- Ht phuung trinh ciin bdng:
Bai 08: TRQNG TAM CUA V~TRAN
Gioi thi~u
Giup h9c sinh biit clu(JC ccic khcii nif m vi tr9ng tam cua vgt rdn. Ccich phan tich va xcic clinh tr9ng tam vgt rdn.
Ml}.c tieu th\fC hi~n:
Xcic cltnh clu(JC tr9ng tam cua ccic Hinh ph6.ng clan gian.
Xcic clinh clu(JC tr9ng tam cua ccic vgt rdn c6 Hinh kh6i clan gian: kh6i lljp phuang, kh6i tr~, kh6i cdu, kh6i chop cl6i xung
Nqi dung chinh:
8.1. Cong thtrc tinh tn,mg tam m9t s6 hlnh phfulg don gian
8.1.1 Dinh ngh'fa ma sat Ian
8.1.2 Toq cl<5 tr9ng tam cua hinh ph6.ng
8.1.3 8.2. Cac phuong phap xac dµih tr9ng tam
8.2. 1. Phuang phcip th11c nghifm.
c6ng thuc tinh tr9ng tam cita m9t s6 hinh kh6i clan gian
Cac hinh thfrc hqc t~p:
- H9c tren 16-p v~ cac khai ni?m va cac phuong phap giai cac bai toan ma sat truqt, ma sat Ian
- H9c theo nh6m.
Nqi dung:
8.1. Cong thtrc tinh tr9ng tam m9t s6 Hinh phfulg don gian
8. 1. 1 Dinh ngh'fa gia su v~t rful A (Hinh 11.8 .1) ta chia v~t ra thanh n phfui tu nh6 sao cho m6i phfui tu nh6 fa m9t ch!t diem. M6i phfui tu nh6 nay c6 tr9ng Iµc fa(A,P2 ,.--::,PN )va cac Iµc nay c6 phuong thfulg dung, c6 hqp Iµc fa P d~t a
diem c6 dµih C, c6 tri s6:
P = P1 + P2 + ... + Pn = LP;
Lµc P g9i fa tr9ng Iµc. DiSm d~t C cua tr9ng Ive g9i fa tr9ng tam ta c6 dµih nghla:
~
· Tr9ng tam cua v~t dn la diSm d~t cua tr9ng l\fC.
H i n h 1 0 1 p r Xe 8 X .1 Hinh 11.8.2
B.1.2 To~ d(J tr9ng tam cua hinh phimg
Gia sir v~t riln d6ng chit lat~ phfulg S, c6 di~n tich F, chi~u day b, kh&i luQTig
rieng g. Ta chia v~t rin ra tharih n phftn tu, c6 cac tr9ng l\Ic tuong ung P1,P2
, ... ,PNd~t t~i cac diSm c6 to~ de) tuong tmg A1(x1, Yi), Ai(x2, Y2), ... , A(xn, Yn)- Tr9ng l\fc Ji cua t ~ phfulg d~t t<;ti diSm C c6 to<;t d9 tu_.9'Ilg ung C(xc, Yc)- Ch9n h~ tn,Ic to<;t d9 Oxy sao cho tnic Oy song song v6i h;rc P (Hinh 11.8.2)
Theo dinh Ii Varinhong ta c6:
mo(P)=P.xc
Lmo(~)= L~-Xi
M~tkhac Suyra
Thay vai tro tnic x bfulg tnic y ta c6:
Ngoaira: P = m.g = y.F.b.g Pi = mi.g = y.AFi.b.g LP;.xi Lr-AF;.b.g.xi X - = - - - = - - - - c - P - r.F.b.g
8.2. Cac phuong phap xac djnh trc;,ng tam
8.2.1. Phuongphap thvc nghi~m.
Ta treo t§m phifug mong tam giac bfulg m9t sgi day qua dinh A (Hinh 11.8.3) dfiu ducri day bu9c v~t c6 tr9ng luqng P thi sgi day thifug dung trimg vcri trung tuySn am cua tam giac ABD. Di~u nay chung to tr9ng tam cua tam giac nfun tren trung tuySn AM. Cung lam tuong tv nhu v~y v&i di~m B, khi d6 sgi day trimg vcri trung tuySn BN (Hinh 11.8.4). Giao di~m C cua cac trung tuySn AM va BN chinh la tr9ng tam cua tam giac ABD.
D Hinhve Hinhve h Ye G 0 R R Hinh 11.8.4 yd Difntich F=.!:_l.h 2 11il1 f : - 8 D Vi tri f:r<?ng tam 1 x., = 3(ai-b) 1 Yc=3h B+2b h Ye=--.- B+b 3 Yt = 0,2878.d y, = 0,2122.d
8.2.2. Cong thuc tr9ng tam cua ma sat hinh kh<5i don gian
83-IB-$-l ' 1
Cho m9t ban d6ng chM c6 kich thmrc nhu (h inh 11.8.6). Hay xac dinh tr9ng tam cua ban.
Bai giai:
Ta dvng h~ trµc Oxy va chia hinh tren thanh ba phfui. Tinh t9a d9 tr9ng tam cua m6i phfui va di~n tich cua chung. (Hinh 11.8.7)
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