudng bdn trai bao nhieu met. Hai dudng Ox a mep san va Oy d mep tudng bdn trai vudng gdc vdi nhau tao thanh mdt he true toq do vuong goc (ggi tat la he toq dc}) tren mat tudng. Diem O la gdc toq do. Mud'n xac djnh vi trf ciia didm M ta lam nhu sau : — Chgn chieu duong trdn cac true Ox va Oy : ~ Chid'u vudng gdc diem M xudng hai true toa do Ox va Oy. ta dugc cac diem // va / (Hinh 1.3). Vi trf didm M trdn mat tudng se dugc xac dinh bang hai toa do la : .v - OH va v = 01. Hai toa do nay la hai dai lugng dai sd. S 3 D6 xac dinh .v va y ta phai diing thudc. Tuy nhien, cd the diing thudc de chia do san tren hai true Ox va Oy va quan niem he toa do la he hai true da duoc chia dd. Hinti 1.1 B B Co the lay vat nao lam moc de xac dinh vi tri mpt chiec tau thuy dang chay tren sdng ? Hinh 1.2 Yi M O H X Hmh 1.3 D M B Hinh 1.4 S 3 Hay eho bie't eae toa dp cua diem M nam ehinh giiJa mot bdc tudng hinh ehiT nhat ABCD e6 canh AB = 5 m, va eanh AD = 4 m (Hinh 1.4). Lay true Ox doe theo AB. true Oy dpe theo AD. Bang 1.1 Bang gid tau Ill - CACH XAC OINH THdl GIAN TRONG CHUY«^N DONG 1. Moc thoi gian va done h6 D^ md tii chuyen ddng ciia mgt vat, ta phai bidt toa dg ciia vat dd d nhirng thdi diem khae nhau. Mud'n the, ta Ha Noi Nam Oinh Thanh Hoa Vinh Dong Hdi Dong Ha Hue Da Nang Tam Ky Quang Ngai Dieu Tri Tuy Hoa Nha Trang Thap Cham Sai Gon 19 gio 00 phut 20 gid 56 phut 22 gid 31 phut 0 gid 53 phut 4 gio 42 phut 6 gid 44 phut 8 gid 05 phut 10 gio 54 phut 12 gid 26 phut 13 gid 37 phut 16 gid 31 phut 18 gid 25 phut 20 gid 26 phut 22 gid 05 phut 4 gid 00 phut phai chi rd mdc thdi gian (hoac gdc thcfi gian). tiifc la thdi diem ma ta bat dau do thdi gian va phai do khoiing thdi gian trdi di kd tii mdc thdi gian bang mgt cliiec dong ho. Bang gid tau (Bang 1.1) cho ta bidt thdi diem ma doan tau cd mat d cac ga. Ndu bd qua thdi gian tau dd lai d cac ga thi ta cd the tfnh dugc khoang ihdi gian tau chay tii ga ng ddn ga kia. Ne'u lay mdc thdi gian la thdi didm vat bat dau chuyen ddng (thdi diem 0) thi sd chi ciia thdi didm se trung vdi sd do khoang thdi gian da trdi qua kd tir mdc thdi gian. Mdt he quy chid'u gdm ; mdt vat km mdc. mgt he toa do gan vdi vat lam mdc : mgt mdc thdi gian va mdt ddng hd. Hay tinh xem doan tau ehay tu ga Ha Npi den ga -Sai C?6n trong bao lau ? Trong nhieu bai toan co hgc. nhieu khi ndi vd he quy chie'u. nguoi ta chi de cap den he toa do. vat lam mdc va mdc thdi gian ma khdng cdn ndi dd'n ddng hd. sr Chiryrn ddng cia mdt vat la •:AI tJwy ddi vi tn aia vSt do 5o voi cac vht khar ttiec- • \HU'V cjn ct~- n mdt vat lam nxr-c va w t ^ qiJV (ia<:> 'io 0 ^ dinti thoi gian trong ci ; "?. ^'^ ^*" chon mot mdc thdi gian (hay gdc '^hoi 'jiant va diinR n>dt dong ho df rit auY chic>u bao gdm vat tam mdc, ne toa dd, mdc thdi Rian va ddng hd. 10 1. Chat diem la gi ? CAU HOi VA BAI TAP A. Cach diing dudng di va vat lam mdc. B. Cach diing cac true toa dd. C. Dung ca hai each A va B. 2. Neu each xac dinh vi tri cua mot d td tren mdt qudc Id. 3. Neu each xac dinh vi tri cua mdt vat tren mdt mat phang. 4. Phan biet he toa dd va he quy chieu. Trudng hgp nao dudi day co the' coi vat la chat diem ? A. Trai Oat trong chuyen ddng tir quay quanh mmh no. E. Hai hdn bi luc va cham vdi nhau. C. Ngu'di nhay cau luc dang roi xudng nudc. D. Giot nudc mua luc dang rai. Mdt nguoi chi dudng cho mdt l I'l "•4 Hmh 3.3 '-'".•i Hay so sanh dp Idn ciia van tde tdc thdi eiia xe tai va xe eon ve d Hinh 3.3. M6i doan tren veeto van tdc dng vdi 10 km/h. Ne'u xe con dang di theo hudng Nam - Bae thi xe tai dang di theo hudng nao ? Thual ngu "van tdc" duoc dung khong nhumg de chi van tdc la dai luong vecto, ma cdn de chi dp kVn ciia dai luang dd (tdc do). Chi khi mudn nhan manh den phuong va chieu ihi ta mdi dijng thuat ngur vecto \an tdc. T Ll IC 17 esv Hmh 3.4 Gia td'c ciia chuydn ddng cho biet van tdc bidn thidn nhanh hay cham theo thdi gian. Don vi eiia gia tdc la met tren giay binh phuang (m/s-). Trong chuydn ddng thing nhanh dan ddu. gia td'c ludn ludn khdng ddi. /)) \'cctagia tdc Vi vein tdc Id dqi luang vecta nen gia idc cimg la dqi luang vectcf: a = V - VQ _ Av (3.1b) Vi v > V(^ nen vecto Ai; cung phucmg. ciing chieu vdi cac vecto fj^, va v (Hinh 3.4). Vecta a cung phucmg. Cling chieu vdi vecta Ar, ndn nd cung ciing phuong. cung chieu vdi cac vecto van tdc. \ I thi Gia su cd mot chiec xe ma\ Kill vat chuyen dong tfldng nhanh ddn deu, dang chuyen ddng thang \di van tdc yectogia loc cd goc d vqt chuyen dcmg, cd phuong 3 m/s. hone tam: tdc \di "ia tdc i • • . -..• i • i • - ,. ,~ ~ >• ^I't K-c va chieu trunu vol nhuong va chieu cua vecto van 0.5 m/s-. Hav tmh van toe cua .\e , d , • , , .„, , h; , .„ ;. 1, . ,n '"'' 1" <^(> do dai tl le ven do lon cua gia toe theo sau kn I tang toe diroc 10 gui\. , • * mot ti xicli nao dd. Giai: Siiu 10 giay. \an tdc cua .\e tang lupc mdt luong la 0.5,10 = 5 m/s. • -'(>. van toe cua \e sau 10 gia\ la : (=3 + 5 = 8 m/s 2. Van toe eiia chuyein dong th^ng nhanh dan deu a) Cong lliiic liiih van tdc Tra lai cdng thuc (3.1a) Ar V - -f' o 1 - neu lay gdc thdi gian o thdi diem r,, (/ = 0), ta se CO Al = t \a V = VQ + at (3 2) Do la cdng thuc tfnh van tdc. Nd cho ta biei van tdc cua \at d nhung thdi didm khae nhau. 18 28-VA T Li m b) Dd flu vein tc)'c - thcri gian Do thi bieu didn su bie'n thidn cua van td'c tiic thdi theo thdi gian ggi la do thi van tdc - thcjri gian. Dd la dd thi ung vdi cdng thuc (3.2), trong dd v coi nhu mdt ham sd ciia thdi gian t. Dd thi cd dang mgt doan thang (Hinh 3.5). Si 3. Cong thut tinh quang duong di duoe eua chuydn dong thang nhanh dan deu Ggi .V la quang dudng di dugc trong thdi gian t. Tdc do trung binh ciia chuydn ddng la (xem 2.1): s i/(m/s) O Hinh 3.5 SjHa y Viet eong thdc tinn van tdc dng vdi do thi d Hinh 3.5 f^tb = t Ddi vdi chuydn ddng thang nhanh dan ddu. vi do ldn cita vent tcic (tdc do) tdng deu theo thdi gian nen l/(m/s) 0.8 ngUcri ta dd chirng minh elidrc cong thitc tinh tdc dc) trung binh sau clay (xem trang 23) .• Vi, + V vdi V,, la tde dd diu va v la td'c dd cudi. Ma VQ + at. t khae. ta lai cd : i.' Tir cac cdng thiic trdn. ta suy ra 1 1 s = VQI + -af (3.3) Cdng thuc (3.3) la cong thtic tinh qudng chdmg di 0,6 0,4 0,2 o 4 t (S Hmh 3.6 K^Hinh 3.6 la do thj van toe • duqc ciia chuydn ddng thang nhanh dan ddu. Cdng thuc nay cho thay qudng dudng di dirqc trong chiiyctt dcing thdng nhanh ddn deu la niol lidni sdhcic hut cua thoi gian. H3; 150 4. Cong thut lien he giua gia toe, van toe va quang duong di diroe cua ehuyen dong thang nhanh dan deu Loai t trong cac cdng thiic (3.2) va (3.3). ta duoc ; VQ = las (3.4) thoi gian cua mot thang ma trong 4 giay dau ke tu' lue xu phat. Hay xae dinh gia toe : thang may trong giay dau tier; ^HHa y tinh quang duong ma thang may di dupc trong gia thu nha't, kd tu' lue xuat phat a eau i^'i' o M ~Xc - s X Hmh 3.7 [•0 Cho mpt hon bi xe dap ISn xudng mdt mang nghieng nhin, dat (ioe vUa phai (xem Hinh 3.1 d dau bai hoe nay). Hay xay dUng mpt phuong an nghien edu xem chuyen dong ctia hdn bi cd phai la chuyen dpng thing nhanh dan deu hay khdng ? Chu y rang chi CO thude de do dp dai va dong ho de do thai gian. Goi y : Nen chpn .v,, va L',, sao cho phirong trinh (3.5) trd thanh don gian. Sau dd phai ,\ac dinh xem cac dai luong nao can phai do vii dinh luat hien thien nao can phai phat hien. AV a V -••— • Hinh 3.8 " ; (hi: Mdt xe dap dang di thiing vdi . im tdc 3 m/s hdng hiim phanh vii di Jiam diin deu. Mdi giay viin tdc giam 0.1 m/s. Hiiy ti'nh van tdc ciia \e sau khi hiim phanh duac 10 s. Criai : Sau khi ham phanh duoc 10 giay thi van tdc cua xe dap giam mot luong la 0,1.10= 1 m/s. Vdi i.',, = 3 m/s : a = -0,1 m/s- ; t = 10 s thi V = 1 m/s. Vay. van tdc ciia xe dap sau lOgiiiy lit : I' = 3 - I = 2 m/s. 20 5. Phuong trinh ehuydn dong cua chuyen dong thang nhanh dan deu Nd'u cd mdt chat didm M xua't phat td mdt didm A (Hinh 3.7) cd toa do XQ trdn dudng thang Ox, chuydn ddng thang nhanh dan deu vdi van tdc dau VQ va vdi gia tdc a, thi toa do ciia M a thdi diem r se la : .v = .VQ + s hay : X = .XQ + VQI + -at (3.5) Phuomg trinh (3.5) \h phuang trinh chuyen dqng ciia chuydn ddng thang nhanh dan deu. H3 III - CHUYEN DON G THAN G CHAM OAN DEU 1. Gia toe eua chuyen dong thang cham dan deu a) Cdng thitc tinh gia tdc Cdng thuc tfnh gia td'c trong trudng hgp nay ciing tuom 2 tu nhu trdn : Av V -Vn a = At t Ndu chgn chidu ciia cac van td'c la ehieu duomg thi V < VQ va Ar; < 0. Gia td'c a cd gia tri am, nghia la ngugc dau vdi van tdc. b) Vecta gia tdc Ta cd : Av_ 'Ki Vi vecta f cung hudng nhung ngan hom vecto V(), nen vecto At; ngugc chieu vdi cac vecta ? va t^o (Hinh 3.8). Vecto gia toe cua chuyen dqng thdng chqm dan di'it nguoc chieu vin vectcr van tdc. 2. Van toe eiia ehuyen dong th^ng cham dan deu a) Cdng thitc tinh van tdc Chuydn ddng thang cham dan ddu la chuyen ddng thang. cd do ldn van td'c giam ddu theo thdi gian. Ta cd the vid't cdng thu'c tfnh van tdc dudi dang tdng quat : V = VQ + at a ngugc dad vdi VQ. b) Do thi van tdc - thdi gian cd dang nhu d Hinh 3.9. 3. Cong thire tinh quang duong di diroc va phuong trinh ehuyen dong eua chuyein dong thang cham dan deu a) Cong thuc dnh qudng dudng di duqc Chiing minh tuomg tu nhu trong chuyen ddng thang nhanh dan ddu, ta cd cdng thuc tinh quang dudng di dugc cua chuydn ddng thang cham dan deu : 1 1 s = VQt + -at trong dd a ngugc da'u vdi VQ. Chii y rang, trong chuyen ddng thang cham dan ddu cd liic vat se dimg lai (v - 0). Nd'u gia td'c cua vat van dugc duy tri thi vat se chuyen ddng nhanh dan ddu ve phfa ngugc lai. Vi du : ban nhe mdt hdn bi ldn mdt mat phang nghidng. b) Phuomg trinh chuyen ddng tuomg tu nhu phuomg 5 10 15 20 25 30 l{s) Hmh j y H f i Trd lai vf du d muc III.2a. Tfnh quang dUdng ma xe dap di dupc tu liic bat dau ham phanh de'n luc dUng hin. HD Diing cdng thdc (3.4) de trinh (3.5) : Sl BD X = .XQ + VQI + -at'- kiem tra ket qua thu dugc cua cau Si . Chuyen ddng th^ng nhanh (cham) dan deu la chuyen ddng thang cd dd Idn ciia van tdc tang (giam) deu theo thdi gian. Van tdc tuc thdi va gia tdc la cac dai luong vecto. Oon vi ciia gia tdc la m/s^. Cdng thuc tinh van tdc : v = VQ + at. Chuydn ddng th^ng nhanh dan deu : a cung daiu vdi v^. Chuyen ddng thdng cham dan deu : a ngupc daiu vdi v^. Gia tdc a ciia chuyen dpng thdng bien ddi deu la dai luong khdng ddi. Cdng thiit tinh quang dudng di duoc cua chuyen ddng thdng bien ddi deu : s = i\t + at'' ° 2 Phuong trinh chuydn ddng ciia chuyein ddng thdng bien ddi deu : x = XQ+ v^t + at ^ Cdng thiic lien he giiia gia tdc, van tdc va quang dudng dl duoc : o - i 2 as 21 CAU HOI VA BAI TAP lO.Trong cong thUc tinh van tdc eiia chuyen i 1, Viet cdng thiic tinh van tde tiic thoi ciia ;np; vat chuydn dpng tai mpt diem tren quy •:ao. Cho biii: yeu cau ve dp ldn eiia cac dai it'cng ;-ong .:dng thiic do. 2. Vecto van trie tire thoi tai mot diem cua mpt chuy6r dcncj thang duge xac dinh nhu the nao ? 3. CoLiyen dong thing nhanh dan deu, cham a;^- :5ed ia gi ? 4. V- V. oong inue tfnh van tdc cue chuyen dpng dpng thing nhanh dan deu v = VQ + af thi A. 1/ luon luon duong. B. a ludn luon duong. C. a ludn ludn ciing da'u vdi v. D. a ludn ludn nguge da'u vdi v. Chpn dap an diing. 11. Cong thiic nao dudi day la cong thdc lien he giua van td'c, gia tdc va quang dudng di dugc CLia chuydn dpng thing nhanh dan deu ? []-:. -,g nrcnh, cnam dan deu. Noi ro da'u eiia cb dai ii-':'ng tham gia vac cdng thue do. A. 1/ + 1/ 0 2as B. V2 + 1/2 : 2as t. Co toe cua chuyen dpng thing nhanh, cham Cv - 2as D v^-vl = 2as •da:: ieu co dac diem gi ? Gia td'c dugc do b§ng don vi nao ? Chieu cua vecto gia tdc eiia cac chuyfen dpng nay eo dae diem gi ? 6. Viet eong thuc tinh quang dudng di dugc eua cnuyen dpng thing nhanh, cham dan deu. Noi ro da'u eua cac dai lugng tham gia vao edng thiic do. Quang dudng di duoc trong cac ehuyen ddng nay phu thupe vao thdi gian theo ham sd dang gi ? 7. Viet phuang trinh chuyen dpng eiia ehuyen dong thang nhanh, cham dan deu. 8. Thiet lap cong thUe tinh gia td'c ciia ehuyen dpng thang bien doi deu theo van tdc va quang duong di duge. 9. Cau nao diing ? A. Gia tdc cua ehuyen dpng thing nhanh dan deu bao gid eung Idn hon gia tdc cua chuye'n ddng thang eham dan deu. B. Chuyen dpng thing nhanh dan deu co gia tdc Idn thi eo van tde Idn. C. Chuyen dpng thing bien ddi deu eo gia toe tang, giam deu theo thdi gian. D. Gia tdc trong ehuyen dpng thing nhanh dan deu CO phuong, chieu va dp Idn khong ddi. 22 12. Mpt doan tau rdi ga ehuyen dpng thing nhanh dan deu. Sau 1 phiit tau dat tdc dp 40 km/h. a) Tinh gia tdc eiia doan tau. b) Tinh quang dudng ma tau di dugc trong 1 phut dd. c) Ne'u tie'p tuc tang tdc nhu vay thi sau bao lau nua tau se dat tdc dp 60 km/h ? 13. Mpt 6 td dang chay thing deu vdi tdc dp 40 km/h bdng tang ga chuyen dpng nhanh dan deu. Tinh gia tdc cua xe, biet ring sau khi chay dugc quang dudng 1 km thi d td dat tdc dp 60 km/h. 14. Mpt doan tau dang ehay vdi tdc dp 40 km/h thi ham phanh, chuyen dpng thing cham dan deu de vao ga. Sau 2 phut thi tau dung lai d san ga. a) Tinh gia tdc ciia doan tau. b) Tinh quang dudng ma tau di dugc trong thdi gian ham. 15.Mpt xe may dang di vdi tde dp 36 km/h bdng ngudi lai xe tha'y co mpt cai hd trudc mat, each xe 20 m. Ngudi ay phanh gap va xe de'n sat mieng hd thi dUng lai. a) Tinh gia tdc cOa xe. b) Tinh thdi gian ham phanh. Em CO bi€it ? CHUNG MINH CONG THUC TINH TOC DO TRUNC BINH TRONG CHUYEN OONG THANG NHANH DAN OEU i/(m/s) Quang duang di dupc trong chuyen dpng thing d^u I duac tfnh bang cong thuc : s = vt trong do van toe (toe dp) v la mpt dai lugng khong doi. Do thi van tdc ciia chuyen dpng thing deu co dang mpt doan thang song song vai true f (Hinh 3.10). Trong do thi nay, hinh chu nhat co mpt canh la u, mpt canh la f (dugc to mau) se CO dien tfch tf le vai quang dirong di dugc : s = vt. Thuc vay, ne'u van tdc la 1 m/s va thoi gian chuyen dpng la 1 s thi quang duang di dugc se la 1 m. Quang duong di dugc nay ung vai 1 6 nho tren do thi. Neu van toe la 4 m/s va thai gian chuyen dpng la 5 s, thi quang duang di dugc se la 20 m. Quang dudng di dugc nay img vol 20 6 tren do thi van toe. v (m/s) Noi khae di, dien tfch cua hinh chu nhat noi tren phai tfnh theo dan vi o nho, mpt canh ung vai thai gian 1 s, mpt canh ung vol van toe 1 m/s (khong tfnh theo don vi m- hay cm^). Vay, khi ta noi dien tfch hinh chu nhat trong do thi van toe bieu dien quang duang di dugc thi dien tfch nay phai tfnh theo dan vi met chu khong phai met vuong. Ta hay ap dung kei qua tren cho chuyen dpng thing nhanh dan deu. Phuang trinh van toe cua chuyen dpng thin g nhanh dan d^u la i; = f^ + at. O t(s) Hinh 3.10 OP thi van toe eo dang mpt doan thang, eat true v 6 diem i'|, nhu Hinh 3.11. Do la do thi van toe cua ehuyen dpng thang nhanh dan deu. Ta chia khoang thai gian f thanh rai nhieu khoang nho Ar, sao eho trong mPi khoang thai gian nho do cd the coi ehuyen dpng nhu thing deu vol van toe la van toe d diem giua eua khoang do. Quang duang di dugc trong khoang thai gian do duge bieu dien bang dien tfch eua dai hep hinh ehu nhat, mpt eanh la Af, mpt eanh la ;;. Quang dudng di duge trong khoang thai gian Artiep sau eung dugc bieu dien bang dien tfch eua dai hep hinh chu nhat nhu tren, nhung eanh v dai hon mpt ehiit. Cu nhu the, quang duang di dugc trong ea khoang thdi gian f se duge bie'u di^n bin g tong dien tfch cua cac dai hep noi tren. Ne'u lay khoang thai gian Af rat nho thi tong dien tfeh eae dai hep se bing dien tfeh eua hinh thang vuong eo ehieu eao la f, eo cac day nho va day Idn la v^ va v. Ket qua, ta duge : s = -(i;jj + v)t vc Cuoi cung, ta duge v^+at s = D„f + —at' u 2 Ngoai ra, ta con eo s ^,bf tUdo suy ra t;,,, = -(i;,, + I') 23 14 Su ROI TU DO Su roi eiia cac vat la mpt chuyen dpng xay ra rai pho bien quanh ta. Al cung biei, d cung mpt dp eao mpt hon da se rai xuong dat nhanh hon mpt chiec la. Nhieu nguai cho ring, sd dT co hien tupng do la do trpng luc ma Trai Oat tac dung len hon da Ion hon trpng lue ma Trai Oat tac dung len chie'c la. Nguyen nhan do co dung hay khong ? I - SU ROI TRONG KHON G KHI VA SU ROI TUDO 1. Sir roi eua eae vat trong khong khi a) Tha mdt vat tir mdt do cao nao dd de nd chuyen ddng tu do khdng cd van tdc dau, vat se chuyen ddng xud'ng phfa dudi. Dd la sir roi cua vat. Ta hay lam mdt sd thf nghidm de xem trong khdng khf vat nang cd G.GA-LI-L£ (Galileo Galilei. 1564 - 1642) Nha vat li ngudi l-ta-li-a H I - Trong thf nghiem nao vat nang roi nhanh hOn vat nhe ? - Trong thf nghiem nao vat nhe rdi nhanh hon vat nang ? - Trong thf nghiem nao hai vat nang nhu nhau lai roi nhanh, cham khae nhau ? - Trong thf nghiem nao hai vat nang, nhe khae nhau lai roi nhanh nhu nhau ? 24 ludn ludn roi nhanh hom vat nhe hay khdng ? Trong cac thi nghidm nay ta ddng thdi tha nhe nhang hai vat roi xud'ng tir cdng mdt do cao, rdi quan sat xem vat nao roi tdi dat trudc. - Thf nghidm 1. Tha mdt td giay va mdt hdn sdi (nang hom td giay). - Thf nghidm 2. Nhu thf nghidm 1, nhung gia'y vo trdn va nen chat. - Thf nghidm 3. Tha hai td gia'y ciing kfeh thudc, nhung mdt td gia'y dd phing cdn td kia thi vo trdn va nen chat lai. - Thf nghidm 4. Tha mdt vat nhd (ching han, hdn bi d trong Ifp ciia xe dap) va mdt ta'm bia phSng dat nam ngang. b) Tra ldi cau hdi H I c) Sau khi tid'n hanh thf nghiem, ta thay : Khdng th^ ndi trong khdng khf, vat nang bao gid ciing roi nhanh hom vat nhe. Hay suy nghT xem yd'u td nao cd the anh hudng de'n su roi nhanh hay cham .ciia cac vat trong khdng khf ? 2. Su roi cua cac vat trong chan khong (su roi tu do) a) Ong Niu-tan Nha vat If ngudi Anh Niu-tom (Isaac Newton 1642 - 1727) la ngudi dau tien nghidn cuu loai trir anh hudng ciia khdng khf ldn su roi cua cac vat. Ong lam thf nghidm vdi mdt dng thuy tinh kfn (Hinh 4.1) trong cd chu'a mdt hdn bi chi va mdt cai ldng chim. - Cho hai vat ndi trdn roi d trong d'ng cdn day khdng + •/ Khdng khf o rr 13 Chan khong khf thi hdn bi chi roi nhanh hon cai ldng chim. - Hiit hd't''' khdng khf d trong d'ng ra, rdi cho hai vat ndi trdn roi d trong dng thi thay chiing roi nhanh nhu nhau. h) Kei ludn Tit nhidu thf nghidm nhu trdn, ta di dd'n kdt luan : Ndu loai bd dugc anh hudng cua khdng khf thi mgi vat se roi nhanh nhu nhau. Sir roi cua cac vat trong trudng hgp nay ggi la su rai tu do. [ S Thuc ra, mudn cd su roi tu do ta cdn phai loai bd nhieu anh hudng khae nira nhu anh hudng ciia didn trudng, cua tir trudng... Vi vay, khai nidm chfnh xac vd su roi tu do la : Sir roi tu do Id su rcri chi dudi tdc dung cua trqng luc. Thi nghiem cua Ga-li-le a thdp nghieng thdnh Pi-da (Pisa) Trade Niu-tan, Ga-li-le da lam thi nghiem sau : Ong tha nhirng qua ta nang khae nhau rai dPng thdi tix tMg cao ciia tea thap nghieng (Hinh 4.2) d thanh phd Pi-da (I-ta-li-a) xudng va nhan thay chiing rcfi den mat dat gan nhu cung mpt luc. Neu phan tich ki thi nghiem ciia Ga-li-le ta se thay : Trpng luang cua cac qua ta nang rait lon so vdi sue can cua khong khf tac dung len chiing. Do do, ta co the' bo qua sue can nay va coi su rai ciia cac qua ta nhu la sir roi tu do. (1) Trong thiCc te. ta khong the hiit hei khong khi ra duqc. Tuy nhien, khi khong khi trong d'ng loang den mite nao do. ta coi nhu trong dng khong cdn khong khi. Hmh 4.1. 6ng Niu-tan 1 Chira hut chan khong 2 Da hut chan khong IS Su roi cua nhufng vat nao trong 4 thi nghiem ma ta lam d tren c6 the coi la sU roi tu do ? Hinh 4.2. Thap nghieng Pi-da 25 Phuong phap chup anh boat nghiem Xl chu\ en dpng rai tu do xa\ ra rat nhanh nen \ iec do thoi gian rai la rai kho khan. Ngiroi ta thuang dicing phidrng phdp chitp dnh hoat nghiem de nghien ciiu sir roi tu do. Mpt hon bi son trang duoc tha roi truoc mpt cai thuoc dat thang dung trong mot phong toi. Mpt may anh de chup anh hon hi trong suot thai gian roi. Hon bi duoc chieu sang boi nhung chcfp sang xa_\ ra each nhau nhung khoang thoi gian bang nhau. Ket qua la ta se thu dupc anh cua hon bi o mpt loat vi tri each nhau nhiimg khoang thoi gian roi bang nhau. O tTinh 4.3. khoang thoi sian 1 nav la 31 giay. Dua \ao anh hoat nghiem ta co the chung minh su roi tu do la mpt chuyen dpng thang nhanh dan d^u. [ S Phai lam thf nghiem nao de xac nhan dieu khSng dinh nay ? ThL/oc. hon b Hmh 4.3 Anh cua hon bi d nhiJmg vi tri each nhau nhCtng khoang thai gian rai bdng nhau. 26 !l - NGHIEN CUU SU ROI TU DO CUA CAC VAT 1. Nhung dae di^m eua chuydn dong roi tir do a) Phuomg cua chuyen ddng roi tu do la phuong thang dung (phuomg ciia day dgi). ^ hi Chieu cua chuydn dgng rai tu do la chieu tutren xucmg dudi. c) Chuydn ddng roi tu do la chuvcn dcing thdng nhanh ddn deu. d) Cong thitc tinh vein tdc Ndu cho vat rcri tu do, khdng cd van tdc ddu (tha nhe cho roi) thi cdng thuc tfnh van tdc ciia vat roi tu do la : V = gt (4.1) trong dd g la gia tdc ciia chuyen ddng roi tu do, ggi tat la gia tdc nri tu do. ei Cdng thitc tinh qudng dudng di duqc ciia vdt rai lit do : 2'^' (4.2) trong dd 5 la quang dudng di dugc. cdn t la thdi gian roi. 2. Gia toe roi tudo Cd nhidu phuomg phap do gia tdc roi tu do. Thuc nghidm chirng to rang : Tat mut not nhat dinh tren Trai Dat vd d gdn mdt dal. cac veu deu roi tu do voi cung mot gia toe g. Tuy nhien. a nhiimg vT do khae nhau. gia td'c roi tu do se khae nhau. 0 dia cue. g ldn nhat : g = 9.8324 m/s-. 6 xfch dao.,? nhd nhai : g = 9.7805 m/s-. 0 Ha Ndi. ,;.' = 9.7872 m/s Hd Chf Minh. i,' = 9.7867 m/s-. 0 Thanh phd Ndu khdng ddi hdi do chfnh xtic cao, ta cd thd lay g ~ 9.8 m/s- hoac i; = 10 m/s-. Su roi tu do la su roi chi duoi tac dung cua trong int. Trong trudng hop co the bd qua anh hmong ci.i ac yeu td khae len vat roi, ta cd the coi su roi ciia vat nhu la su roi tu do. Chuyen ddng roi tu do la chuyen ddng thang nhanh dan deu theo phuong thang dung, chieu tutren xudng dudi. Tai mdt noi nhat dinh tren Trai Oat va o gan mat dait, mpi vat deu roi tu do voi cung gia tdc g. Gia tdc roi tu do d cac vi dd khae nhau tren Trai Dait thi khae nhau. Nguoi ta thuong lay g~ 9,8 m/s^ hoac g~ ^Q m/s^. CAU HOI VA BAI TAP | A l B. Chuyen dpng cua mpt hdn soi dugc nem WM 1. Yeu td nao anh huong den su roi nhanh, 'heo phuong n^m ngang. cham ciia cac vat khae nhau trong khdng khi ? C. Chuyen dpng cua mpt hdn soi dugc nem 2. Ne'u loai bo duoc anh huong cua khdng khf thi 'h^° P^^^^S xien goc. cac vat se roi nhu the nao ? D. Chuyen dpng eiia mpt hdn soi dugc tha rai 3. Su roi tu do la gi ? 4. Neu cac dac diem eua su roi tu do xuong. 9. Tha mpt hdn da tu dp cao h xud'ng da't. Hdn da rai trong 1 s. Ne'u tha hdn da do tu dp cao 4 h 5. Trong trudng hgp nao cac vat roi tu do vdi xud'ng da't thi hdn da se roi trong bao lau ? Cling mpt gia tdc g ? A 4 s • B 2 s • 6. Viet eae edng thire tinh van tde va quang c. 72 s ; D. Mot dap sd khae. dudng di duac ciia vat rai tu do. 10. Mpt vat nang roi tU dp eao 20 m xudng da't. , ^, .^ ,. , ., . , -.J - - Tinh thdi gian roi va van tdc eua vat khi cham 7. Chuyen dong cua vat nao duoi day se ,.-, ,.-,„, , ' •1 iA - A ^ *u' ^-o dat Layg= lOm/s^. dugc COI la rai tu do neu dugc tha rai ? ' ^ . 11. Tha mot hdn da rai tu mieng mot cai hanq A. Mot cai la cay rung. , .; ,.. ,, _ . i-'.. ,. u^,,-> '^ . , sau xuong den day. Sau 4 s ke tu lue bat dau B. Mpt sgi ehi. (1^^ {|.^i pg|.^g jjg'pig |.^Qp| ^^ r^\\2fm vao day. Tinh C Mpt chie'c khan tay. ehieu sau cua hang. Biet van td'c truyen am D. Mpt mau pha'n. trong khdng khi la 330 m/s. Lay g - 9,8 m/s^. 8. Chuyen dpng nao dudi day cd the coi nhu la 12. Tha mpt hdn soi tu tren gae cao xudng dat. chuyen dpng roi tu do ? Trong giay cudi cung hdn soi roi duoc quang A. Chuyen dpng cua mpt hon soi dugc nem '^^^"Q ^^ m. Tinh dp cao cua diem tU do bat len eao. <33u tha hdn soi. Lay g = 10 m/s^. 27 Em CO biet ? PHL/ONG PHAP THL/C NGHIEM Phuang phap thirc nghiem la phuang phap ma nguai ta thuang dung de thie't lap cac djnh luat vat If ma ta gpi la cac dinh luat there nghiem. Ching han, khi chua biet ro nguyen nhan ciia ehuyen dpng rai tu do, viec nghien cuu quy luat bie'n doi ciia gia tdc rai tu do bang thuc nghiem dugc tien hanh theo tinh than cua phuang phap thirc nghiem. — Thoat tien, can cu vao cac ket qua quan sat, cac kinh nghiem hang ngay hoac cae thi nghiem sa bp... de de ra mot gia thuyet ban dau. Trong bai nay, gia thuye't ban dau la vat nang rai nhanh han vat nhe. — Tie'p theo, phai lam nhiiu thi nghiem de xac nhan hay bae bo gia thuyet ban dau. Cae thf nghiem nay phai co tinh thuye't phuc, nghla la phai xem xet dii mpi trudng hap, mpi khia canh va phai dua den mpt ket luan chic chan. Neu gia thuyet nay duqc xac nhan thi no tra thanh mot dinh luat thuc nghiem. Trong bai nay, ta lam 4 thi nghiem va thu duac nhieu ke't qua mau thuin vai gia thuyet ban dau, nen gia thuyet nay da bi bae bd. — Trong trudng hop gia thuye't ban dau bi bae bo, ta phai phan tich ket qua thi nghiem de de ra mot gia thuyet khae. Trong bai nay, ta thay khong the ndi vat nang rai nhanh ban vat nhe duac. The thi phai giai thfch hien tuang hon sdi rai nhanh ban ta giay nhu the nao ? Phai de ra gia thuyet nao de no phu hgp vai kei qua cua ca 4 thi nghiem ? Ta nghT den anh hudng ciia khong khf len su rai cua cac vat. Tu do ta de ra mgt gia thuyet mai : neu loai bd dugc anh hudng cua khong khf thi co le cac vat se rai nhanh nhu nhau. — Tuy gia thuye't mai co the giai thfch dugc cac kei qua cua ta't ca cac thi nghiem da lam, nhung phai tie'n hanh them mot loat thf nghiem khae de kiem tra tfnh dung din cua gia thuyet moi. Trong bai nay, thf nghiem dng Niu-tan va thi nghiem cua Ga-li-le d thap nghieng thanh Pi-da dong vai tro cac thi nghiem kiem tra. Cu nhu the cho de'n khi xay dung dugc mpt dinh luat thuc nghiem. — Cudi cung, phai ap dung dinh luat nay vao nhieu tinh hudng mdi khae nhau de tim ra gidi han ap dung ciia no. Chang han, quy luat rai ty do khong the ap dung cho cac vat d trong eon tau vu tru bay quanh Trai Oat hoac cho cac phan tu trong mpt khoi khf. 28 CHUYEN DONG TRON DEU Chuyen dpng ciia diem dau mpt chiec kim giay dong ho va diem dau mpt canh quat may co nhung diem gi gidng nhau va khae nhau ? I-DINH NGHIA 1. Chuyen dong tron Chuyen dqng trdn Id chuyen dqng co quy dqo Id mqt dudng trdn. Vi du : Khi chie'c du quay quay trdn, quy dao ciia diem treo cac ghe ngdi trdn chid'c du quay la nhung dudng trdn cd tam nam trdn true quay (Hinh 5.1). Hmh 5.1 2. Toe do trung binh trong chuyein dong tron Tuomg tu nhu trong chuydn ddng thang, ta dinh nghia td'c do trung binh trong chuyen ddng trdn nhu sau : Td'c dd ^ 9 dai cung trdn ma vat di dugc trung binh -ph^i gj^n chuyen ddng 3. Chuydn dpng tron deu Chuyen dqng tron deu la chuyen ddng cd quy dao trdn vd cd toe dq trung hinh tren moi cung trdn la nhu nhau. (Hinh 5.2). Si SS Hay neu mpt vai vf du ve chuyen dgng tron deu. Hinh 5.2 29 [ S Mpt chiec xe dap ehuyen dpng deu tren mdt dudng trdn ban kfnh 100 m. Xe ehay mdt vong het 2 phiit. Tfnh tdc dp dai ciia xe. Hinh 5.3 Hinh 5.4 Khai niem tdc dp goc chi noi len sir quay nhanh hay cham ciia ban kinh OM. 30 II - Tdc 0 0 DAI VA TbC DO GOC 1. Toe do dai Ggi As la do dai ciia cung trdn ma vat di dugc tir die'm M dd'n didim M' trong khoang thdi gian rat ngan At. Khoang thdi gian nay phai ehgn ngan dd'n mue ed the coi cung trdn nhu mdt doan thang. Ta ggi thuomg sd: As v - ^ (5.1) la tdc do dai ciia vat tai didm M. Tdc do dai chfnh la do ldn ciia van tdc tiic thdi trong chuyen ddng trdn ddu. Trong chuydn ddng trdn ddu thi As ludn ludn ti Id \'di At, ndn v la mdt dai lugng khdng ddi va bang tdc do trung binh ciia vat. Trong chuyen dcing iron deu, tdc dtp ddi ctia vcit khong ddi. 2. Vecto van toe trong chuy§n dong tron deu Trong didu kidn cung trdn cd do dai rai nhd. ed the coi nhu mgt doan thang. ngudi, ta dung mdt vecto As vira de chi quang dudmg di dugc, vira de chi hudng chuydn ddng. As ggi la vecta dep dcri Khi dd. van td'c se dugc bidu didn bang vecta vein tdc, cung phuomg. ciing chidu vdi vecto do ddi : ^ _ A? ^' ~ ^ Vi As triing vdi mdt doan cung trdn tai M ndn nd nam dgc theo tiep tuyen vdi dudng trdn quy dao tai M. v ciing hucVng vdi As nen nd cung niim theo tidp tuyen tai M (Hinh 5.3). Vecto vqn toe trong chuyen dong tron deu luon CO phuong tiep tuyen vdi ducmg tron quy dao. 3. Toe do goe. Chu ki. Tan so a) Dinh nghia Ggi O la tam va r la ban kfnh cua dudng trdn quy dao. /W la vi trf tiic thjdi ciia vat chuyen ddng. Khi vat di dugc mdt cung A.v trong khoang thdi gian Al thi ban kinh OM quay dugc gdc Aa (Hinh 5.4). Thuoms sd : CO = Aa ~At~ (5.2) ggi la tdc dc) girc cita chuyen dcJng trdn. Trong chuydn ddng trdn ddu thi gdc Aa tang ti le thuan vdi thdi gian At. nen td'c do gdc co ludn khdng ddi. Toe dq goc cuu cliuycn dqng tron la dqi luong do hdng gdc md han kinli OM quel duoc trong mqt dim vi thin gian. Toe do goc cua cliuycn dong trdn deu Id dqi luqng khong doi. h) Dan vi do tdc do goc Nd'u gdc Aa do bang dom vi radian, thdi gian Ar do bang dom vi giay thi tdc do gdc co do bang don vi radian tren gidy (vie't tat la radls). Sl c) Chu ki Chu kl T cua chuyen dong tron deu la thcri gian de vqt di duqc mot vong. Cdng thuc lien he giua td'c do gdc co va chu ki T ; 7 = ^ (5.3) (0 Dom vi chu ki la giay (s). [ S d) Tdn sd Idn so f cua chuyen dong trdn deu Id so vong md vqt di duoc trong I giay. Cdng thuc lidn he giiia chu ki va tiin sd : J J (5.4) Don vi ciia tan sd la vdng tren giav (vdng/s) hoac hec (Hz), ffi c) Cdng tlufc lien he Ciifa tdc do ddi vd tdc do ecic Ta da bidt. trong hinh trdn thi : do dai cung = ban kfnh x gdc d tam chan cung. Nhu vay. ta cd : A.s = / A«, vdi Aa do bang radian. ^ - . • . ' . - ^^ ^01 Tu he thuc tren. suy ra : — =; /• Ar Ar Sl 06 loai dong ho treo tudng ma kim giay quay deu lien tue. Hay tinh tde dp goe ciia kim giay trong dong ho nay. LdHa y chdng mmh cong thue (5.3). 143 Hay ehu'ng minh cong thdc (5.4). f.' Hay tfnh tdc do gdc cua hay H3 V = roj (5.5) chiec xe dap trong cau --.- 31 M, Hinh 5.5 I nh 5.6 Ill - GIA TOc HLTONG TA M 1. Huong eua veeto gia toe trong ehuyen dong tron deu Dt xet gia tdc ciia vat tai diem / (Hinh 5.5), ta khao sat su bid'n ddi vecto van tdc U ciia vat khi no chuyen ddng trong khoang thdi gian rat ngan Ar tir didm A/j dd'n didm M, trdn cung dudng trdn cd trung didm la /. Hai vecta van td'c ij^ va u., tai cae diem M^ va MT cd do dai bang nhau, nhung cd hudng khae nhau vl chiing lan lugt vudng gdc vdi cac ban kfnh OM, va OM^. Neu tinh tidn hai vecto v va v.^ dd'n diem /, ta se tim dugc vecto AS bie'u didn su thay ddi hudng ciia van tdc (Hinh 5.5) : v^ + Av = iJ-, hay Av - v^ - iJ^ Vi cung MiMo rat nhd va vat chuydn ddng trdn ddu. nen ta cd the: coi hai didm Mj va M-, gan nhu triing nhau tai / va vecto At; bidu didn su thay ddi Can cii vao hai tam giac dong dang Iv.v^ \ii OM.M^ tren tfinh 5.5. ta co : ciia van tdc tren doan dudng M^M~, nay. AT M|/W, OM, v-M vM r /Sv V Cd the chung minh vecta Ar; ludn ludn nam dgc theo ban kfnh va hudng vao tam O ciia quy dao. Ji.' = . suy ra : u^^ ~ M ' r Vidii : .\lpt ve tinh nhan tao chuyen dpng Vecta gia td'c a ciia chuydn ddng trdn deu cung dugc xac dinh bang cdng thiic (3.1b) : A ^ tron deu quanh Trai Dat tren mpt qus dao co Iam la tam Trai Dat va co ban kinh 7 000 km. Toe dp dai ciia (7 = Af \e linh lii 7.57 km/s. Tinh gia tdc hucmg tam ciia ve tinh. Vecto d ciing hUdng vdi vecta Av ndn nd cung nam dgc theo ban kfnh va hudng vao tam (Hinh (7,57.10')- Giiii 7 000.10 32 = 8.2 m/s 5.6). Do dd ngudi ta ggi gia td'c trong chuyen ddng trdn deu la gia tdc hudng tdm va kf hidu la a^^. Trong ehuyen dong trdn deu, tuy van toe co do lan khong doi, nhung cd hucrng luon thay doi, nen chuyen dong ndy co gia toe. Gia toe trong chuyen dqng trdn didi luon hucrng vdo tam cua quy dao nen gqi Id gia toe hudng tam. 2. Do Ion eiia gia toe huong tam Cdng thurc tinh gia td'c hudng tam la : .2 «ht = V r (5.6) HflHay chimg minh cdng thdc : m am = rco^ (5-7) ''r. Chuyfen ddng trdn deu la chuydn ddng cd cac dac di6m : Quy dao la mdt duong tron : Tdc dd trung binh tren moi cung tron la nhu nhau. S Vecto van tdc cua vat chuyen dpng trdn deu cd : phirong tiep tuydn vdi dirong tron quy dao ; do Idn (tdc dd dai): i' = ' ' Toe dd goc : CO = ; Aal a gdc ma ban kinh ndi tutam den vat quet duoc trong Al' thdi gian At. Don vi tdc dd gdc la rad's. Cdng thuc lien he giua toe do dai va tdc do gdc : v = ro). Chu ki cua chuyen ddng trdn deu la thoi gian de vat di diroc mdt vdng. Cong thut lien he giua chu ki va tdc dd goc : 2n "•-,. . . . i Tan sd cua chuyen ddng tron deu la sd vdng ma vat di duoc trong 1 giay. Oon vi tan .>:, so la vdng/s hoac htc (Hii. , Cdng thirc lien he friira chu •<; •-! lan so ; ' '' Gia tdc trong chuven done uor ..e;j •uon huon ; vno tam quv d.io va rn •_(• ipp ia : 3A - VAT Ll 10 3 3 -. .„ HOI VAB Al TAP a>^ I B. Tdc dp goc cua chuyen dpng trdn deu phu ~" 1. Chuyen dong trdn deu la gi ? thupe vao ban kfnh quy dao. 2. Neu nhung dac diem cua vecto van tdc cua ^' ^^^ ^ '^ ^ ^h° ^'^^'' ^'' *° ' ^^"^"^ *'"^ ehuyen ddng tron deu phu thudc vao ban kinh quy dao^ D. Ca ba dai luong tren khong phu thuoc vao 3. Td'c dp goc la gi ? Tdc dp goe dugc xac dinh j^gp, y^^^^ ^uy ^^^ nhu the nao ? ..A ,-u' - • 10. Chi ra cau sai. 4. Viet cong thirc lien he giua td'c do dai va tdc _, .-. ,. . . ,.. , , .- ,.;j„ ^„ ^. . , ,_ ., ^. , , ,.: Chuyen dong tron deu co cac dac diem sau: do goc trong chuyen dong tron deu. / . r ^ • , , • „ , A. Quy dao la dudng trdn; 5. Chu ki cua chuyen dpng tron deu la gi ? Viet g ^^^j ^ ^. ^ ^.^ ^^^^g 3... cdng thiic lien he giUa chu ki va toe dp gdc. ^ j^^ ^^ g^^ ^^^^ng ddi; 6. Tan so cua chuyen dpng trdn deu la gi ? Viet D. Vecto gia td'c ludn hudng vao tam. cong thirc lien he giUa chu ki va tan sd. ^ -, _ |^5t q^at may quay vdi tan sd 400 vdng/phiit. 7. Neu nhung dac diem va vie't cdng thirc tinh Canh quat dai 0,8 m. Tinh td'c dp dai va tdc dp gia td'c trong chuyen dpng trdn deu. goc cua mpt diem 0 dau canh quat. 12. Banh xe dap co dudng kinh 0,66 m. Xe dap chuyen dpng thang deu vdi van tdc 12 km/h. Tinh td'c dp dai va td'c dp goc cua mpt diem 8. Chuye'n ddng cua vat nao dudi day la chuye'n *^^" ^^"^ banh ddi vdi ngudi ngoi tren xe. dpng trdn deu ? 13. Mpt dong ho treo tudng co kim phut dai 10 cm vA. Chuye'n dpng cua mpt con lac dong ho. kim gid dai 8 cm. Cho ring cac kim quay deu. TinB. Chuyen dpng ciia mdt mat xich xe dap. tdc dp dai va tdc dp goc cua diem dau hai kim. ^ _, .. ,. , ..... J J... 14. Mot diem nam tren vanh ngoai cua mot lop xe mC. Chuyen dong cua cai dau van xe dap doi ,• ^ ,_. ,_ ^„ ,, , .,• ^ ,z ;., . u J- cach true banh xe 30 cm. Xe chuyen donq thanq voinguoi ngoi tren xe, xe chay deu. ... ,,:.... ^ ^.. .' ,.-.^,, .^ , , deu. Hoi banh xe quay bao nhieu vpng thi so chi trD. Chuyen ddng cua cai dau van xe dap ddi ^g^g ho tdc do cua xe se nhay mdt sd iJng viS 1 vdi mat dudng, xe chay deu. ._ ...^ u - .- ^ , 15. Mpt chiec tau thuy neo tai mpt diem tren Cau nao dung ? 3^;grlg xfch dao. Hay tinh td'c dp goc va td'c dp A. Tdc dp dai ciia chuyen dpng trdn deu phu dai cua tau doi vdi true quay cua Trai Dat. Biet thuoc vao ban kinh quy dao. ban kfnh ciia Trai Da't la 6 400 km. 34 •'AT Ll 10 iJ TlNH TUONG D6 I CUA CHUY6N DONG CONG THLTC CONG VAN Mpt di§n vien xiec dung tren lung mpt con ngua dang phi, tay quay tit mpt cai gay, d hai dau co hai ngpn dudc. Odi vai dien vien do thi hai ngpn duoc chuyen dpng tron. Con ddi vai khan gia thi sao ? I - TINH TUONG DOI CUA CHUYEN «•'^'^G 1. Tinh tuong doi eua quy dao Mdt ngudi ngdi trdn xe dap va mdt ngudi dumg bdn dudng cimg quan sat chuyen ddng cua eai dau van banh trudc xe dap dang chay. Ngudi dumg bdn dudng tha'y chide dau van chuydn ddng theo mdt dudng cong liic ldn cao, liic xud'ng thap (Hinh 6.1). Hinh dcii: 'in cttti chityct: .//'//<,' trong cut he quy , •:ic iihtttt tlu ihuc nhut' - quv dan 2. Tinh tirong c Mdt hanh khach dang ngdi ydn trong mdt toa tau chuydn ddng vdi van td'c 40 km/h. Dd'i vdi toa tau thi van td'c ciia ngudi dd bang khdng (ngudi ay ngdi ydn). Ddi vdi ngudi diing dudi dudng thi hanh khach dd dang chuye'n ddng vdi van td'c 40 km/h Cling vdi toa tau. N h u vay, •'• ' ' cua vut chuyen dong dot i", hicu khae nhon thi khae nhau. Vun lue CO mill lutriiii dot. NgUdi ngoi tren xe se thay dau van chuyen dpng theo quy dao nhu the nao quanh true banh xe ? Neu mpt vf du khae ve tfnh tuong ddi eua van tde. y 4 "nb Hmli 11 - CONG THUC CONG VAN TOC 1. He quy chieu dung yen va he quy ehieu chuyen dpng Mdt chide thuydn dang chay trdn mdt ddng sdng. Ta se xet chuyen ddng cua thuydn trong hai he quy chidu : - He quy chid'u (xOy) gan vdi bd coi nhu he quy chie'u dijmg ydn (Hinh 6.2a). - He quy chid'u (x'O'y') gan vdi mdt vat trdi theo ddng nudc la he quy chid'u chuyen ddng (Hinh 6.2b). 2. Cong thtrc cong van toe a) Trudng hap cdc vein tdc cUng phuang ciing chieu Thuydn chay xudi ddng nudc. Ggi i^tb la van td'c cua thuydn dd'i vdi bd, tiic la ddi vdi he quy chie'u diing yen. Van td'c nay ggi la vein tdc tuyet ddi. Ggi i^tn la van tdc cua thuyen dd'i vdi nudc, hie la dd'i vdi he quy chidu chuydn ddng. Van td'c nay ggi la vein tde tuang ddi. Ggi i^nb Is van tdc cua nudc dd'i vdi bd. Dd la van td'c cua he quy chie'u chuyen ddng so vdi he quy chieu diing yen. Van tdc nay ggi la van tdc keo theo. Dd dang tha'y rang : ^tb ^ ^m + i^nb(Hinh 6.3). He thiic nay cd the vid't dudi dang : I'U ^ ^1,2 + ^2,3 (6.1) Vi du : ne'u v , = 2 km / h, Trong do : sd 1 iing vdi vat chuyen ddng ; so 2 nb D,^ = 30km/hthi i;,^ = 28km/h. 36 umg vdi hd quy chid'u chuydn ddng ; sd 3 iing vdi he QUV chid'u diing ven. b) Trudng hop van tdc tuang ddi cdng phuang, nguac chieu vdi vein tdc keo theo Thuydn ehay ngugc ddng nudc. Vecta van td'c tuomg dd'i ?tn se ciing phuang, ngugc chieu vdi vecta van td'c keo theo v^^ (Hinh 6.4). Vd do ldn, rd rang la van td'c cua thuyen dd'i vdi nudc phai trii di van td'c chay cua ddng nudc mdi thanh van td'c ciia thuydn dd'i vdi bd : KbI = If^tnl - l^nbl Tuy nhidn, dudi dang vecto, ta van phai vidt : ^tb = ^tn + V nb (?,b la tdng ciia hai vecta ciing phuang, ngugc chidu) S 3 Nhu vay cdng thufc (6.1) cd tfnh tdng quat. Dd la cong thitc cdng van tdc. Vecta vein tdc tuyet ddi bdng tdng vecta ciia vein tdc tuang ddi vd van tdc keo theo. S-f" Vtb Vr,b Hmh 6.4 t ^ Mpt con thuyen chay ngugc dong nude di duge 20 km trong 1 gid ; nudc chay vdi van tde 2 km/h. Tfnh van tde eua thuyen ddi vdi nude. Quy dao va van tdc cua ciing mdt vat chuyein ddng ddi vdi cac he quy chieu khae nhau thi khae nhau. Cdng thdc cong van tdc : Vecto van tdc tuyet ddi bSng tdng vecto ciia van tdc tirong ddi va van tdc keo theo : F = r, + T\ ,. Van tdc tuyet ddi la van tdc ciia vat ddi vdi he quy chieu dung yen ; van tdc tirong ddi la van tdc ciia vat ddi vdi he quy chieu chuyetn ddng ; van tdc keo theo la van tdc ciia he quy chieu chuydn ddng ddi vdi he quy chieu dung yen. CAU HOI VA BAI TAP 7 1. Neu mpt vf du ve tfnh tucmg ddi ciia quy dao cua chuyen dpng. 2. Neu mpt vi du ve tfnh tuong ddi ciia van tdc cua chuyen dpng. Trinh bay cdng thUc edng van tdc trong trudng hgp cac chuyen dpng eung phuang, cung ehieu (ciing phuong va ngugc chieu). Chpn eau khang dinh diing. Dirng d Trai Oat, ta se tha'y 37 A. Mat Trdi dUng yen, Trai Oat quay quanh Mat Trdi, Mat Trang quay quanh Trai Da't. B. Mat Trdi va Trai Da't dirng yen, Mat Trang quay quanh Trai Da't. C. Mat Trdi dirng yen, Trai Oat va Mat Trang quay quanh Mat Trdi. D. Trai Da't dirng yen. Mat Trdi va Mat Trang quay quanh Trai Oat. Mpt chie'c thuyen buom chay ngugc ddng song, sau 1 gid di dugc 10 km. Mpt khue gd trdi theo ddng sdng, sau 1 phiit trdi dugc — - m. Van toe ciia thuyen buom so vdi nudc bang bao nhieu ? A. 8 km/h. B. 10 km/h. C. 12 km/h. D. Mpt dap sd khae. 6. Mdt hanh khach ngoi trong toa tau H, nhin qua cira sd tha'y toa tau N ben canh va gaeh lat san ga deu chuyen dpng nhu nhau. Hoi toa tau nao chay ? A. Tau H dirng yen, tau N chay. B. Tau H chay, tau N dirng yen. C. Ca hai tau deu chay. D. Cac cau A, B, C deu khdng dung. 7. Mpt 6 to A chay deu tren mpt dudng thing vdi van td'c 40 km/h. Mpt d td 6 dudi theo oto A vdi van tdc 60 km/h. Xac dinh van tdc cua 6 td 6 ddi vdi 6 td >4 va ciia oto A ddi vdi d td 6. 8. A ngoi tren mpt toa tau chuye'n dpng vdi van tdc 15 km/h dang rdi ga. 6 ngoi tren mpt toa tau khae chuyen dpng vdi van toe 10 km/h dang di ngugc chieu vao ga. Hai dudng tau song song vdi nhau. Tfnh van td'c cua 6 ddi vdi A. Em c6 biet ? \'\N TOC ANH SANG Mpt 6 to dang chay vai van toe v thi bat den pha (Hinh 6.5). Doi vai ngudi lai xe, anh sang truyen di vai van toe c{c= 3.10" m/s). Odi voi ngudi dung ben le duang thi co le anh sang se CO van toe c + u. Khong dau. Can cir vao cae thi nghiem rai chinh xac ma nhieu nha bae hoc loi lac da tien hanh vao cuoi the ki XIX de nghien ciru su truyen anh sang trong eae moi truang, Anh-xtanh (Einstein) da di den kei luan la, van toe anh sang ddi voi mpi he quy chieu khae nhau la nhu nhau va deu bang c. Cong thuc cpng van toe ma ta hoc d day khong dung cho truang hpp cac vat chuyen dpng vai van tdc rai lan (so sanh duac vai van toe anh sang). Cae em se biei ro dieu nay trong Thuyet tuang doi cua Anh-xtanh (1905). Hinh 6.5 38 V SAI SO CUA PHEP DO CAC OAI LlTONG VAT Ll Khi nghien cuu cac hien tuang tu nhien, trong vat If hoc nguai ta thudng dung phuang phap thuc nghiem : tien hanh phep do cac dai luang vat If dac trung cho hien tuang, xac dinh moi lien he giua chung, tu do rut ra quy luat vat If. Oe thuc hien cac phep do, ta phai co cac dung cu do. Tuy nhien trong thuc te, hau nhu khong mpt dung cu da nao, khong mpt phep do nao co the cho ta gia tri dung cua dai krpng can do. Cac kei qua thu duac chi la gan dung. Vi sao vay I Oieu nay co mau thuan hay khong voi quan niem cho rang vat If la mpt mon khoa hpe chfnh xac ? De tra lai cau hoi nay, truac hei ta can lam ro khai niem : phep do cac dai lupng vat If la gi I Vi sao co su sai lech giua gia tri dung cua dai lupng can do va kei qua do ? Tir do xac dinh kei qua va danh gia duac dp chfnh xac cua phep do. I - PHEP DO CAC DAI LUONG VAT Li. HE DON VI SI 1 Phen do car dai lironp vat li Ta dung mdt cai can de: do khdi lugng mdt vat. Cai can la mdt dung cu do, va phep do khd'i lugng ciia vat thuc chat la phep so sanh khd'i lugng ciia nd vdi khdi lugng cua cac qua can, la nhumg mau vat dugc quy udc cd khdi lugng bang mdt dom vi (1 gam, 1 kildgam...) hoac bang bdi so nguydn lan dan vi khdi lugng. Vay : l^hep clo mot dai luong vat li la phep so sanh no vtn dai luong cimg loai ducrc quy uirc lam dim vi. Cdng cu dd thuc hidn vide so sdnh ndi trdn ggi la dung cu do. phep so sanh true tidp thdng qua dung cu do ggi Vaphep do trite tie'p. Nhieu dai lugng vat If cd thd do true tid'p nhu do dai. khdi lugng, thdi gian,... trong khi nhirng dai lugng vat If khae nhu gia td'c. khd'i lugng rieng, thd tfch... khdng cd san dung cu do dd do true tid'p, nhung cd thd xac dinh thdng qua mdt cdng thiic lidn hd vdi cac dai lugng do true tid'p. Vi du : gia tdc rai tu do g 2v ' cd thd xac dinh theo cdng thirc i^ = ^- , thdng qua hai phep do t' true tid'p la phep do do dai quang dudng di dugc .s va thdi gian rai r. Phep do nhu the ggi la phep do gidn tiep. 39 He SI quy dinh 7 dan vi c0 ban, do la : — dem vi dp dai : met (m) — don vi thai gian : giay (s) — dan vi khoi luang : kilogam (kg) — dan vi nhiel dp : kenvin (K) — don vi cuong dp dong dien: ampe (A) — don vi cuong dp sang : candela (Cd) — don vi lupng cha't : moi (moi) Ngoai 7 don vi co ban, cac don vi khae la nhirng don vi ddn xuat, duoc suy ra tir cac don vi co ban theo mpt cong thuc. Vi du : don vi lire T la niutan (N), duoc dinh nghla : 1 N = 1 kg.m/s2 A (T) Hinh 7.1 H ] Em hay eho bie't gia tri nhiet dp ehi tren nhiet ke d Hinh 7.1 b§ng bao nhieu ? Hinh 7.2 ^Q lech diem 0 ban dau cua vdn ke gay ra sai so he thong. 40 2. Don vj do Mdt he thd'ng cac dan vi do cac dai lugng vat If da dugc quy dinh thd'ng nhat ap dung tai nhidu nudc trdn the gidi, trong dd cd Viet Nam, ggi la he SI (Systeme Intemational). II-SAI SO PHEP DO 1. Sai so he thong Gia sir mdt vat cd do dai thuc la / = 32,7 mm. Diing mdt thudc cd do chia nhd nhat 1 milimet dd do /, ta chi cd the xac djnh dugc / cd gia tri nam trong khoang giira 32 mm va 33 mm, cdn phan le khdng thd dgc dugc trdn thudc do. Su sai lech nay, do chfnh dac didm cau tao ciia dung cu do gay ra, ggi la sai sddung cir.H] Sai sd dung cu la khdng thd' tranh khdi, tham chi nd cdn tang ldn khi diem 0 ban dau bi lech di, ma ta so suat trudc khi do khdng hidu chinh lai (Hinh 7.2). Ket qua la gia tri thu dugc ludn ldn hom, hoac nhd hem gia tri diing ciia dai lugng can do. Sai lech do nhirng nguydn nhan trdn gay ra ggi la .sai sdhe thdng. 2. Sai so ng^u nhien Lap lai phep do thdi gian rai tu do ciia ciing mdt vat giua hai didm A. B ta nhan dugc cac gia tri khae nhau. Su sai lech nay khdng cd nguydn nhan rd rang, cd thd do ban che vd kha nang giac quan ciia con ngudi dan dd'n thao tac do khdng chuan, hoac do dieu kidn lam thf nghidm khdng dn dinh, chiu tac ddng ciia cac yd'u td ngau nhidn bdn ngoai... Sai sd gay ra trong trudng hgp nay ggi la .ud .sdngdu nhien. 3. Gia tri trung binh '^''" > Sai sd ngau nhidn lam cho ke't qua phep do trd ndn kem tin cay. " ^"' "'' ('^ '''f-''' TA-' I u - i_ V. , , • , . t ,..-,. - T^u• , ,.~ do lech dtem 0 han De khae phuc nguai ta ap ai phep do nhieu lan. Khi do A? lan ,. ;., .. . cung mdt dai lugng A , ta nhan dugc cac gia tri khae nhau : ^/^j , j^^j „.,j, ;,^j„j, A^, A2, •••A^. each hieu ehinh Gia tri trung binh dugc tfnh theo cdng thiic : T _ A + ^2 + - Al chinh .xdc diem 0 han ddu ciia ditng eu do trudc khi lien n \) hdnh do. — Sai sol : trong la gia tri gdn diing nhdt vdi gia tri thuc ciia dai lugng A . ^'" '^'^' '^" '^ '^'^ mac phdi sai sot. Do loi sai sot. kei qud nhqn dut/c khdc .xa gid tri thuc. Trong 4. Cach xac djnh sai so ciia phep do truang hop nghi ngd , _, . .»,-.,• - .- • ~ . , . , , , ^ . . . , CO .sai sot, cdn phdi a) Tn tuyet doi cua hieu so giua gia tri trung binh va gia trt cua ^^ ,^- ,,^ j^^- ^^. ^.^ mdi ldn do ggi la .sai sd tuyet ddi iimg vdi lan do dd. tri sai sot. ^A^ =\A-A^\;AA2 =\A-A2\; M 3 =|A-A3|.. . (7.2) So; sd tuyet ddi Uung hinh ciia n lan do dugc tfnh theo cdng thuc : —- AA, + AA-, + ... + AA, AA = — i 2 ':^2rL (73 ) n Gia trj AA xac dinh theo (7.3) la sai sd ngdu nhien. Nhu vay, de xac dinh sai sd ngau nhidn ta phai do nhieu lan. Trong trudng hgp khdng cho phep thuc hidn phep do nhieu lan (/; < 5), ngudi ta khdng tfnh sai sd ngau nhidn bang each lay trung binh (7.3), ma chgn gia tri ldn nhat (AA)^.^^ trong sd cac sai sd tuydt dd'i thu duge tir (7.2). Chii y rang, trong (7.2) cac kf hidu AA,. AA-,,... dugc dimg de! chi cac sai sd tuydt dd'i ; chung la nhumg dai lugng khdng am. Can phan bidt cac dai lugng dd vdi cac gia so thudng diing trong dai sd : AA, = A-A - Gia sd AAj cd the duomg hoac am. b) Sai sd tuydt ddi ciia phep do la tdng sai so ngau nhidn va sai .sd dung cu : AA = AA + AA' (7.4 ) 41 trong dd sai sd dung cu AA' thdng thudng cd thd lay bang nua hoqc mqt do chia nho nhdi trdn dung cu. Trong mdt s'd dung cu do cd ca'u tao phii:c tap, vf du ddng hd do didn da nang hidn sd, sai sd dung cu dugc tfnh theo mdt cdng thiirc do nha san xua't quy dinh. 5 et qua do Kdt qua do dai lugng A khdng cho dudi dang mdt con sd, ma cho dudi dang mdt khodng gid tri. trong dd chdc chdn cd chu'a gia tri thuc ciia dai lugng A : (^-AA) < A < ( A-I-AA) Ngudi ta didn ta kei qua trdn bang each viet : A = A±AA (7.5) Chu y : Sai so tuydt ddi ciia phep do AA thu dugc tir phep tfnh sai sd thudmg chi dugc viet dd'n nwt hoiic tdi da Id hai chit sd cd nghia. edn gia tri trung binh A dugc vidi ddn bae thap phan tuang ung. Cac chii sd cd nghia la tat ca cac chii' sd cd trong con sd. tfnh tir trai sang phai, kd tir chir sd khae 0 ddu tidn. Vi du : phep do do dai quang dudng di dugc .v cho gia tri trung binh J - 1.36832 m, vdi sai sd phep do tfnh dugc la As - 0,0031 m, thi kdt qua do dugc vidi, vdi As lay mdt chu sd cd nghla, nhu sau : .v = ( 1,368 ± 0,003) m 6. Sai so ti doi Sai sd tl dd'i 5A ciia phep do la ti sd giira sai so tuydt dd'i va gia tri trung binh ciia dai lugng can do. tfnh bdng phdn tram : AA 5A = ^-\m% (7 6) A Sai sd ti ddi cang nhd thi phep do cang chfnh xac. 7. Cach xac dinh sai so cua phep do gian tiep Dd xac dinh sai sd ciia phep do gian tid'p. ta cd thd' van dung quy tac sau day : a) Sai sd tuydt ddi ciia mdt tdng hay hieu thi bdng tdng cac sai sd tuyet ddi ciia cac sd hang. 42 b) Sai so tl ddi ciia mdt tfch hay thuomg thi bdng tdng cac sai sd ti ddi ciia cac thira so. Vi du : Gia sir F la dai lugng do gian tid'p. cdn X, Y, Z la nhumg dai lugng do true tid'p. -Ndu f" = X-l-K-Z thi AF = AX+Ar-HAZ - Ndu T = X^ thi SF = 5X-\- dY+ SZ Nd'u trong cdng thufc vat If xac dinh dai lugng do gian tid'p cd chii:a cac hdng sd {vi du : n. e....) thi hdng sd phai dugc lay gan dung dd'n sd le thap phan sao cho sai sd ti ddi do phep lay gdn dung gay ra cd thd bd qua, nghia la nd phai nhd hom — tdng cac sai sd ti ddi cd miit trong ciing cdng thirc tfnh. Vi du : Xdc dinh dien tfch mdt mat trdn thdng qua phep do JT/j~ true tie'p dudng kfnh J ciia nd: 5 = • Biet ^ = 50,6 ± 0,1 mm. • , 4 Sai sd tl ddi cua phep do dai lugng 5 tfnh bdng : AS 2Ad An ^ ,^, An ^ = -^^ + = 0.4% + S d n n Trong trudng hgp nay. phai lay n = 3,142 dd cho < 0,04%. n Ndu cdng thii'c xac dinh dai lugng do gidn tie'p tuomg ddi phu'c tap vd cac dung cu do true tidp cd do chfnh xac tuomg ddi cao. sai sd phep do chii yd'u gay bdi cdc yd'u td ngdu nhien, thi ngudi ta thudng bd qua sai .so dung cu. Dai lugng do gidn tid'p dugc tfnh cho mdi lan do, sau dd lay trung binh va tfnh sai sd ngdu nhidn trung binh nhu trong cdc cdng thii:c (7.1), (7.2) va (7.3). Phep do mdt dai lirong vat li la phep so sanh nb voi dai luong cung loai duoc quy udc lam don vi. P^ ep so sanh true tiep nhd dung cu do goi la phep do true tiep. Pnep xac dinh mdt dai luong vat li thdng qua mdt cdng thirc lien he vdi cac dai lirong do true tiep, goi la phep do gian tiep. A + 4, + ... + 4 Gia tri trung binh khi do nhieu lan mdt dai lirong A : A = —— " , la gia tri gan dung nhat voi gia tri thuc cua dai lirong A. Sai sd tuyet ddi ung vdi mdi lan do : A/», ^\A - 4,1 ; AA^ = \A - A^l : AA^ = \A - A^\... 43 Sai sd ngau nhien la sai sd tuyet ddi trung binh ciia n lan do .\A = AA, A/1-, +...+AA 2 n Sai sd dung cu AA' cd the; laiy bang nira hoac mot dd chia nhd nhait tren dung cu. K^t qua do dai lirong A duoc vi§t dudi dang : A = A ± AA , trong do AA la tdng ciia sai sd ng^u nhien va sai sd dung cu : "^A =K> - \A, diroc lay tdi da den hai chCrsd CO nghia. con A diroc viet dein bae thap phan tuong img. Sai sd ti ddi 5 4 cua phep do la ti sd giQa sai sd tuyet ddi va gia tri trung binh ciia AA dai luong do, tinh bang phSn tram : 6A = _ .l007o. A Sai sd cua phep do gian tiep, duoc xac dinh theo cac quy tac : Sai sd tuyet ddi cua mdt tdng hay hieu thi bSng tdng cac sai sd tuyet ddi oia cac sd hang; ?3S? Sai sd ti ddi cua mdt tich hay thuong thi bang tdng cac sai sd ti ddi ciia cac thua so. BAI TAP Dung mpt dong ho do thdi gian co dp chia nhd nha't 0,001 s de do n lan thdi gian roi tu do cua mpt vat bat dau tU diem A (i/^ = 0) de'n diem 6, ke't qua cho trong Bang 7.1. 1. Hay tinh thdi gian rai trung binh, sai sd ngiu nhien, sai sd dung cu va sai so phep do thdi Dua vao cac ke't qua do d tren va cac quy tac tinh sai sd dai lugng do gian tie'p, hay tinh V, g,Av,Ag, 8v, 8g va viet cac ket qucuoi cung. Bang 7.1 T gian. Phep do nay la true tie'p hay gian tie'p ? Ne'u chf do 3 lan {n = 3) thi ke't qua do bing bao nhieu ? 2. Dung mpt thudc milimet do 5 lan khoang each s giua hai diem A, B deu eho mpt gia tri nhu nhau bang 798 mm. Tinh sai sd phep do nay va vie't ke't qua do. 3. Cho edng thUe tinh van td'c tai 6 : 2s ..... . ^ 2s V = — va gia toe roi tu do : g = -2" • 44 3 ! 4 I 5 ' 6 Trung binh t 0,398 0,399 0,408 0,410 0,406 0,405 0,402 '"J'At, Af - • tJ THl/C HANH : KHAO SAT O CHUYEN DONG ROI TIJ DO XAC DINH GIA T6C ROI TU DO I - MUC DICH Do dugc thdi gian rai t cixa mdt vat trdn nhirng quang dudng di dugc s khae nhau, ve va khao sat dd thi s ~ t^, de rut ra kd't luan vd tinh cha't cua chuyen ddng roi tu do va xac djnh dugc gia td'c rai tu do. II - CO SO Ll THUYET Tha mdt vat (tru bdng sdt, hdn bi...) tir do cao 5 tren mat dat, vat se rai rdt nhanh theo phuang thang diimg (phuang cua day dgi). Trong trudng hgp nay anh hudng cua khdng khf khdng dang ke, vat chi chuyen ddng dudi tac dung cua trgng luc, nen cd th^ coi la vat rai tu do. Khi mdt vat cd van tdc ban ddu bdng khdng, chuyen dqng thdng nhanh ddn deu vdi gia td'c a, thi quang dudng di dugc s sau khoang thdi gian t (tinh tit luc vat bdt ddu chuyen ddng) dugc xac dinh bdi cdng thdc : 1 2 s = --at 2 Dd thi bieu didn quan he giira s va r^ cd dang mdt dudng thing di qua gd'c toa dd va cd he so gdc : a tana = — 2 45 Bo thi nghiem do gia toe rai tu do. #^ # • ..)•- «: Dong ho do thai gian hien so. Cong quang dien 46 .M . UiMo CU CAN THIET Gia dd thdng dimg cd day dgi va ba chan cd vft didu chinh thang bdng. ^. Tru bdng sdt lam vat rai tu do. Nam cham didn N cd hop cdng tdc ddng ngdt didn de giii' va thd rai vat (Hinh 8.1). H Cdng quang didn £ (Hinh 8.1). S Ddng hd do thdi gian hidn sd, do chia nhd nhat 0,001 s (Hinh 8.2). Thudc thdng 800 mm gdn chat vdo gid dd. Mdt chiec ke vudng ba chidu dung xdc dinh vi tri dau cua vat rai. Hop dung cat khd (cd phii mid'ng vai trdn mat) dd dd vat rai. \\. MJNG CU DO Ddng hd do thdi gian hien sd (Hinh 8.2) la loai dung cu do thdi gian chfnh xac cao (do chia nho nha't 0,001 - 0,01 s). Nd cd thd boat ddng nhu mpt ddng hd bam giay, dugc didu khien bang cdng tde hoac cdng quang didn. Cdng quang didn (Hinh 8.3) gdm mdt didt D, phat ra tia hdng ngoai, va mdt didt D-, nhan tia hdng ngoai tir D, chidu sang. Ddng didn cung cap cho D ^ dugc lay tir ddng hd do thdi gian. Khi cd vat chdn chiim tia hdng ngoai chie'u tir D, sang D^, thi D-, se phdt ra tin hieu tmydn theo day ddn di vao ddng hd do thdi gian, didu khien nd boat ddng. Trdn mat ddng hd do thdi gian co hai d cdm 5 chan A va B. mdt cdng tdc nhdn RESET, mdt niim gat diing chgn thang do 9,999 .v va 99,99 s, mdt niim chuyen mach chgn kidu lam vide MODE. 6 A cd 5 chan, dugc nd'i vdi hop cdng tdc (nhd mdt phfch cdm 5 chan), de cap didn cho nam cham didn hoat ddng. Khi khdng nha'n cdng tdc, nam cham dugc cap didn, nd hut va giir tru sdt. Diing mid'ng ke dp sdt vao tru sdt dd dgc vi trf ddu ciia nd trdn thudc. Khi nha'n cdng tdc, nam cham bj ngdt dien, vat dugc tha rai, ddng thdi bd dd'm thdi gian bdt dau dd'm. Ta cdn nhd nhanh cdng tdc trudc khi vat roi den cdng quang didn E. O B dugc ndi vdi cdng quang didn E, vira cap didn cho cdng E, vira nhan tin hidu tir E giri ve, ldm ddng hd do thdi gian ngimg dd'm. Cdng tdc nha'n RESET dd dua so chi ciia ddng hd ve gid tri 0.000. Dat niim gat chgn thang do d vi trf 9,999 s. Chuyen mach MODE diing de chgn kieu lam vide cho ddng hd do thdi gian. Trong bdi nay ta dat ddng hd d vi trf A <-^ B. Cac MODE khdc khdng dung den. MODE A (r^ B hoat ddng nhu sau : - Khi nhan cdng tdc ndi vdi d A thi ddng hd do bdt ddu boat ddng ; - Khi cd tfn hidu tir cdng E chuydn vao d B thi may do ngimg hoat ddng. Khoang thdi gian ngan each tir liic ed tfn hidu thii' nha't dd'n liic cd tfn hidu thu hai dugc hidn trdn mat hidn sd ciia ddng hd. Nam cham didn N ldp trdn dinh gid dd, dugc ndi qua cdng tdc vao d A ciia ddng hd do thdi gian. O A vira cap didn cho nam cham, vira nhan tin hidu tir cdng tdc chuyen vd. Cdng E lap d dudi, dugc nd'i vdi d B. Didu chinh vi trf thdng diing cho gid dd bdng each quan sat qua dgi phd'i hgp van cdc vft d dd' ba chan, sao cho qua dgi ndm dd'i tam vdi Id trdn T. Hop dd vat rai dugc dat ndm d phfa chan gid dd. Bat cdng tdc cap didn cho ddng hd do thdi gian. Cho nam cham hut giir vat rai. Dimg chide ke vudng ba chidu dp sat ddy vat rai de xac dinh vi trf ddu SQ ciia vat. Ghi gid tri SQ vao Bang 8.1. Cd the didu chinh djch chuydn nam cham didn sao cho vj trf .V,, triing vdi vach 0 trdn thudc do. 47 VI - TIEN HANH THJ NGHIEM Do thoi gian roi ung vol cac khoang each s khae nhau 1 -Ndi long vft va djch cong quang didn E vd phfa dudi each s^ mdt khoang 5 = 0,050 m. An nut RESET trdn mat ddng hd dd dua chi thi sd ve gia trj 0. 000. An niit tren hop cdng tdc de tha vat rai, rdi nhd nhanh nut trudc khi vdt rai den cdng quang dien E. Ghi thdi gian rod cua vat vao Bang 8.1. Lap lai phep do trdn them 4 ldn, ghi vao Bang 8.1. Thdi gian mdt vat rai tu do khdng van td'c ddu tren quang dudng 0,050 m vao khoang 0,1 s. Nhu vay, de c6ng quang dien E cd thi tac ddng khi vat roi dd'n E, thdi gian nham va nha cdng tdc kep phai nhd han 0,1 s. De thuc hidn dugc ddng tac nay, hgc sinh cd the ba'm thit cdng tdc kep nhu sau : Xoay chuyen manh MODE cua ddng hd do thdi gian vi vj tri A. Nha'n va nha nhanh cdng tdc kep, quan sat thdi gian chi thj trdn ddng hd. 2.Ndi long vft va djch cong quang dien E \i phia dudi, each vj trf SQ mdt khoang s = 0,200 ; 0,450 ; 0,800 m. Lftig vdi mdi khoang each 5, tha vat roi va ghi thdi gian tuang umg vao Bang 8.1. Lap lai phep do nay thdm 4 ldn. S.Kei thiic thi nghiem : Nhdn khoa K, tdt dien ddng hd do thdi gian hidn sd. 48 Hp va ten : ; Ldp : Ten bai thuc hanh : Ngay: 1 Tra loi /A, I hr- Su rcri tu do la gi ? Neu dac diem cua chuye'n dpng rai tu do va vie't cong thirc tinh gia tdc roi tu do ? 2. Ket qua Bang 8.1. Khao sat chuyen dong toi tit do: Do thai gian rai itng vai cac khoang each s khae nhau. Vj tri dau cua vat roi: Sg = (mm) I '^ Lan do Thdi gian roi t (s) - 2s. 2s. s(m) 0,050 0,200 0,450 0,800 1 ' ' Theo Bang 8.1: Khao sat chuyen dong rai tu do Tinh t , t umg vdi mdi cap gia In (s, 0 va ghi vao Bang 8.1. Ve do thi: Dua vao ke't qua trong Bang 8.1, chpn ti ie thich hgp tren cac true tung va true hoanh de ve do thi s = s{t'^). 4A-VAT Ll 10 49 aj Nhan xet: 06 thi s = s{t^) co dang mdt dudng Nhu vay chuye'n dpng ciia vat rai tu do la chuye'n dpng b) Khi da xac dinh duac chuyen ddng roi tu do la mot chuye'n ddng nhanh dan ,' ' 2.V . . deu, ta CO the xae dinh cac gia tri cua g theo cdng thirc i,' = -ip va van tdc 2v ' .'" cua vat rai tai cdng E theo edng thire : y = ^ Ung vdi mdi lan do. Hay tfnh cac gia tri tren va ghi vao Bang 8.1. ' cj Ve do thi V = v{t) dua tren cac sd lieu ciia Bang 8.1, de mpt lan nua nghiem lai tinh chat ciia chuyen dpng rai tu do. Do thi V - 1/(0 CO dang mpt dudng tire la van td'c roi tir do theo thoi gian. Vay chuyen dpng ciia vat rai tu do la chuyen dpng djTinh g= -••• 4 v a Ag^ = 1^ - .?i| ; Agj = 1^ - .?2| :••• ej Viet ke't qua ciia phep do gia tdc rai tu do : g= g±{Ag)^.,^= ± (m/s2) CAU HOI 1. Khi tinh g theo each neu tren, ta da quan tam 2. Em co the de xuat mpt phuang an thf nghiem chu ye'u den loai sai sd nao va bo qua khong khae, van diing cac dung cu neu tren, de do g tinh den loai sai sd nao ? Vi sao ? dat ke't qua chinh xac hon. 50 4B-VAT Li 10 6 N G KET CHUONG I DONG HOC CHAT DIEM / I - CAC KHAI NIEM CO BAN 1. Chuyen dpng. Chat dieJm. Quy dao 2. He quy chieu he toa do : vat lam mdc, he true toa do. ddng hd, mdc thdi gian. 3. Toe dp trung binh: („, 4. Van toe tuc thoi: ; A.S 15 la quang dudng di dugc. t la thdi gian chuydn ddng. 7 ; A.V vd Ar rat ngdn. r. ^. -• - Av 5. Gia toe : Tau keo H;r/i J.-t N 2 y' Liia Hinh 9.5 canh, cdn OD la dudng cheo (Hinh 9.6). Hinh 9.6 c) Thay ddi do ldn va hudng ciia cdc luc F, va F^, g g jU thf nghiem tren ta rut ra thi khi vdng nhdn dumg ydn ta vdn cd nhan xet nhu dugc ke't luan gi ve tinh chat the. Si ^^ 3 '"^^^ •^ 55 F2 Hinh 9.7 Tong hop hai Idc dong quy. 2. Dinh nghla Tong hop luc Id thay the cdc luc tac dung ddng then vao cung mcU vat hdng mot luc cd tac dung i'lom; het nhu cac luc ay. Luc thay thd' nay ggi la hop luc. 3. Quy tac hmh binh hanh _ _ . Sell hai luc ddng qu\ lam thanh hai canh cua mdt K : Trong trudng hop cd nhieu . i i i i , .i ' J . , i . i- A .,_- - .i tmh hmh hanh. till duirni! cheo ke tu ciiem dong lue dong quy thi van dung quy , , ciT,r.h a i\ ti c nay nhuthe nao ? '""' ''"'" ''"'" '"'" ''"' ''"" '''"'"' ("•" " ^•^^• Vd mat toan hgc, ta vie't : F - F\ -\- F2. 11: . oiFi I i^fPN CAN BANG CUA CHAT DIEM Vdi khdi nidm hgp luc, ta cd th^ phat bidu didu kidn can bdng cua chat diem nhu sau : Muon cho mcjt chdt diem dung can bang thi hop life cua cac luc tde dung len nd phdi bdng khdng. F = F, + F2 + ... = 0 IV - PHAN TICH LUC f^ 1. Ta cd thd giai thfch sir can^bdng cua vdng nhdn Fi N O theo mdt cdch khdc. Luc F3 trong thf nghiem d Hinh 9.5 cd hai tac dung. Mdt mat nd keo day 1 Fo O _ theo hudmg MO, mat khae nd keo da^ 2 theo hudng ^2 NO. Do dd, ta cd thd' thay thd' luc F3 bdng hai lUc F,' va F2' theo hai phuang MO va NO. Hai luc nay Hinh 9.8 F\ can bdng vdi hai luc F^ va F2 (Hinh 9.8). 2. Djnh nghla Than tich luc la tliay the mot luc hdng hai hay nhii'u luc CO tdc dung giong hei nhu lue du. Cdc luc thay the nay ggi la cac luc thdnh phdn. 56 M N 3. Mud'n phan tfch luc F, thdnh hai luc thanh phdn ^ F|' va F2' theo hai phuang MO vd NO, ta lam nhu ^ sau : Tir ddu miit C cua vecta F3 ta ke hai dudng ^^2 F\ thdng song song vdi hai phuomg dd, chiing cdt G p nhiimg phuomg nay tai cac didm E va G. Cac vecta I ^ OE va OG bidu didn cdc luc thdnh phan F,' va F,' C H/nAj 9.9 (Hinh 9.9). 4 C>^" " Phan tfch luc Id phep lam ngugc lai vdi tdng hgp luc, do dd nd ciing tuan theo quy tdc hinh binh hanh. Tuy nhidn, chi khi biei mat luc co tdc dung cu the theo hai phuang ndo thi mdi phdn tich luc do theo hai phuang dy. Luc la dai luong vecto dac trung cho tac dung ciia vat nay vao vat khae ma ket qua la gay ra gia tdc cho vat hoac lam cho vat bien dang. Duong thdng mang vecto lire goi la gia cua luc. Oon vi cua luc la niuton (N). Tong hop luc ia thay the cac lut tac dung ddng thdi vao cimg mdt vat bang mo irc co tac dung gidng het nhu cac luc ay. Luc thay the nay goi la hop luc. Quy tdc hinh binh hanh : Neu hai lire ddng quy lam thanh hai canh cua mdt hinh binh hanh, thi dudng cheo ke tudiem ddng quy bieu dien hop lire cua chung. Dieu kien can bang ciia mdt chat diem la hop luc cua cac luc tac dung len no phai bang khdng: F = F^ + F2 + • •• = 0. Phan tich luc la thay the mdt lire bang hai hay nhieu luc ed tac dung gidng het nhu luc do. Phan tich mdt luc thanh hai lut thanh phan dong quy phai tuan theo quy tac hinh binh hanh. Chi khi biet mot lut cd tac dung cu the theo hai phuong nao thi mdi phan tich lut theo hai phuong ay. 57 CAU HOI VA BAi TAP Phan tfeh luc F thanh hai luc F, va F.^ theo 1. Phat bie'u dinh nghla cua luc va dieu kien can bdng eiia mot chat diem. hai phuang OA va OB (Hinh 9.10). Gia tri nao sau day la dp Idn eiia hai lue thanh phan ? / 2. Tdng hgp luc la gi ? Phat bieu quy tac hinh binh hanh. 3. Hgp luc F CLia hai luc ddng quy F, va F, ^.F, B . F •F; 1 30° CO do Idn phu thuoc vao nhUng yeu td nao ? 4. Phan tfch lire la gi ? Neu each phan tfeh mot luc thanh hai luc thanh phan ddng quy theo ^-•2- 2^ ' C.F^ =F2 = 1,15F D. F^ = F2 = 0,58F :CCA. 30° O fi Hinh 9.10 hai phuang eho trudc. Mdt vat CO trong lugng P = 20 N dugc treo vao mot vdng nhan 0 (coi la chat die'm). Vdng nhdn dugc giu yen bang hai 5. Cho hai luc ddng quy eo dp Idn bang 9 N va 12 N. a) Trong sd cac gia trj sau day, gia trj nao la do Idn eua hgp lue ? A. 1 N ; B. 2 N ; C. 15N; D. 25N. day OA va 06 (Hinh 9.11). Bie't day OA nam ngang va hgp vdi day 06 mot gde 120°. Tim luc cang cua hai ® \ 120° _._ 0^ L JP A b) Goe giua hai luc ddng quy bang bao nhieu ? day OA va 06. Hinh 9.11 6. Cho hai luc ddng quy co cung do Idn 10 N. a) Goc giua hai luc bang bao nhieu thi hgp luc cung cddp Idn bang 10 N ? A. 90°; B. 120°; C. 60°; D. 0°. b) Ve hinh minh hoa. 58 9. Em hay dirng vao giua hai chie'c ban dat gan nhau, mdi tay dat len mot ban rdi diing sire ehdng tay de nang ngudi len khdi mat da't. Em lam lai nhu the vai lan, moi lan day hai ban ra xa nhau mot chiit. Hay bao cao kinh nghiem ma em thu duac. w B A DINH LUAT NIU-TON I - DINH LUAT I NIU-TON Luc cd cdn thie't dd duy tri chuydn ddng ciia mdt vat hay khdng ? Dc tra ldi cau hdi nay, ta hay thir ddy mdt quydn sdch trdn ban. Ta phai ddy thi nd mdi chuydn ddng va khi ngimg ddy thi nd dtmg lai. Hidn nay ai ciing bid't cd luc ma sat can trd chuydn ddng cua vat. Nhung nd'u dat minh vdo thdi dai md mgi ngudi cdn chua biet de'n m.a sdt, thi ta se tin ngay rdng luc la can thiet dd duy tri chuydn ddng ciia vat. Ngudi ddu tidn khdng tin nhu vay, dd la nhd vat If Ga-li-le. 1. Thi nghiem Ijch sir cua Ga-li-le Ga-li-ld la ngudi ddu tidn da lam thf nghidm de' nghien cdu chuydn ddng. Ong diing hai mdng nghidng gidng nhu mdng nudc, bd trf nhu Hinh 10.1 rdi tha mdt hdn bi cho lan xud'ng theo mdng nghieng 1. Ong nhan thay hdn bi lan ngugc ldn mang 2 dd'n mdt do cao gan bdng do cao ban ddu (Hinh 10.1a). Khi ha thap do nghidng ciia mang 2. dng tha'y hdn bi lan trdn mang 2 dugc mdt doan dudng dai horn (Hinh 10.1b). Ong cho rdng, hdn bi khdng lan dugc dd'n do cao ban ddu la vi cd ma sdt. Ong tien dodn rdng, idu khong cd ma sdt vd neu mdng 2 ndm ngang thi hdn hi sc^ ldn voi vein tdc khdng ddi mdi mdi (Hinh 10.1c). Nhu vay, bdng thuc nghiem Ga-li-le da phdt hidn ra mdt loai luc "giau miit" la lue ma sat va tin rdng nd'u khdng cd ma sat thi khdng can den luc dd duy tri chuydn ddng ciia mdt vat. a) b) c) Hinh 10.1 Thi nghiem cua Ga-li-le de nghien ciru chuyen dong. 59 H I Tai sao xe dap chay duge them mdt quang dudng nOra mac du ta da ngimg dap ? Tai sao khi nhay tU bae cao xudng, ta phai gap chan lai ? 60 2. Dinh luat I Niu-ton Vd sau, Niu-tan da khai qudt cdc kd't qua quan sat vd thf nghidm thdnh dinh luat sau day, ggi la dinh ludt I Niu-tan : .Sen mot vat khong chiu luc dung cua luc nao hodc chiu tac dung cua cac luc co hirp luc hang khong. thi vat dang dung yen se tiep tuc dung yen. dang chuyen dong sc dep luc chuyen dong ihdng deu. 3. Quan tinh Dinh luat I cho phep ta phdt hidn ra rdng, mgi vat ddu cd mdt tfnh chat md nhd nd vat tid'p tuc chuydn ddng dugc, ngay ca khi cdc luc tdc dung vao vat mat di. Tfnh chat ay ggi la qudn tinh. ,_^<.iw< ,,,•,, IL. ..y./. c7;a/ cua inqi vat co xu hutrng hao toan van toe ca ve hudng va do hm. Djnh luat I dugc ggi la duih ludt qudn tinh va chuyen dqng thdng deu dugc ggi la chuyen dqng theo qudn tinh. ^Si II - DINH LUAT II NIU-TON Ta hay hinh dung phai ddy mdt chid'c xe d td bi hdng mdy trdn dudng bang phdng. Nd'u it ngudi ddy thi chi gay ra cho xe mdt gia tde nhd dd'n ndi phai mat mdt thdi gian dai thi ta mdi nhan thay su tang td'c do ciia nd. Nhung nd'u nhieu ngudi ddy thi hgp luc tac dung vao xe se ldn hom nhieu va xe se chuyen ddng nhanh dd'n mii:c ta phai chay theo xe. Dd la vi luc ldn hon gay ra cho xe mdt gia td'c ldn hom. Kinh nghidm cdn cho thay rdng, khdi lugng ciia vat ciing anh hudng dd'n gia td'c ciia nd. Ciing chju mdt luc, vat ndo cd khdi lugng nhd hom se thu dugc gia td'c ldn hom va se chuydn ddng nhanh hom. Tuy nhidn mdi lien he djnh lugng giua gia td'c, luc va khd'i lugng nhu the ndo thi ta cdn chua bie't. 1. Dinh luat II Niu-ton Tir nhiimg quan sat va thf nghidm (bao gdm ca nhiimg quan sdt thidn van), Niu-tan da xdc dinh dugc md'i lidn he giira gia td'c, luc va khd'i lugng ciia vat (coi la chat diem) va ndu ldn thdnh dinh luat sau day, ggi la dinh ludt II Niu-tan : Gia toe cua mot vat cung hudng ven luc Uu Bang I'I. Do Idn cua mpt so lire dung len vat. Do lon cua gia toe it le thuan ven do Urn ciia luc va d le nghich voi kiwi lucmg cua vcU. ^rpng luong cua qua can 1 kg : 9,8 N Luc keo cua mpt ngudi F dan onq cd gang vCra phai: 200 N d = — (10.1) y y y m Luc keo cua con ngua : - cd gang vira phai: 700 N Suy xa: F = md -co gang het sire: 4 000 N Trong trudng hgp vat chju nhieu luc tac dung Li/c keo cua mpt 6 td F,, F2, F3, ... thi F la hgp luc cua cdc lire dd : ' <^^n dudng phing : 1 000 N F = F -\- R + FT -\- ... Li/c hut cua mpt nam cham dien ldn : 30 000 N 2. Khoi luon g va muc qua n tm h Luc keo ciia mpt ,„•,, - dau may xe lira: 200 000 N a) Dmh nghia Liic dau khd'i lugng chi dugc hidu la mdt dai lugng diing de chi luang chat chura trong vat. Nhung djnh luat II Niu-tan' cdn cho ta mdt each hidu mdi'vd ® ^ho hai vat chju tac dyng 1 u— 1 __ rs i cua nhiJmg luc co do Idn bang khoi luang.Lay , u - ^ . '.»• u 1 -* M • " nhau. Hay van dung dmh luat II That vay, theo djnh luat I I Niu-tan, khd'i lugng Niu-ton de suy ra rang, vat nao cdn duac diing de chi mdc qudn tinh cua vat. Cdch ^6 khd'Mugng Idn hon thi khd lam ..x- '^ - u u ' t ' u^u••^J,^ ' thay doi Van toc cua nd hon. tdc hieu moi nay cho phep ta so sanh khoi luomg cua ,, . . • ... . ,x, ... . ' ,\ ,v , r f- V , - ,• ,, la CO muc quan tmh lon hon. eae vat bat ki, du lam bang cung mgt chat hay lam bdng cdc cha't khdc nhau. Cd vat nao cd miirc qudn tinh ldn hom thi cd khd'i lugng ldn hom va nguge lai. Tir dd ta cd djnh nghia : j\hoi luong ta dui luirng ddc Irung cho mile • ^ai sao may bay phai chay ,' , , m mdt quang dudng dai tren dudng bang mdi cat canh dugc ? c/ncin tmh run itit l*S , • ,.„.,, ..^ , „ ^ b) Tinh chdt cua khdi luqng - Khd'i lugng la mdt dai lugng vd hudng, duomg va khdng ddi dd'i vdi mdi vat. - Khd'i lugng cd tinh chat cdng : Khi nhidu vat dugc ghep lai thanh mdt he vat thi khdi lugng ciia he bdng tdng khd'i lugng ciia cac vat dd. 61 H 3 Hay giai thfch tai sao 6 ciing mot noi ta luon co -!- = —*-. P. m.. ^ B' Hmh 10.2 Hmh 10.3 3. Trong luc. Trong luong a) Trgng luc la luc ciia Trdi Dat tac dung vao cac vat, gay ra cho chiing gia td'c rai tu do. Trgng luc dugc kf hidu la P. O gdn Trai Dat, trgng luc cd phuomg thdng dumg, cd chidu tir trdn xudng va dat vao mdt diem dac bidt ciia mdi vat, ggi la trqng tdm ciia vat. b) Do ldn ciia trgng luc tac dung ldn mdt vat ggi la trqng luqng ciia vat, kf hidu la P. c) Cdng thifc cua trqng life Ap dung dinh luat II Niu-tom vao trudng hgp mdt vat rai tu do, ta tim dugc cdng thuc ciia trgng luc : P = mg (10.2) B3 III - DINH LUAT III NIU-TON 1. Su tirong tac giua cac vat Ta hay xet mdt vai vf du : a) Bdn mdt hdn bi A vao mdt hdn bi B dang dumg ydn, ta thay bi B lan di, ddng thdi ehuydn ddng cua bi A cung bi thay ddi (Hinh 10.2). h) Hinh 10.3 chup mdt cdi vgt dang dap vao mdt qua bdng tennit. Ta thay ca qua bdng va mat vgt ddu bi bid'n dang. cj Hai ngudi trugt bang dang dung sat nhau (Hinh 10.4). Mdt ngudi diing tay day ngudi kia cho chuyen ddng ve phfa trudc thi thay chfnh minh cung bi ddy vd phfa sau. 2. Djnh luat Tir nhiimg quan sat va thf nghidm ve su tuomg tac giira cae vat (bao gdm ca cac quan .sat thidn van), Niu-tom da phat hidn ra djnh luat, ggi la dinh lucit UI Niu-tan : Trong men truong hop, khi vqt A tdc dung len vqt B mot luc, thi vat H cung tdc dung tai vdt ,1 mot luc. Hai luc ndy cd cung gid, cung do hm, nhung nguac chieu. ^B^A - ^A^B hay ^BA = -^AB (10.3) 3. Lut va phan lire Mdt trong hai luc tuomg tdc giira hai vat ggi la life tdc dung cdn luc kia ggi la phdn luc. a) Luc vd phdn life cd nhifng ddc diem gi ? - Luc va phan luc ludn ludn xuat hien (hoac mat di) ddng thdi. - Luc va phan luc cd ciing gia, ciing do ldm, nhung ngugc chidu. Hai luc cd dac diem nhu vay ggi la hai luc true ddi. - Luc va phdn luc khdng can bdng nhau vi chiing dat vdo hai vat khdc nhau. b) Vi du Khi ta mudn budc chan phdi vd phfa trudc thi chan trai phai dap vdo mat da't mdt luc F' hudng vd phfa sau. Ngugc^lai, dat cung day lai chan ta mdt phan lire F = -F' hudmg vd phfa trudc (Hinh 10.6). Vi Trdi Dat cd khdi lugng rat ldn ndn luc ciia ta khdng gay ra cho Trdi Dat mdt gia td'c nao dang kd. Cdn ta cd khdi lugng nhd hem khd'i lugng Trdi Da't rat nhieu, ndn phan luc ciia mat dat gay ra cho ta mdt gia td'c, lam ta chuydn ddng ve phfa trudc. () Ghi chu : Khi xet tuomg tdc giira hai vat thi hai vat dd tao thdnh mdt he. Luc tuomg tdc giira hai vat dugc ggi la iwi life. Cac luc khdc tdc dung ldn hai vat ggi la cdc ngoqi life. zl Hay van dung djnh luat III Niu-ton vao vf du diing biia ddng dinh vao mgt khue gd (Hinh 10.5) de tra Idi cac eau hoi sau day : ~ Cd phai biia tac dung lUc len dinh cdn dinh khong tac dung lUc len biia ? Ndi mpt each kbac, lUc cd the xua't hien don le dugc khdng ? - Neu dinh tac dung len biia mdt luc cd do Idn bang lUe ma bua tac dung len dinh thi tai sao dinh lai khong dimg yen ? Noi mgt each khae, cap "lUc va phan lUc" CO can bang nhau khdng ? Hinh 10.5 Hinh 10.6 63 Oinh ;. :on : Neu khong ehiu tac dung cua luc nao hoac chiu tac dung ciia cac luc CO tiLip luc bang khong. thi vat dang dung yen se tiep tuc dung yen. dang chuven dong se tiep tuc chuyen ddng thang deu. Quan tinh 'a tmh chat cua moi vat eo xu huong bao toan van tdc ca ve huong va dd lon. Chuyer ang deu duoc goi la chuyen dong theo quan tmh. Omh luat ii Niu-ton : i Gia toe cua mot vat cung huong voi luc tac dung len vat. Do lon cua gia tdc ti le thuan vol dd lon cua luc va ti le nghich voi khdi luong cua vat. I f - - a = hay F - ma m iTrong truong hop vat chiu nhieu luc tac dung thi F la hop luc cua cac luc do). Khdi luong la dai luong vd huong. dac trung eho muc quan tinh cua cae vat. Trong luc la luc cua Trai Dat tac dung vao cac vat, gay ra cho chung gia toe roi tu do. Do Ion cua trong luc tac dung len mot vat goi la trong luong cua vat. Cong thuc eua trong luc : P = mg . Omh luat ill Niu-ton : Trong moi truong hop. khi vat A tac dung len vat B mot luc. thi vat B cung tac dung lai vat A mot luc. Hai luc nay co cung gia, eung dd lon, nhung nguoc chieu. •<- : ''^ Trong tuong tac giira hai vat. mdt luc goi la luc lac dung, con luc kia goi la phan luc. Cap luc va phan luc co nhung dac diem sau day : Luc va phan luc luon ludn xuat hien (hoac mait di) dong thoi. }-,-.., Luc va phan luc la (lai lire true ddi. Luc va phan luc khong can bang nhau vi chiing dat vao hai vat khae nhau. CAU HOI VA BAI TAP 4. Trpng lugng cua mpt vat la gi ? Viet cong thiic cua trpng luc tac dung len mpt vat. 1. Phat bieu dinh luat I Niu-tan. Quan tinh la gi ? 5. Phat bieu va viet he thUc ciia dinh luat III 2. Phat bie'u va viet he thirc ciia dinh luat II Niu-ton. Niu-tan. 6. Neu nhGmg dac diem cua cap luc va phan luc" 3. Neu dinh nghla va cac tinh chat ciia khdi lugng. trong tuong tac giUa hai vat. 64 7. Mpt vat dang chuyen ddng vdi van tdc 3 m/s. Neu bdng nhien cac luc tac dung len no mat di thi A. vat dUng lai ngay. B. vat ddi hudng chuyen dpng. C. vat chuyen dpng cham dan rdi mdi dUng lai. D. vat tie'p tuc chuye'n dpng theo hudng cu vdi van tdc 3 m/s. Chpn dap an dung. 8. Cdu nao dung ? A. Neu khdng chiu lire nao tac dung thi mpi vat phai dirng yen. B. Khi khdng cdn luc nao tac dung len vat nOra, thi vat dang chuyen dpng se lap tire dimg lai. C. Vat chuydn dpng dugc la nhd co luc tac diing len no. D. Khi thay van tdc cua vat thay ddi thi chac chan la da co luc tac dung len vat. 9. Mpt vat dang nam y§n tren mat ban nam ngang. Tai sao ta co the khdng dinh rang ban da tac dung mpt luc len no ? 10. Trong cac each viet he thirc cua dinh luat II Niu-ton sau day, each vie't nao dung ? A. F = ma ; B. F = - ma ; C. F = ma ; D. - F = ma . 11. Mpt vat CO khdi lugng 8,0 kg trugt xudng mpt mat phang nghidng nhin vdi gia tdc 2,0 m/s^. Luc gay ra gia tdc nay bang bao nhieu ? Em c6 Diet ? So sanh do Idn cua luc nay vdi trpng lugng cua vat. Lay 9 = lOm/s^. A. 1,6 N, nhd han. B. 16N, nhd hon. C. 160 N, Idn han. D. 4 N, Idn han. 12. Mpt qua bong, khdi lugng 0,50 kg dang nam yen tren mat dat. Mpt cau thii da bong vdi mpt luc 250 N. Thdi gian chan tac dung vao bong la 0,020 s. Qua bong bay di vdi tdc dp A. 0,01 m/s. B. 0,1 m/s. C. 2,5 m/s. D. 10 m/s. 13. Trong mpt tai nan giao thdng, mpt 6 td tai dam vao mpt 6 td con dang chay ngugc chieu. 0 td nao chiu luc ldn hon ? 0 td nao nhan dugc gia tdc Idn han ? Hay giai thi'ch. 14. De xach mpt tiii dirng thirc an, mpt ngudi tac dung vao tui mpt luc bang 40 N hudng len tren. Hay mieu ta "phan luc" (theo dinh luat III) bang each chi ra a) dp Idn cua phan luc. b) hudng cua phan lire. c) phan luc tac dung len vat nao ? d) vat nao gay ra phan luc nay ? 15. Hay chi ra cap "luc va phan luc" trong cac tinh hudng sau : a) 0 td dam vao thanh chan dudng ; b) Thil mdn bat bong ; c) Gio dap vao canh cira. CHUYEN OON G TR^ N 'DEM KHI" May the ki da troi qua ma nguai ta van khong tao ra duac mot thi nghiem nao co the kiem chung true tiep duac dinh luat I Niu-ton vi khong loai bo dugc ma sat va luc hut cua Trai Oai. Nhung nguai ta vhn tin vao dinh luat nay vi no da dua de'n nhi§u he qua co the kiem chung duac. 5A- VAT Ll 10 65 Chi den thai dai hien nay, bang kT thuat tao ra "dem khi", nguoi ta gan nhu loai bo duae luc ma sat. Vat ehuyen dong tren "dem khi" ehi chiu tac dung ciia hai luc can bang, do la trpng lue va phan luc cua "dem khi". Cac hmh duiri da\' mieu ta mot thi nghiem ve chuyen dpng cua mpt vat tren "dem khi" gom : — Mpt bang dem khi co tiet dien ngang hmh chu V ngupc, tren hai mat bang co nhieu 16 nho dupc phan bo deu doc theo bang iHinh 10.7 va 10.8). Tam can Cdng quang dien quang Vat tn/ot Cong quang dien ff\ A." ft Gia yTM ^ / t-A y^^'^^ Vat truot D6m khi ThuOc do khoang each Hinh 10.7. He thong bang dem khi Lo thoat khi Hinh 10.8. Tiei dien ngang cua bang dem khi — Mpt \ at trupt CO tiei dien ngang hinh chu V ngupc, phia tren co ranh de cam cac tam can quang co chieu dai / khae nhau (Hinh 10.91. — Hai eong quang dien. — Mpt dong hd hien so co the do dupc nhung khoang thai gian rai nho, co 1 ms den 10 ms (Hinh 10.101. Dung mpt may bom day khong khi da bi nen vao trong long mang. Luong khi phut ra tir cac lo tao ra mpt "dem khi" giua vat va mang khien vat chuyen dpng de dang. Mudn do van toe cua vat, ta cam mot tam can quang vao ranh cua \at. Khi mep truac ciia tam can quang tai cong quang dien thi dong ho bat dau tinh thai gian va khi mep sau di qua cong quang dien thi nb ngung lai. Oong ho se hien len thai gian de vat di dupc doan dudng /. Ti/ do tinh dupe van toe cua \at di qua moi eong quang dien, v = — • Thi nghiem cho thay vat chuyen dpng deu tren mang trupt. Ta'm can quang lep truoc cry Mep sau • i \ Lo thoat khi i , - * ^^^B flHMi s , C R£S£- -•Sr -. # UOOE m « ' .•^7" i 1 Hinh 10.9 Vat truqt tren bang dem khi. Hinh 10.10. Dong ho do thai gian hien so. 5B-VAT Ll 10 Lire HAP DAN DINH LUAT VAN VAT HAP DAN Luc nao giu cho Mat Trang chuyen dpng gcin nhu tron deu quanh Trai Oai ;" Luc nao giCr cho Trai Oai chuyen dpng g^n nhu tron deu quanh Mat Troi ^ (Hinh 11.1) I - mc HAP DAN Niu-ton Id ngudi ddu tidn da ket hgp dugc nhirng kdi qua quan sdt thidn van ve chuyen ddng ciia cac hanh tinh vdi nhirng kdi qua nghidn cihi vd su rai ciia cac vat tren Trdi Ddt vd do dd da phat hidn ra rdng, moi veil trong vil tru deu hut nhau vdi nwt life, gqi Id life hdp ddn. Luc ha'p ddn giiJa Trai Dat va Mat Trang giii cho Mat Trang chuydn ddng quanh Trdi Dat. Luc ha'p ddn giira Mat Trdi va cac hdnh tinh giir cho cdc hdnh tinh chuyen ddng quanh Mat Trdi. Khdc vdi luc dan hdi va luc ma sat la luc tid'p xiic, luc ha'p ddn la luc tdc dung tir xa, qua khoang khdng gian giira cac vat. II - DINH LUAT VAN VAT HAP DAN l.Oinh luat Nhung dac didm cua luc ha'p ddn da dugc Niu-tan ndu ldn thanh dinh luat sau day, ggi la dinh luat van vat hdp ddn : Luc hap ddn giita hai chat diem bed ki d le thuan vdi tich hai khdi lucmg ciia chung va die ui^hich voi hinh phucmg khortr<^' rach gitia chdng (Hinh 11.2). Mat Trai Trang Dat Mat Troi Hmh 11.1 m, Hinh 11.2. Luc hap dan giija hai chat diem niim tren dUdng thing noi hai chat diem. 67 2. He thuc 1;' " _ m,m2 Vat 1 Vat 2 Hinh 11.3. Luc hap din giita hai vat d' -q rhai. co dang hinh cau. 68 trong dd w,, m~, la khd'i lugng ciia hai chat didm, r la khoang each giiia chiing, he sd ti Id G dugc ggi la hdng sd hd'p ddn. Han mdt the ki sau, cdc phep do chinh xdc cho thdy : C = 6,67.10"''N.m"/kg-. He thii:c (11.1) dp dung dugc cho cdc vat thdng thudng trong hai trudng hgp : - Khoang cdch giira hai vat rat ldn so vdi kich thudc ciia chiing ; - Cdc vat ddng chdt va cd dang hinh cdu. Khi ay /• la khoang each giira hai tam va luc hdp ddn ndm tren dudng ndi hai tam va dat vdo hai tam dd (Hinh 11.3). Ill - TRONG LUC LA TRUONG HOP RIENG CUA LUC HAP DA N Theo Niu-tan thi trgng luc md Trdi Ddt tdc dung ldn mdt vat la luc ha'p ddn giiia Trai Dat va vat dd. Trgng luc dat vao mdt didm dac bidt ciia vat, ggi la trgng tam ciia vat. Do ldn ciia trgng luc (tuc trgng lugng)theo (11.1) bdng : mM P = G {R + h)" trong dd m la khdi lugng ciia vat. h la do cao ciia vat so vdi mat dat. M va 7? la khdi lugng va bdn kinh ciia Trdi Dat. Mat khdc, ta lai co : P = mg Suy ra : GM Nd'u vat d gdn mat da't (h « R) thi : GM S = ~^ (11.3) Cdc cdng thuc (11.2) va (11.3) cho thay, gia td'c roi tu do phu thudc vdo do cao h va cd thd coi la Bang 11.1. Gia tri cua g theo dp cao d viae 45°. nhu nhau dd'i vdi cdc vat d gdn mat dat {h « R). Cac he qua nay hoan todn phii hgp vdi thuc nghidm (Bang 11.1). /J (km) 0 1 4 8 16 g (m/s2) 1 9,806 9,803 9,794 9,782 i 9,757 Djnh luat van vat hap ddn : Luc hap ddn giiia hai chat di§m bat ki ti le thuan vdi tich hai khoi luong ciia chung va ti le nghich vdi binh phunng khoang each giua chung. m.,m^ ^hd = G G la hdng so hap din, cd gia trj b^ng 6,67.10 .„ N.m^ kg^ Trong luc ciia mdt vat la luc hap din giua Trai Dit va vat dd. Trong tam ciia vat la di^m dat ciia trpng luc ciia vdt. CAU HOI VA BAI TAP 1. Phat bieu dinh I'jat van vat hap dan va viet he thirc ciia luc ha'p ddn. 2. Neu dinh nghla trong tam cua vat. 3. Tai sao gia tdc rcri tu do va trong luong ciia vat cang len cao thi cang giam. Mpt vat khdi lugng 1 kg, d tren mat da't co trong lugng 10 N. Khi ehuyen vat tdi mot diem each tam Trai Oat 2R [R la ban kinh Trai Da't) thi nd CO trong lugng bang bao nhieu ? A. 1 N ; B. 2,5 N ; C. 5N ; D. 10N. 69 5. Hai tau thuy, mdi chie'c c6 khdi lugng 50 000 tan d each nhau 1 km. Lay g = 10 m/s^. So sanh luc ha'p ddn giua chung vdi trong lugng ciia mot qua can co khoi lugng 20 g. A. Ldn hon. B. Bdng nhau. C. Nho hon. D. Chua the bie't. Em CO biet ? Trai Dat hiit Mat Trang vdi mpt luc bang bao nhieu ? Cho bie't khoang each gida Mat Trang va Trai Da't la R = 38.10^ m, khoi lugng cua Mat Trang m = 7,37.10^2 kg, khdi lugng ciia Trai 031 ^ = 6,0.102" kg. Tinh trpng lugng ciia mpt nha du hanh vu tru cd khoi lugng 75 kg khi ngudi do d a) tren Trai Dat (lay g = 9,80 m/s^). b) tren Mat Trang (lay g^^ - 1,70 m/s^). c) tren Kim Tinh (lay g^^ - 8,7 m/s^). NIU-TON KIEM CHUNG DjNH LUAT VAN VAT HAP DAN NHU THE NAO ? Othai Niu-tan ngudi ta chua co dieu kien lam thi nghiem do luc hap dan giua hai khoi luang. Vay, CO sa nao de ong tin vao sir dung din ciia dinh luat nay ? Niu-ttm cho rang, co the kiem chung dinh luat nay bang nhieu each. Mot trong nhung each kiem chung la van dung dinh luat de tien doan mot vai dac diem nao do ve chuyen dpng cua mot hanh tinh va xem su tien doan co phii hgp vdi kei qua quan sat duac eiia hanh tinh do hay khong. Niu-tan da biei rang, Mat Trang a each xa tam Trai Oat khoang 60 lan so vai mpt vat d be mat Trai Dai. Do do, luc hut cua Trai Oai gay ra cho Mat Trang mpt gia toe nho han gia toe rcyi tu do (60)- lan, tuc la a =—'- = 2,72.10' m/s~. Mat khae, Niu-tan cune biei ring 3 600 6 5 khoang each tir Trai Dai den Mat Trang \a r = 3,8.10" m, chu ki ciia Mat Trang T = 27,3 ngay dem = 2,3.10^ s, nen gia toe huang tam ciia Mat Trang la : 4;r- 4;r^3,8.10' ' , , , ,1 = co-r = — - r = ——r- = 2,8.10 ' m/s" T- (2,3.10'')^ So sanh hai gia tri cua gia tdc, ta tha'y chung xap xi bang nhau. 70 Lire DAN H6I CUA L6 XO DINH LUAT HUG O Trung hoc ca sa ta da biei, luc ke la dung cu diing de do luc va bp phan chii yeu ciia no la mot 16 xo. Tuy nhien, ta con chua biei dupc viec che tao lire ke dua tren dinh luat vat li nao. I - HUONG VA DI^M DAT CUA LUC DAN H6| CUA Lb XO H I Diing hai tay keo dan mdt Id 1. Luc ddn hdi xudt hidn d hai ddu cua Id xo va tdc dung vdo cdc vat tid'p xiic (hay gdn) vdi Id xo, lam nd bidn dang. 2. Hudng ciia luc dan hdi d mdi ddu Id xo ngugc vdi hudng ciia ngoai luc gay bid'n dang (Hinh 12.1b). Cu the la, khi hi ddn, life ddn hoi cua Id xo hucmg theo true ciia Id .xo vdo phia trong, cdn khi hi nen, lUc ddn hoi ciia Id .xa hucmg theo true ciia Id .xo ra ngodi. II - DO LON CUA LUC DAN HOI CUA LO XO. DjNH LUAT HUC Ai cung bidt, mudn Id xo dan nhidu han thi phdi keo manh han. Dd Id vi luc dan hdi da tang theo dd chd'ng lai lire keo. Tuy nhien, do ldn ciia luc dan hdi lien quan ddn do dan cua Id xo nhu the ndo thi khdng phdi ai cung bidt. Nhd vat If ngudi Anh Rd-bdt Hue (Robert Hooke, 1635 - 1703) la ngudi ddu tien da nghidn cuu va giai quydt dugc van dd nay. xo (Hinh 12.1a). a) Hai tay cd chiu lUc tac dung cua 16 xo khdng ? Hay neu rd diem dat, phuong va chieu cua cac luc nay. b) Tai sao 16 xo chi dan de'n mgt mdc nao do thi ngimg dan ? c) Khi thdi keo, lUc nao da lam cho Id xo lay lai chieu dai ban dau ? •rr. ^mmrnmm^ a) '-^^^^ -wsmmtssm^. %>- - b) ' dh Hmh 12.1 71 [ S LUc cua 16 xo d Hinh 12.2b cd do Idn bang bao nhieu ? Tai sao ? Mudn tang lUc cua Id xo len 2 hoae 3 lan ta lam each nao ? a) b) 1. Thi nghiem Diing mdt Id xo va mdt sd qua can gid'ng nhau rdi bd tri thf nghiem nhu d Hinh 12.2. Khi chua treo qua can vdo Id xo. Id xo chua bi dan va cd do ddi tu nhidn IQ (Hinh 12.2a) Khi treo qua can (ggi la tai) cd trgng lugng P vdo Id xo. Id xo dan ra ddn mdt miirc ndo dd thi dimg lai (Hinh 12.2b). BB Theo dinh luat III Niu-tan thi luc ma qua can keo Id xo va luc ciia Id xo keo qua can ludn cd do ldn bang nhau va bdng F. Khi qua can diing ydn ta cd F = P = mg. Treo tid'p 1, 2 qua can vao Id xo (Hinh 12.2c, d). O mdi ldn. ta do chieu ddi / cua Id xo khi cd tdi va IQ khi bd tai rdi tfnh do dan Al = I - IQ. Sau dd ghi cdc kd't qua vao mdt bang. Bang 12.1. Ket qua thu duac tir mpt lan lam thi nghiem. Hmh 12.2 3,0 F = P(N) i 0,0 i 1,0 ^ 2,0 4,0 5,0 6,0 06 dai Z (mm) | 245 06 dan A/(mm) j 0 i S 3 Cac ket qua trong Bang g ] 12.1 CO ggi y eho ta mdt mdi lien he nao khong ? Ne'u eo thi hay phat bie'u mdi lien he dd. 285 ' 324 40 i 79 1 366 121 405 160 446 201 484 239 2. Gioi han dan hoi ciia 16 xo Thf nghidm cdn cho thay, nd'u trgng lugng ciia tai vugt qua mdt gia tri ndo dd, ggi la gidi hqn ddn hoi, thi do dan cua Id xo se khdng cdn ti Id vdi trgng lugng ciia tdi vd khi bd tai di thi Id xo khdng co dugc ve ddn chidu ddi /Q nira. 72 3. Djnh luat Hue Khi nghidn ciiru md'i lien he gitra do ldn ciia luc ddn hdi vdi do bien dqng (do dan hay do nen (Hinh 12.3)) ciia Id xo, Ro-bdt Hue da phdt hidn ra dinh luat sau day, ggi la dinh lucit Hiic : Trong gidi hqn ddn hdi, dei ldn cua luc ddn hoi ciia Id xo U le thudn vdi do hien dang eiia Id xo. ^dh k\Al\ (12.1) He sd ti Id k ggi la do cimg (hay he so dan hdi) ciia Id xo. Khi ciing chiu mdt ngoai luc gay bid'n dang. Id xo nao cdng ciing thi cdng ft bi bid'n dang, do dd he sd k cang ldn. Dan vi ciia do ciing la niuton trdn met, kf hidu la N/m. 4. Chu y a) Ddi vdi day cao su hay day thep, luc ddn hdi chi xuat hidn khi bi ngoai luc keo dan. Vi the trong trudng hgp nay luc dan hdi dugc ggi Id luc cdng. Luc cang cd didm dat va hudng gid'ng nhu luc dan hdi ciia Id xo khi bi dan. h) Dd'i vdi cdc mat tidp xiic bi bid'n dang khi ep vdo nhau thi life ddn hdi cd phuang vudng gdc vdi mat tiep xiic. Hinh 12.3. Khi 16 xo bi nen thi do nen la (l^ -1) va F^^ = kfl^ -1). Luc dan hoi ciia Id xo xuSt hien d ca hai d^u ciia Id xo va tac dung vao cac vat tiep xuc, (hay gdn) vdi nd lam nd bien dang. Khi bi dan, lire dan hdi ciia Id xo hudng vao trong, cdn khi bi nen, luc dan hdi ciia Id xo hudng ra ngoai. Djnh luat Hue : Trong gidi han dan hdi, dp Idn ciia luc dan hoi ciia Id xo ti le thudn vdi dp bien dang ciia Id xo : F^ = /cl A/I trpng dd k la dp cung (hay he sd dan hpi) ciia Id xp, cd don vi la N/m, I A/I = 1/ - /^l la dp bien dang (dp dan hay nen) ciia Id xp. Ddi vdi day cap su, day thep..., khi bj kep luc dan hdi dupc gpi la luc cang. Ddi vdi cac mat tiep xuc bj bien dang khi ep vao nhau, luc dan hdi cd phuong vudng gpc vdi mat tiep xiic. 73 CAU HOI VA BAI TAP 4. Mdt Id xo CO chieu dai tu nhien bang 15 cm. Ld xo duge giU co dinh tai mpt dau, cdn dau kia 1. Neu nhung dac die'm (ve phuong, chieu, diem dat) cua luc dan hoi cua a)Id xo. b) day cao su, day thep. c) mat phang tie'p xiic. 2. Phat bie'u dinh luat Hue. Phai treo mpt vat co trpng lugng bang bao nhieu vao mot 16 xo co dp cirng k = 100 N/m de no dan ra duoc 10 cm ? chiu mot luc keo bang 4,5 N. Khi ay Id xo dai 18 em. Do cimg ciia Id xo bdng bao nhieu ? A. 30 N/m ; B. 25 N/m ; C. 1,5 N/m; D. 150 N/m. 5. Mpt Id xo CO chieu dai tu nhien 30 cm, khi bi nen Id XO dai 24 cm va luc dan hoi cua no bdng 5 N. Hdi khi luc dan hoi ciia Id xo bi nen bdng 10 N thi chieu dai ciia no bang bao nhieu ? A. 18 cm; B. 40 cm ; C. 48 cm ; D. 22 cm. 6. Treo mpt vat co trong lugng 2,0 N vao mpt Id xo, Id xo dan ra 10 mm. Treo mpt vat khae co trpng lugng chua bie't vao Id xo, no dan ra 80 mm. A. 1 000 N C. ION; Em c6 bi§t ? LlJCKf B. 100 N D. 1 N. 1 a) Tinh do cirng cua Id xo. b) Tinh trpng lugng chua bie't. Dua vao djnh luat Hue nguai ta che tao ra lire ke. Tren lire ke, ung vai moi vach chia dp nguai ta khong ghi cac gia tri ciia do dan ma ghi gia tri ciia luc dan hdi tuang img. Tuy theo cong dung ma lue ke CO cau tao va hinh dang khae nhau (Hinh 12.4). Tuy nhien, bp phan chii yeu vdn la mpt 16 XO. Luc ke la mpt dung cu dp luc rai thuan tien nhung khong duac chinh xac lam. Khi sir dung, khong duac do luc Idn qua gidi ban dan hdi cua l6 xp luc ke. 74 1_ 2 J 1 4 N Hinh 12.4. Ba kiSu luc ke Id xo Luc MA SAT Nguai ta thuong noi den luc ma sat nhu nai den mpt luc can tra chuyen dpng. Neu chi co luc ma sat thi mpi true ciia dpng ca se ngirng quay, mpi banh xe se ngung lan. Nhung neu khong co luc ma sat thi ta khong the di bp hay di xe dupc. Tai sao vay ? Viec nghien cuu lire ma sat se giup ta nhan ra va giai thich duac nhieu hien tupng ma ta khong ngd la da eo lue ma sat tham gia, tham chi con giCr vai tro chii ye'u. I - LUC MA SAT TRUOT (J Trung hgc ca sd ta da bid't, khi mdt vat chuyen ddng trugt trdn mdt bd mat, thi be mat tac dung len vat (tai chd tid'p xiic) mdt luc ma sat trugt can trd chuyen ddng ciia vat trdn mat dd. 1. Do do Ion cua luc ma sat truot nhir the nao ? Thi nghiem : Mdc luc ke vao mdt khiic gd hinh hop chu nhat dat trdn bdn rdi keo theo phuong ngang cho khiic gd chuyen ddng gdn nhu thdng deu (Hinh 13.1). Khi ay, luc kd'chi do ldn ciia luc ma sat trugt tdc dung vdo vat. Ta ldm nhu the vdi ldn, mdi ldn ghi gid tri ma luc kd' chi. Sau dd lay gia tri trung binh lam dd ldn cua luc ma sdt truot. H I 2. Do Ion cua luc ma sat trupt phu thuoc nhCh:^ yeu to nao ? Cac thf nghidm cho thdy, do ldn ciia luc ma sat trugt: a) khdng phu thuoc vdo dien tich tiep xuc vd tdc do ciia vdt. b) d le vdi do ldn cua dp luc. c) phu thuoc vdo vdt lieu vd tinh trqng ciia hai mat tiep .xiec. «Ea»-^£^"M— Hmh 13.1 H I 06 Idn cua lUe ma sat trugt phu thupe vao nhung ye'u td nao trong cac yeu td sau day ? ~- Dien tich tie'p xiic cua khue gd vdi mat ban. — Td'c do cua khue go. — Ap lUc len mat tie'p xuc. — Ban chat va cac dieu kien be mat (do nham, dp sach, do kho,...) cua cac mat tie'p xiie. Em hay thd neu cac phuong an thi nghiem kiem chimg, trong do chi thay ddi mgt ye'u td cdn cac ye'u td khae thi giQf nguyen. 75 Bang 13.1. He so ma sat truot (gan diing) ciia mpt so cap vat lieu. 3. He SO ma sat trirot Vat lieu Go tren g5 Thep tren thep Nhom tren thep Kim loai tren kim loai (da boi tron) Nirdc da tren nudc da Cao su tren be tong kho Cao su tren be tong udt Thuy tinh tren thuy tinh /^t 0,2 0,57 0,47 0,07 0,03 0,7 0,5 0,4 He sd ti Id giua do ldn ciia luc ma sat trugt va do ldn ciia dp luc dugc ggi la he sdma sdt truqt. ki hieu la /z,. A^t = mst (i3.i; He so ma sdt trugt phu thudc vao vat lieu va tinh trang ciia hai mat tid'p xiic. Nd khdng cd dan vi va dugc diing dd tfnh do ldn ciia luc ma sdt trugt. 4. Cong thiic cua luc ma sat truot ^mst=/^t ^ (13.2) [ ^ j Bimg eho h6n bi lan tren mat san ndm ngang. a) Tai sao h6n bi lan cham dan ? b) Tai sao hdn bi lan dugc mgt doan dudng kha xa mdi difng lai ? Hinh 13.2 Hmh 13.3 76 II - LUC MA SAT LAN Luc ma sdt lan xuat hidn khi mdt vat lan tren mat mdt vat khdc, dd can lai chuyen dgng lan ciia vat. Thf nghiem cho thdy luc ma sdt lan rat nhd so vdi luc ma sat trugt. [ S Trong trudng hgp ma sat trugt cd hai can phai gidm thi ngudi ta thudng dimg con lan hay d bi dat xen vdo giua hai mat tid'p xuc (Hinh 13.2 va Hinh 13.3). Ill - LUC MA SAT NGHI 1. The nao la luc ma sat nghi ? 6 thf nghidm trdn Hinh 13.1, nd'u ta keo luc ke vdi mdt luc nhd thi khiic gd chua chuyen ddng. Mat ban da tdc dung vao khiic gd luc ma sdt nghi can bdng vdi lire keo, lam khiic gd dimg ydn. 2. Nhung dac diem ciia luc ma sat nghi a) Luc ma sdt nghi cd hudng ngugc vdi hudng ciia luc tac dung song song vdi mat tid'p xiic, cd do ldn bdng do ldn ciia luc tdc dung, khi vat cdn chua chuyen ddng. b) Khi luc tac dung song song vdi mat tie'p xiic ldn hon mdt gia tri nao dd thi vat se trugt. Dieu dd chirng td luc ma sdt nghi cd do ldn cue dqi bdng gid tri nay. Thf nghidm cdn chiing td, khi vat trugt, luc ma sat trugt nhd ban luc ma sdt nghi cue dai. 3. Vai tro cua luc ma sat nghi Nhd cd luc ma sat nghi ta mdi cdm dugc cdc vat tren tay, dinh mdi dugc giir lai d tudng, sgi mdi kdt dugc thdnh vai. Ciing nhd cd luc ma sat nghi ma day cua roa chuyen ddng, bang chuyen chuydn dugc cac vat tir ncri nay dd'n ncri khdc. Dd'i vdi ngudi, ddng vat, xe eg, luc ma sat nghi ddng vai trd luc phdt dqng lam cho cdc vat chuyen ddng dugc. Khi ngudi di (Hinh 13.4), ban chan dap vdo mat dat mdt luc ma sdt nghi F^^^^ hudng ve phfa sau. Mat da't da tdc dung vao ban chan mdt luc ma sdt nghi ^sn hudng vd phfa trudc (Hinh 13.4). Luc nay ddng vai trd lire phdt ddng lam cho ngudi di dugc. Vi du : Mot thung g6 co trpng lugng 240 N chuye'n dong thing diu tren san nha nho mot lire daiy nam ngang co do ldn 53 N. , a) Tim he sd ma sat trugt giira thiing g6 va san nha. h) Thiing g6 liic dau dung yen. Neu ta day no bang mot lire 53 N theo phuong ngang thi no co chuyen dong khong ? Gidi: a) Do san nha nam ngang nen : N = P = 240 N. Vl thung g6 chuydn dong thdng deu ; ^,s, = ^ = 53N F 53 He so ma sat trugt : A', - "^' - ^^Q = 0.22. h) Khong. Vl luc di lam cho thiing g6 chuySn dgng tir dUng yen ldn hon luc aiO cho thiing g6 chuySn dong thang dfiu. LdL- ' msn ' msn Hinh 13.4 77 1.1 Luc ma sat trirot: Xuat hien d mat tiep xuc ciia vat dang trupt tren mdt be mat; Cd huong ngiroc vdi hudng ciia van tdc ; CP dd Idn ti le vdi dp Idn ciia ap luc ; He sd ti le giiia dd ldn ciia luc ma sat truot va dd Idn ciia ap luc gpi la he SP ma sat truot. He sd ma sat trirot phu thudc vao vat lieu va tinh trang ciia hai mat tiep xuc va duoe diing d^ tinh luc ma sat trupt. - Cdngthuc:F^^^ = p^N Luc ma sat lan : Xuat hien d chd tiep xuc ciia vat vdi be mat ma vat lan tren dd d§ can trd chuyen ddng lan ; Rdt nhd so vdi luc ma sat trupt. Luc ma sat nghi: - Xuat hien d mat tiep xuc ciia vat vdi be mat del giir cho vat dung yen tren be mat dd khi vat bi mdt luc tac dung spng song vdi mat tiep xuc ; Co dd Idn cue dai; luc ma sat nghi cue dai Idn hpn luc ma sat trupt. l!«s; CAU HOI VA BAI TAP 1. Neu nhung dac diem ciia luc ma sat truot. 4. Trong cac each viet cdng thUc eiia luc ma sat - ,, . truot dudi day, each vie't nao dung ? 2. He sd ma sat trugt la gi ? No phu thuoc vao nhung ye'u td nao ? Viet cdng thirc cua luc ma ^-'^mst = A't'^ ' °- mst = Ih^ '< sa^t^^^- ' C.F^,, =p,N ; D. F^3, =^,A/. 3. Neu nhung dac diem ciia luc ma sat nghi. 5_ Q^ylp ggch nam yen tren mat ban nam ngang co chiu luc ma sat nghi hay khdng ? 78 """