BQ GIAO DUG VA DAO TAO TRUONG DAI HOC DAN LAP ClfU LONG Nguyen Hoang Tuyen Nguyen Thi Ngoc Van Gido Trinh VAT LY DAI CUONG • • Phan Cd Hoc Liiu hdnh noi bo p; ■■4 Vinh Long - 2009 I ' ■ Ldl DE TUA Trtfcfng Dai hoc Dan lap Ccfu Long muon khing dinh la trung tam dao tao nguon nhan li/c co trinh cao cho khu vifc dong bang song Cdu Long de phuc vu cho- cbng cuoc cong nghiep hoa, hien dai hoa dat nifdc thi phai nang cao chat litong dao tao toan dien Mot nhtfng yeu to yeu la doi ngu thay co, he thong cac giao trinh va trang thiet bi day hoc Gung vdi cac nganh cac cap toan quoc dang day nhanh tien xay dting va cung co vi the xu the hoi nhap, triidng Dai hoc Dan lap Ciki Long dan tiing biidc hoan thier de difo'ng dau vdi nhtfng thach thu’c do, gop phan difa nen giao due dai hoc Viet Nam diing vffng, ngang tarn khu vile va the gidi Ke hoach xay difng ve mot Bo giao trinh sir dung cho cac giang vien lam tai lieu co ban de giang day, cho sinh vien nghien cdu tham khao hoc tap la nhu cau cap bach cua nha trifdng An pham n&y la gido trinh Vat Ly Dai Ciiong - Phan Co Hoc cua Khoa Khoa Hoc Co Ban, Trird’ng Dai hoc Dan lap Cdu Long, ThS Nguydn Hoang Tuyen va ThS Nguydn Thi Ngoc Van bien scan Lanh dao triTdng Dai hoc Dan lap Cufu Long tran nhtfng cdhg hien, dong gop cua Quy thay co mdi giang cung nho cac thay co can bo - giang vien co huh cua nha trOdng Hy vong rang, mot khong xa Tnfcrng Dai hoc Dan lap Guru Long se cd day du mot Bo giao trinh hoan chinh dung nha trirdng Tran gidi thieu gido trinh den Quy thay co vd cac em sinh vien trildng Dai hoc Dan lap Cdu Long Vinh Long, thang 09 nam 2009 Q HIEU TRLfdNG ThS Nguyen Cao Dat Chitong DONG HOC CHAT DIEM • • I nhUng khai Chat diem va NIEM Md DAU chat diem • Chat diem : Mot vat co kick thiidc nhd khong dang ke so vdi nhttng khodng each, nhdng kick tkiidc ma ta dang khdo sat got la chat diem Chat diem goi la hat Vi du : xet vien dan bay khong khi, trai dat quay quanh mat trefi, ta co the xem vien dan, trai dat la nhiing chat diem Khi do, cac vat the dUOc khao sat nhu" cac diem (hinh hoc) chuyen dong cua no NhUng can lifu y rang, mot vat dUOc xem la chat diem hay khong, khong phai kich thudc rieng cua nd xac dinh, ma ty so' gitfa kich thub'c cua nd va dai dac trimg cho chuyen dong cua nd xac dinh Ta biet rMng, bdn kinh cua trai dat (R = 6,4.106 m) rat nhd so vdi khoang each trung binh gitfa nd va mat trd'i (r = 1,5 x 1011 m) Vi vay, xet trai dat chuyen dong ttf quay quanh true cua nd, ta khong the xem trai dat la chat diem dtfdc Khi khao sat chuyen ding mot vat, neu ta khong quan tarn den stf quay cua nd va stf dich chuyen gitfa cac bo phan cua nd dbi vdi nhau, ta cd the didn ta vat bang md hinh chat diem Chat diem chuyen dong thtfdng dtfqc goi tat la dong diem • He chat diem : Mot tap hap gom nhieu chdt diem, ma cac chat diem he co tiiang tdc vdi goi la he chdt diem He chat diem dtfqc goi la he hat Vi du: tap hop cac phan ttf mot binh chtfa la mot he chat diem, tap hop cac hanh tinh he mat trdi la mot he chat diem Chuyen dpng cof hoc va hp quy chieu • Chuyen dong cot hoc : Su" chuyen dcfi vi tri cua mot vat doi vdi cac vat the khac khong gian theo thcri gian goi la chuyen dong co hoc Chuyen dong co hoc goi tdt la chuyen dong • He quy chieu : Mot vat dope chon lam moc g&n vdi mot he toa va mot gdc thcri gian cung vdi mot dong hd hop mot he quy chieu Chon he quy chieu khac nhau, ta se nhin thay chuyen dong cua cung mot vat didn don gian hay phdc tap Khi nghien ciiu chuyen dong mot vat, ta nen chon he quy chieu nao de chuyen dong cua vat ay dien don gian nhat Nham bieu dien toan hoc cho mot chuyen dong, ta thucfng chon mot he toa gan vdi he quy chieu Co the chon cac he toa thudng dung giai tich : he true toa Descartes vuong gdc, he true toa doc cdc, he true toa tru, he true toa dp cau, Nhuhg, tiiy theo dang chuyen dong cua chat diem, ta nen chon mot he toa dp phu hup de sd didn ta toan hoc cho chuyen dpng cua chat diem la rd rang va thuan tien nhat Khong gian va thdri gian (theo cd hoc cd dien) • Khong gian ccf hoc dupe quan niem khong phu thupc vao thdi gian vzl vat the chuydn dpng dd Khong gian cd tinh dong nhat va ding hdd’ng, do thda man cdc tinh chat cua khong gian Euclid, cac tien de Euclid va cac dinh ly cua hinh hoc Euclid ddefe sd dung Khong gian ndi tren ddtfc goi la khong gian tuyet ddi • Then gian cung ddp’c quan niem khong phu thupc vao khong gian, vao vat the chuyen dpng, trdi deu td qua khd, qua hien tai den tUtfng lai, ddi vdi moi he quy chieu Thbi gian ndi tren cung dupe goi la thefi gian tuyet do’i II PHUONG TRINH CHUYEN DONG - QUY DAO Viec xac dinh vi tri cua mot chat diem chuyen dong theo thdi gian gpi la xac dinh chuyen dong cua nd Day la bai toan co ban cua dong hoc chat diem Do cd nhieu phunng phap xac dinh vi tri cua chat diem, nen cd nhieu each xac dinh chuyen dong cua chat diem PhtfoTng phap vector Ta cd the xac dinh vi tri cua dong diem M d moi thdi diem b^ng vecto f diIng tef diem gdc O tdi diem M (O dtfpc chon y va dufng yen) OM = r , r difpc goi la vecto ban kinh (hay vectcr tia) cua M Khi M chuyen dong, r se thay doi theo thbi gian ca ve Idn Idn phifcmg, chieu Do do, r la ham vectcr phu thuoc dd'i so vd hifdng t (thdi gian) M f (C) Cd the viet : r = r(t) (1) Neu xac lap ttfbng minh diipc bieu thde (1), ta cd the dung dilpc vectcr r tai tiing thdi diem t Dau mut cua r d tiTng thdi diem t ay chinh la vi tri cua M luc nd chuyen dong Nhif vay, bieu thde (1) xac dinh quy luat chuyen dong cua M dtidi dang vectcr, nen (1) dupe goi la phiiang trinh chuyen dong dang vecto Phitong phdp thifcrng diftfc dung ly thuyet, cho phep ta nghien cdu, bieu di§n chuyen dong mot each co dong, tong quat Quy dao cua dong diem M Id ditdng no vach khong gian qua trinh chuyen dong Quy tich cac diem ngon cua vectcr f t bien doi chinh la quy dao cua M Phtfdng phap toa dp Tif diem O, ta dung mot he true toa vuong goc Oxyz Khi ay vi tri cua M dupe xac dinh bdi cac toa (x,y,z) cua no Ro rang : f = {x,y,z} Vdi he true toa dp nay, de xac dinh chuyen dong cua M ta can phai biet sir bien doi cua toa dp cua no theo thdi gian, nghia la can xdc dinh cdc ham : ZA f y I ■J-' x X = x(t) y = y(t) z = z(t) (2) goi la phtfcmg trinh chuyen dong dang toa (2) • Neu chuyen dong cua M mat phang Oxy thi z = z(t) = Phifcfng trinh chuyen dong phang co dang : x = x(t) y = y(t) • Neu M chuyen dong tren difcfng thang Ox thi y = y(t) = , z = z(t) = Phifcfng trinh chuyen dong thang co dang : x = x(t) Phifcfng phap toa thildng dtfac dung thifc hanh tinh toan vi cu the va thuan tien Muon tim quy dao cua M, ta can tim bieu thdc lien he gitfa cac toa cua M bang each khd t cac phifcfng trinh chuyen dong (2) Vi du, khd t (2) ta diftfc phifcfng trinh co dang : 'fx(x,y) = f2(y,z) = Day la cac phifcfng trinh cua mat tru cd cac difcfng sinh tifefng dng song song vd'i cac true z va true x Giao tuyen cua mSt chinh la quy dao cua dong diem M khong gian Phifcfng phap tif nhien Neu quy dao cua M da biet, ta cd the lay mot diem O bat ky tren quy dao (C) lam goc va chon mot chieu difcfng tren (C) s M Do dai dai so cua cung OM ro rang xac dinh hoan toan vi tri cua M Ky hieu : s = OM, s goi la hoanh cong cua M 114 Ly cua mot dao dong td dieu hoa cho bdi phitong trinh : x = A sin(cot + cp) Biet r&ng vao then diem t = dao dong td co ly xq va van tdc v0 Tinh A va (p Mot hat dao dong dieu hoa tren true x vdi bien a, hat chuyen dong td diem cd tpa x den diem cd toa x + dx het mot khoang thdi gian dt Chdng to rang xac suat de tim thay hat khoang td x den x + dx la : dx 7i(a2 -x2)1/2 Tha mot phu ke co can la mot dhg hinh tru dtfdng kinh D vao mot binh diTng chat long co khoi Iwong rieng p Kich dong nhe phu ke theo phifcfng thing ddng, phu ke se dao dong Tim chu ky dao dong cua phu ke theo khdi lifo’ng m cua no Bo qua ma sat giila phu ke va khdi chat long Cho gia tdc tnldng g = 9,81 m/s2 e.'.i S Mot chide xe cd khdi IdOng 10 kg ddpc de len hai Id xo dan hoi Biet rang, dddi sdc nen cua mot Ide F = 9,8 N thi Id xo co lai cm Xe chay tren mot ddcfng go ghe, cd each 30 cm lai cd mot ga Hoi vdi tdc bao nhieu thi xe bi rung dong manh nhat ? Mot chat diem tham gia hai dao dong cung chu ky T va pha ban dau