- Ht phuung trinh ciin bdng:
Bai 01: MA sAT Gioi thi~u
.Gioi thi~u
- Giup h9e sinh biit au(le ecic khai niim v€ ma sat
- Caeh phan tieh Ive ma sat va tinh Ive ma sat
Mvc tieu thvc hi~n:
- Nh(in biit va phan biit GU(le eae Ior;d ma sat.
- Tinh toan au(le eae ma sat: tru(Jt, !an theo eae e6ng thue tla h9e.
Nqi dung chinh:
7.1. Ma sat trugt
7.2. Ma sat Ian
7.3. Phuong phap giai cac bai toan v~ ma sat
Cac hinh thfrc hqc t~p:
- H9c tren lap vS cac khai ni~m va cac phuong phap giai cac bai toan ma sat truQ't, ma sat Ian
- H9c theo nhom.
Nqidung:
7. I. Ma sat truQ't
7.1.1. Thi nghifm:
thi nghi~m culong da chi ra rfulg trong truong hqp ma sat truqc finh co th€ co gia trj bfrt ky trong mc)t miSn xac djnh:
Trong do: pnax ms, la gia tri gi6i h<;1n (16n nhfrt) Hinh 7.1 cua h;rc ma sat ma v~t con co kha nang can bfulg.
-
N
Nhu v~y khi h;rc ma sat d<;1t d6n gia tri nay thi v~t chuy€n dc)ng tir tr<;lllg thai can bfulg sang tr<;lllg thai chuy€n dc)ng. Bfulg nhiSu thi nghi~m Culong da tim ra gi6i h<;lll 16n nhfrt nay cua l\fC ma sat: no ty 1~ v6i gia tri cua phan l\fC phap tuy6n v&i
F,:X =fN h~ s6 ty 1~ f duqc g9i la h~ s6 ma sat truqc tinh: h~ s6 ty 1~ f duqc g9i la h~ s6 ma sat truqc tinh:
H? s6 ma sat truqc tinh la mc)t hu s6, no ph1,1 thuc)c vao nhiSu y6u t6 nhu v~t li?u va tr<;lllg thai cua cac bS m~t ( duong) ti6p xuc nhu de) g& ghS, boi tron, nhi~t, ... h~ s6 ma sat truqc tinh duqc ghi trong "s6 tay cua ky su". V~y diSu ki?n can bfulg khi co ma sat truqc la:
Fms~ fN
No duqc g9i la djnh lu~t Culong vs ma sat truqc.
VS m~t Hinh h9c dinh lu~t Culong chi ra rfulg khi can bfulg thi phan h;rc toan ph§n R = N +Fms nfun bfrn trong Hinh non, co goc & dinh b~ng 2Wms
v6i tgw ms = F hay w ms =arctgF
Theo dinh lu~t I khi v~t rful can bfulg thi hqp l\fc cua cac l\fc d~t vao ( cac l\fc ho<;1t dc)ng) tn;rc d6i ( can bfulg) v6i phan l\fc toan phk R . Do do khi cac l\fc d~t vao co hqp l\fc cit bfrn trong non ma sat thi
v~t can bfulg, me khong th€ chuySn dc)ng duqc, nghla la v~t bi t\f ham. V~y:
DiJu kifn ad vgt tv ham la hqp h;rc cua cac l\fC d~t vao (h;rc ho<;1t dc)ng) cit bfrn trong non ma sat (Hinh 11.7.2)
7.1.1. Cac afnh lugt
7.2. Ma sat Ian
La hi~n tuqng can chuySn dc)ng Ian
Khai ni?m: Hi~n tuqng ~an chuy€n dc)ng Ian khi mc)t v~t Ian (ma sat Ian dc)ng) ho~c c6 khuynh hu6ng Ian nhung chua Ian (ma sat Ian tinh) d6i v6i. mc)t v~t khac. Ma sat Ian dugc gay nen do cac v~t tit~p xuc v6i. nhau kh6ng phai t~ mc)t diSm ma theo mc)t ducmg ho~c mc)t m~t. Do d6 xufit hi~n kh6ng phai la mc)t Ive ma la mc)t h~ cac phan Ive lien tiep, n6 duc;rc thay the bfulg mc)t Ive R ( dugc thay the bfulg
phan Ive phap tuyen N va Ive ma sat tnrgt F ms) va mc)t ngftu Ive chinh la ngftu Ive ma sat Ian m 1 n6 c6 tac dgng can tra chuy€n dc)ng Ian (Hinh 11.6.1 ). Thi nghi~m chi ra rfulg khi con Ian can bfulg ngftu Ive ma sat Ian c6 th€ c6 mc)t gia ti bfit k.y J
trong khoang O,m1max , trong d6: m1max ty I~ v&i gia ttj cu.a phan Ive phap tuyen N v6i. h~ s6 ty I~ k. Nhu v~y: 0~1:SkN. E>6 la dinh lu~t v€ ma sat Ian. H~ s6 ma sat Ian k ph\l thuc)c vao nhi€u yeu t6 nhu v~t li~u, de) bien d.µig cu.ab€ m~t tiep xuc va n6 gia ttj be hon nhiSu so v6i. h~ s6 ma sat trugt tfuh: k < < f. Cac gia tri cu.a h~ s6 ma sat Ian cilng dugc cho trong s6 tay cu.a ky su. V~y diSu ki~n dS con Ian can bfulg la: Fms:S fN; m1 = kN chu y rfulg khac v&i h~ s6 ma sat tnrgt h~ s6 ma sat Ian c6 thu nguyen de) dai, n6 chinh la tay don cu.a phan Ive phap tuy€n N (Hinh 11.2.23).
Cac dinh lu~t
7.3. Phuong phap giai cac bai toan vS ma sat
Vi d1,ll : Tren mr;i,t phdng ob c6 thi quay quanh 0, ta d~t v~t n~g A tr9ng luqng P. H~ s6 ma sat tnrgt gifra v~t n~g va m{lt OD-la F. Tim g6c a bao nhieu d€ v~t A bilt d~u tmgt (Hinh 11.7.3)
Bai giai: Hinh 1 1. 1 .3
Ia ~ao sat v~t A can b~ng, du6i. tac dl)ng cu.a phap tuy~ N tr9ng luc;mg P , Ive ma sat F ( F hu6ng lfin vi v~t A c6 xu hu6ng tmgt xu6ng). Vi v~t can bfulg:
(P~N~F)~O L~p cac phuong trinh can bfulg :
LX=F-Psina=O Ly =N-Pcosa=O
F =f.N
Giai cac phuong trinh tren ta tim dugc : tga = f.
Khi v~t A a tr.µig thai can bfulg gi6i. h.µi thi tga = tgco hay a= co (1) (2) (3)
nhu v~y khi g6c a bkg g6c ma sat v~t se truqt. Day ciing la thi nghi~m dS tim g6c ma sat w va tu d6 suy ra h~ s6 ma sat f.
Vi d1J 2: Cho m9t h~ nhu hinh ve. DS gift v~t Q khong wi xu6ng din tac dµng Ive P nh6 nh~t bao nhieu ? Cho bi~t h~ s6 ma sat truqt gifra ma ham va banh xe la f. Bo qua b6 day ma ham Q.
Giai
Ta chia bai toan nay ra hai bu&c :
Bu&c 1: Ta khao sat banh xe va tn,ic 0 a tr~ng thai can bkg gi&i h~n, nghia la :
F = Fmax = fN
0 banh xe va tn,ic 0 giin ch~t v&i nhau. H~ Ive tac d\l Hinh 11. 7.4 (Q, Ro, :Ft Fms) ~ o
Trong d6 Ro la phan Ive & tfl)C 0, Ne la phan Ive phap tuySn cua ma ham ap 1~ banh xe. F ms la Ive ma sat truqt do ma ham d~t I~ banh xe (Hinh 11. 7 .5)
'I,m0(.F) = -Q.r + F mr·R = 0
Ta l~p phuang trinh momen d6i v&i 0: Va di6u ki~n cu.a h_rc ma sat la: Fms = F.Nc
Hinh 11.7.5
Hinh 11.7.6
a C b
R
Tir dieu ki~n (1) va (2) ta suy ra :
N = r.Q
C f.R
Bu&c 2: Xet can b5.ng don AB v&i cac lµc tac d1,mg :(RA,N c' ,F ms, ,F min) ~ 0 (Hinh
11.7.6) _ _ _
Trong d6 fie' va F,ns' la n(H lµc cua h~ nen khi tach ra ta ve ngm;rc chieu v&i Neva -
F ms tac d\lllg l§n banh xe. Vi xet can b5.ng gi&i h1;lll nen lµc P = P min , n6u P>P min thi Ne cang l&n va tai cang can b5.ng, n6u P<P mm thi Ne se nho khong du sue gifr v~t Q
va tai O quay. Ta l~p di@u ki~n can bkg la phuong trinh m6men d6i v&i A.
Suy ra: b
a+ Nc=--Pmin
a