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- UY BAN NHAN DAN QU4-N 5
TRUONGTRUNGCAPNGHEKYTHUATCONGNGHEHUNGVUONG
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GIAOTRINH
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Nghe: Cat gQt kim Io~i
TRINH DO• TRUNG CAP
TPHCM-2019
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LOI GIOI TH}¥U
Ghio trinh CO' ky thu~t ra doi nhim dap frng nhu c!u giang d~y mon
CO' ky thu~t t~i tnrrrng Trung c§p ngh~ ky thuit cong ngh~ hung Vll'O'ng.
Giao trinh dtrgc bien so~n theo dung n(H dung qui djnh cua chtrO'ng trinh
mon h9c CO' ky thu~t trong chtrO'ng trinh khung dao t~o ngh~ C~t g9t kim
lo~i.
Trong qua trinh bien so~n giao trinh, tac gia da dtrgc S\f h6 trg nhi~t
tinh cu.a cac d6ng nghi~p. Chan thanh cam O'n cac giao vien va lanh d~o
khoa da dong g6p y ki~n d~ hoan thi~n giao trinh.
Quqn 5, ngay thang nam 20 ...
Tham gia bien soqn
Chu bien
Nguy@n Hfru Nhan
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MlJCLlJC
BEMVC TRANG
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Lm '''th'" •~u ·············•o••··············· . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Myc lye ............................................................................................................................................................................................................... 2
Ch U'O'Dg I: Tinh HQC ................................................................................................................................ o••·············3
BAI 1: Nhfrng· khai ni~m CO' ban va cac tien d~ tinh hqc ......................... 3
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BAI2: He". hrc ph8ng ..... a ........................................................................................................................................ 00.12
BAI 3: H~ l\fC khong gian .......................................................................... 24
Chuo-ng II: l>Qng HQc ............................................................................................................................................................... 28
BAI 1: Chuy~n d{>ng ciia ch~t di~m ......................................................... 28
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BAI 2: Chuyen clQng cO' b3n ciia vit ran ................................................. 37
BAI 3: T6ng hgp chuy~n d{>ng ................................................................. 43
BAI 4: Chuy~n d{>ng song phing ciia v~t riin ........................................ .46
CHUONG III: Sfrc B~n V~t Li?u ............................................................. 50
BAI 1: Cac khai ni~m CO' ban .................................................................... 50
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BAI 2: Keo - nen diing tam, cat ............................................................... 56
BAI 3: f>~c trung hinh hqc cua hinh phing ............................................ 70
BAI 4: Xoiin thu~n tuy nhfrng thanh trOn .............................................. 7 4
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BAI 5: U6ng phing ciia thanh thiing ....................................................... 82
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CHUONG IV: Chi tiet may ...................................................................... 92
BAI 1: M6i ghep dinh tan ......................................................................... 92
BAI 2: M6i ghep han ................................................................................. 97
BAI 3: M6i ghep ren ................................................................................ 105
BAI 4: M6i ghep bing then va then boa
CHUONG V: Cac chi ti~t may truy~n d{>ng ........................................... 92
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BAI 1: BQ truyen dai ................................................................................. 92
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BAI 2: B{> truyen bSnh ma sat ........................................................... ., ...... 97
BAI 3: B{> truy~n trgc vit ........................................................................ 105
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BAI 4: BQ truyCn b3.nh rang ................................................ ., .................... ., .. .
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CHUONG 1 TiNH HOC
Gi6i thieu: Chuong tToh h9c giai quySt cac bai toan vs sv tuong tac gifra cac
V?t th@ c6 mBi lien kSt v6i nhau.
Ml}.C tieu:
- Trinh bay dugc cac tien dS, cac khai ni~m, each bi@u di@n Ive, cac lo~i lien
kSt ca ban, h~ Ive, phuong phap hgp Ive d6ng quy, tach Ive d6ng quy.
- Phan tich dugc Ive tac dvng va cac phan Ive lien kSt, cac momen cua Ive
dBi v6i m9t di@m, ng~u Ive.
- Tinh dugc Ive tac dvng va cac phan Ive lien kSt, cac momen cua Ive dBi
v6i m9t di@m, ng~u Ive.
- Tinh dugc lgc b~ng phuong phap da giac, phuong phap chiSu dS giai cac
bai toan vS h~ Ive bfit ky.
- L~p dugc phuong trinh mo men tinh toan h~ lvc tac dvng.
- Giai dugc cac bai toan h~ Ive ph~ng song song.
- Ren luy~n tinh ky lu?t, kien tri, ctn th?n, nghiem tuc, chu d9ng va tich eve
sang t~o trong h9c t?p.
N{H dung:
Bai 1: NHUNG KHAI NI~M co BAN vA cAc TIEN DE
TiNHHQC
I. cAc KHA.I NitM ca BAN
1. Vit ri\n tuy~t dBi
Vi)t r&n tuy¢t a6i la VCJt r&n c6 hznh dq,ng hznh h9c kh6ng thay a6i trong qua
trinh chiu luc
Thv·c ts· cac V?t r~n khi chiu lvc dSu c6 biSn d~ng, nhung biSn d~mg d6 nit
nho ta c6 th@ bo qua dS nghien cuu hi~n tugng dugc dan gian hon, nhung v~n
bao dam d9 chinh xac theo yeu cfiu k1 thu?t
d CHlfONG 1 khi xem xet V?t, ta coi v~t la v~t r~n tuy~t dBi
2. Trang thai can biing
' ' ? ' ,
V?t ran 6 tr~mg thai can bang khi v?t dung yen ho~c chuyen d9ng deu doi v&i
h~ qui chiSu (h~ tn;c to~ d9 ch9n lam chuan)
3. L\fC
a. IJjnh nghia:
L11c la tac dimg tuong h6 giua cac V(Jt ma kit qua la gay nen Slf thay a6i
trq,ng thai CO' h9c cua v9t thi dy ( baa g6m Slf thay a6i vt trf
va ca biin dq,ng)
Thi dv: du6i tac dvng cua lvc, V?t dang dung yen
chuy@n sang chuySn d9ng, v~t dang chuySn d9ng dSu
chuy@n sang chuySn d9ng nhanh dfin dSu ho~c ch~m dfin
dSu .. Hoijc thanh gi~ng du6i tac d9ng cua tr9ng v?t n6 ciing Kmh 1-1
chiu tac d9ng 1 Ive keo ho~c Ive nen ( tuy khong gay ra
chuySn d9ng nhung n6 ciing gay ra biSn d6i tr~ng thai ca h9c)
- 4
b.Cacyiut8cual~c
Lvc duqc d~c tnmg boi 3 y@u t6: di@m d~t, hu6ng va tri s6
- Di@m d~t la ph§n tu v~t chit thrn)c v~t ma qua d6 tac dµng tuong h6 duqc
truySn dSn v~t
- Huong ( phuong va chiSu cua Ive) la hu6ng chuy@n d9ng ma Ive gay ra
cho v~t
- Tri s6 cua Ive hay cuong d9 cua Ive la d9 m
- 5
khong lam thay d6i tn;mg thai chuySn d9ng cua v~t. H~ h;rc ("""if,"""fi;,"""fi;,.... .Fn ) can
bing ki hi?u la("""if,"""fi;,"""fi;,..... ~)= o
+ H9'p hrc: Hqp Ive la rn9t Ive duy nhfit
tuong duong voi h? Ive. R la hqp Ive cua h~ h;rc
~)=
thi (}{~Ji;,..... R
b. Momen va ngfiu life
H'inh 1-5
* Mo men cua mot luc a6i vbi 1 aidm
Khi 1 Ive tac dµng len v~t riln, n6 c6 thS lam v~t di
chuySn nhung cling c6 thS lam v~t quay ho~c ca vua
quay vua di chuySn
Gia SU v~t riln co thS quay quanh diSrn O c6 dinh, tac
d\lllg ma Ive F gay ra cho v~t ph\l thu9c vao tri s6 Ive F
va khoang each a tu diSrn O d@n duong tac d1,1ng cua Ive.
16
Con chiSu quay ma Ive gay cho v~t c6 thS la nguqc chiSu H'inh -
ho~c cung chiSu kirn d6ng h6. D~i luqng d~c trung cho ca tac d1,1ng quay va
chiSu quay do g9i la mo men cua Ive d6i voi rn9t diSm
Dinh nghza: Mo men cua hrc a6i vbi 1 aidm la 1 dr;zi lu(mg dr;zi s6 c6 gia tri
tuy¢t a6i b&ng tich s6 giif:a tri s6 cua hrc vbi canh tay don va c6 ddu (+) hay ddu
(-) tuy theo chi§u quay cua lL;Cc F quanh tam O la ngu(Jc hay thugn chi§u kim
d6ngh6
ki hi?u m0 (F) = ±F.a (1-4)
Trong d6:
mo (F) la ki hi~u mo men cua h;rc Fd6i voi diSm 0
F la tri s6 cua Ive
a la canh tay don
Khi chi cfin dS y dSn tac d1,1ng quay ma khong quan tarn dSn chiSu quay ta c6
tri s6 mo men cua 1 lgc d6i voi 1 di Sm, ki hi~u la mo mo (F)
= F.a (F)
Mo men cua Ive d6i voi diSrn bing khong khi Ive di qua diSm lfiy mo men (a
=0).
* Ngdu luc
Khi c6 2 Ive F; , F 2 song song nguqc chiSu c6 tri s6 bing nhau tac d\lng len
v~t riln. M~c du R = F; - F2 = O nhung h~ ( F;,;;) khong can bing vi F; , F
2
khong cung duong tac d1,1ng. Nhu v~y ( F;, Ji;,) khong c6 hqp Ive nhung n6 c6
khuynh hu6ng lam cho v~t riln quay, nen duqc g9i la ng&u Ive.
Dinh nghza: Ngdu lvc la m9t hi g6m 2 lvc song song, ngu(Jc chidu, c6 tri
s6 b&ng nhau nhung khong cimg duimg tac d1Jng
Ccic yiu t6 cua ngdu lvc
m
Ng&u Ive c6 3 ySu t6:
a
ffinh 1-7
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M~t philng tac dl_lng: la m~t philng chua cac Ive cua ngfiu Ive
ChiSu quay cua ngfiu Ive trong m~t philng ngfiu Ive: thu~ v6i chiSu kim
d6ng h6 ho~c nguqc l~i
Cuong d9 tac dl)ng cua ngfiu Ive duqc d~c trung boi tich s6 cua Ive v6i
canh tay don g9i la tri s6 mo men cua ngfiu Ive :
m=F.a (1-6)
Trong d6 : m la tri s6 cua ngfiu Ive
Fla tri s6 cua Ive
a la canh tay don
Bon vi dS do tri s6 mo men la NiuTon met. Ki hi~u la Nm,
Cac tinh chdt cua ngdu htc:
Tac dl)ng cua ngfiu Ive len v~t rfm
khong thay d6i khi doi n6 dSn dSn m~t
philng song v6i n6.
H1nh 1-8
C6 thS doi ngfiu Ive trong m~t tac
dl_lng thi tac dl_lng cua ngfiu Ive len v~t rin khong thay d6i
C6 thS thay d6i tuy y tri s6 cua Ive va canh tay don cua ngfiu Ive nhung
vfin gifr nguyen mo men thi tac dl_lng cua ngfiu Ive len v~t rin khong thay d6i.
II. cAc DINH LUAT TiNH HOC
Tien d~ 1 ( iljnh lu{U ·vi 2 life can bring)
DiJu ki¢n cdn Vet au ai 2 Ive tac d?mg !en 1 vcjt r&n can bang
la 2 Ive phai cung phuong,
ngm;rc chi€u vet c6 cung trj s6 IDnh 1-9
Ive b&ng nhau
Tien d~ 2 ( iljnh lu~t them, but 2 --- -----~ life can
b&ng) H'mh 1-10
Tac d¥ng cua 1 h¢ Ive !en 1 vcjt rdn khong thay a6i khi ta them vao hay bat
di 2 Ive can b&ng nhau
He quii: ( iljnh If tric(J't life)
Tac d'?[ng cua 1 Ive !en 1 vcjt
r&n kh6ng thay a6i khi ta truQ't
Ive tren aucmg tac d¥ng cua n6
Th~t v~y gia SU c6 Ive F tac H'mh 1-11
dl_lng len v~t rin a diSm A (hinh
1-13 ). d diSm B b~t ki tren duong tac dl)ng cua Ive Fta d~t them vao 2 Ive can
b§.ngFr,F'.i. Hai Ive nay can b§.ng cung phuong v6i Ive F va c6 cung tri s6 cua
Ive F. Theo tien dS 2: F~(F,Fr,F.i). Hai Ive (F,P.i)can bing nhau (theo tien dS
1) nen theo tien dS 2 ta I~i c6 th@ bot 2 Ive nay va c6 F ~(F,Fr,Fi) ~Fi. Fi chinh
- 7
la Ftrugt tir A t6i B. Nhu v~y lvc tac d\lng len v~t r~n tuy@t d:6i dugc biSu diSn
bfulg vec ta trugt
Tien a~ 3 ( tljnh lu~t vi qui tdc hinh binh hanh lz.rc)
R
Hai hrc aij,t tc;zi 1 aidm tuang auang vai 1 ll:fC aij,t tqi
ai&m a6 va au(Yc bi&u diin b6-ng vecta auirng cheo hinh binh
hanh c6 2 cc;znh la 2 Ive aa cha
Theo phep c9ng vec ta thi R la t6ng cua ]{,Ji; tuc la
R=F'i +F2 Hinh 1-12
Tien a~ 4 ( iljnh lu~t vi tac dimg va phiin tac d{lng)
Lvc tac d¥ng Va lvc phan tac d¥ng cimg phuang, ngu(YC
chiiu va c6 tri s6 b&ng nhau
Chu y: Lgc tac d\lng va phan tac dvng khong phai la 2 Ive
can b~ng vi chung d~t vao 2 v~t khac nhau
Tien a~ 5 ( tljnh lu~t thay thl lien klt)
V~t khong tv do can b~ng c6 th@ dugc xem la v~t can b~ng, Hinh 1-13
b~ng each giai ph6ng tfit ca cac lien kSt va thay thS tac d\lng cac
lien kSt duc;rc giai ph6ng bfulg cac phan Ive lien kSt thich hgp
III. LIEN KET VA PHAN L~fC LIEN KET
1. Khai niem
a. V~t /If do va v9,t chju lien klt
Vijt r&n c6 thi thvc hi¢n m9i di chuy&n trong khong gian g9i la wjt r&n tv do.
Thi d\l qua bong nhy bay la lung trong khong gian g9i la v~t r~ tv do
Vqt r&n c6 1 vai di chuy&n bi can tra au(Jc g9i la vqt khong tv do hay vgt
chtu lien kit. Thi d\l quySn sach d~t tren ban
la v~t chiu lien kSt vi n6 can tr& chuySn
d:9ng thtlng dung di xu6ng
b. Lien klt va phiin llfC lien klt
Nhfmg aiJu ki¢n can tra chuy&n a9ng tv
do cua vq,t au(JC g9i la lien kit. V~t gay ra
gay ra can trcr chuy@n d9ng cua v~t khao sat
dugc gQi la v~t gay ra lien kSt. Thi dv quySn p p
sach dat tren ban la v~t khao sat, con cai Hinh 1-14
ban la v~t gay ra lien kSt
Do tac d¥ng tuang h6, tc;zi lien kit vgt gay lien kit tac d¥ng len vgt khao sat,
lvc a6 au(Jc g9i la phan lvc lien kit. Phan Ive lien kSt chinh la lvc can tr&
chuySn d:9ng tg do cua v~t khao sat
c. Tfnh ch8t cua phiin life lien klt
- Phan lvc lien kSt bao gia ciing d~t len v~t khao sat t~i ch6 tiSp xuc v6i v~t
gay lien kSt
- Phan Ive lien kSt cung phuang va ngugc chiSu v6i chuySn d9ng bi can tr&
cua v~t khao sat
- 8
- Tri s6 cua pha? Ive lien k~t phµ thut;>c rao ~ac Ive tac d1µ1g len V?t khao sat
Qua cac tinh chat tren ta thay phan Ive lien ket la lo~i Ive bi dt;>ng, khac v6i
cac Ive tac dl,lng len v~t khao sat d6 la cac Ive da cho hay Ive chu dt;>ng
2. Cac lien k~t thrrcrng g~p
a. Lien kit tzra
ia
Lien kit tl:{a lien kit ma eek vg,t chi c6 tac
d~ng ila ldy nhau. V 6i gia thiSt bo qua ma sat, lien
kSt tva can tr& chuySn dt;>ng cua V?t khao sat theo
phuong vuong g6c v6i m~t tiSp xuc chung gifra
V?t gay lien kSt va V?t khao sat. Phan Ive lien kSt
tva c6 phuong vuong g6c v6i m~t tiSp xuc chung,
chiSu di tu V?t gay lien kSt vao V?t khao sat va c6 Hlnh 1-15
1 ySu t6 chua biSt d6 la tri s6. Phan Ive lien kSt tva
thuong dugc ki hi~u la N
Chuy:
- Truong hgp m9t trong hai tiSp xuc la m9t
diSm thi phan Ive phap tuySn theo phap tuySn cua m~t
con l~i
- G6i tva di d9ng cung la d~ng lien kSt tva
b. Lien kit day mim
Lien kSt day can tr& chuySn d9ng cua v~t khao sat theo chiSu cang cua day.
Phan Ive hu6ng theo phuong cua day theo chiSu tu V?t khao sat di ra va c6 m9t
ySu t6 chua biSt la tri s6. Phan Ive cua lien kSt day mSm thuong dugc ki hi~u la
r va con g9i la Ive cang day
c. Lie'! kit b~n Ii phdng , , ,
Lien ket ban le phang c6 2 lo~i la ban le di d9ng va ban le co dinh
• Ban l~ di i16ng
Ban IS di d9ng cho phep V?t khao sat (v?t B) quay R
quanh tfl,lc ban IS va di chuySn theo phuong song song
v6i m~t tva, con can chuySn dt;>ng theo phuong vuong
g6c v6i m~t tva: phan Ive ( thuong dugc ki hi~u la R) c6
phuong vuong g6c v6i m?t tva, tri s6 chua biSt. C6 thS Hinh 1-17a
1
gia dinh cho phan Ive 1 chiSu nao d6, nSu kSt qua tinh ra duong thi chiSu gia
dinh dung v6i chiSu thvc, con kSt qua mang d~u am thi chiSu thvc ngugc v6i
chiSu gia dinh
• Ban l~ c6 ilinh
Lien kSt ban IS c6 dinh chi cho phep V?t khao sat (v~t
B) quay quanh trl,lc ban IS con m9i di chuySn dSu bi can
tr&. Phan Ive lien kSt R co tri s6 va phuong chua biSt, Hinh 1-l?b
con chi@u thi gia dinh nhu da n6i a tren. DS thu~n ti~n khi tinh toan ta thuong
- 9
phan R lam 2 thanh ph§.n ~ va Ii; vuong g6c v6i nhau, hie d6 phan Ive cung
c6 2 tri s6 cua ~ va Ii;
d. Lien kit thanh
Lien kSt thanh g6m m9t thanh thing ho~c
thanh cong c6 2 d§.u la 2 ban 16 c6 dinh va tren
thanh khong c6 Ive tac d\lllg (bo qua tn;mg lm;mg D
thanh) Hinh 1-18
Lien kSt thanh can tr& chuySn d9ng cua v~t
khao sat theo phuong n6i 2 ban l@ 6 2 d§.u thanh.
Phan Ive lien kSt thanh c6 phuong la ducmg n6i kh6p a d§.u thanh, c6 tri s6
chua biSt, con chi@u thi tru6c khi tinh cung c§.n gia dinh nhu da neu a tren. Phan
Ive cua lien kSt thanh thucmg duqc ki hi~u la s
e. Lien kit ngiim
La lien kSt khi v~t duqc n6i cung vao 1 v~t khac. (
dinh duqc dong cung vao tuong)
/
·----=R_x_ _ ___,
Trong truong hqp ngam phan Ive lien kSt g6m 2 Ive
thfulg g6c v6i nhau va 1 ng~u Ive n&m trong m~t phing Hinh 1-19
chua 2 thanh ph§.n lvc va cung la m~t phing tac dµng cua
h~
3. Khao sat v~t ri\n can bing bing each giai ph6ng lien k~t
Tren CO' SO' dinh lu~t 5, dS khao sat can b&ng cua v~t riln ta c§.n co l~p n6 ra
khoi cac v~t thS xung quanh, xem nhu n6 khong chiu cac lien kSt, tuc la giai
ph6ng cac lien kSt cho v~t, r6i d~t C ac Ive da cho va cac phan Ive lien kSt len v~t
thay thS cho cac lien kSt bo di. Khi d6 ta c6 thS xem v~t chiu lien kSt can b&ng la
v~t rfu tv do can b&ng du6i tac d1.1ng cua cac Ive da cho va cac phan Ive lien kSt.
Vi df.11
Qua c§.u d6ng chfit c6 tn;mg luqng P duqc treo vao m~t tucmg nh~n thing
dung nha day OA (hinh12). Hay d~t tit ca cac Ive tac d1.1ng len qua c§.u
Gicd y
Khao sat qua c~u, cac Ive tac d\lllg len qua A
'
cau c6:
- Tr9ng Ive P d~t t~i tam O va hu6ng thing
dung xu6ng du6i
- Phan Ive lien kSt tva N( thay cho lien kSt B
tva & B)
- Lvc ding dayr ( thay cho lien kSt day) IDnh 1-20
Nhu v~y sau khi bo cac lien kSt di va thay
bfulg cac phan Ive lien kSt tuong ung ( cong vi?c nay g9i la giai ph6ng lien kSt ta
c6 thS xem qua c§.u nhu v~t riln tv do can b&ng du6i tac d1.1ng cua h? Ive (r,N,P).
DS cho g9n sau nay ta ve ngay cac phan Ive va Ive da cho vao hinh c6 ca cac
lien kSt
- 10
Vi dfi: Thanh d6ng ch§.t c6 tn;mg lm;mg P chiu tac d1;mg cua Ive F. Thanh
duc;rc lien kSt bfing m9t g6i c6 dinh va m9t g6i di d(;ng (hinh 1-21). Xac dinh h~
Ive tac dvng len thanh
Giai
Lvc da cho tac dvng len thanh AB g6m
tr9ng Ive P ( d~t gifra thanh va hu6ng xu6ng)
va Ive F . Phan Ive lien kSt g6m x A , ~ , r;
Nhu v~y thanh AB chiu tac dvng cua H1nh 1-21
CAU HOI ON TAP
1. ThS nao la v~t r1n tuy~t d6i? Khi nao c6 thS xem v~t d.n va v~t dn my~t
d6i
2. Lvc la gi? Neu cac ySu t6 cua Ive va trinh bay each bi@u diSn Ive
3. Hai h~ can bfing c6 tuang duang khong? Vi
sao?
4.Neu va giai thich cac dinh lu~t fi'nh h9c
5.Vi sao c6 thS coi Ive la vec ta truqt?
6. Fi
Cho 2 lvc va ~ cung d~t t~i diSm 0
( hinhl-4)
- V 6i g6c a b&ng bao nhieu thi hqp Ive c6 tri s6 16n nh§.t?
- B~t them vao o Ive ~ nhu thS nao ? dS h~ (~;;:~) can bfing
7. Vi sao Ive tac d\lllg va Ive phan tac dvng khong phai la 2 Ive can bfing?
8. Mo men Ive d6i v6i 1 diSm la gi?
9. Ng~u Ive la gi? Neu cac ySu t6 cua ng~u Ive.
10.Vi sao n6i ng~u Ive khong tuang duang v6i 1 Ive?
11.Lien kSt la gi? Phan Ive lien kSt la gi? Neu cac tfnh ch§.t cua phan Ive lien kSt
12.Ve cac lien k@t thucmg g~p, sau d6 ve phan lgc cua cac lien k@t d6
Giai ph6ng lien k@t la gi? Vi sao phai giai ph6ng lien k@t?
- 11
A ,2
Bai 2: H~ Ll}C PHANG
H
- 12
- d la khoang each thiing g6c tu O dtefn duong tac dl;lng cua Ive du
- 13
2. Thu gQn h~ hfc ph~ng v~ tam 0
Liy m9t di€m O trong mijt ph~ng tac dvng cua h~ h.fc gQi la tam thu gQn.
sfr dvng djnh Ii doi Ive song di doi cac Ive v€ tam 0
/F1 F{
- F2 =
-
m
RR F;
=
-
m
.(.' -
R
\p3
ffinh 2-4
-Fi= iFi va ngau
~ Ive ml= mo (-)
Fi
~=Ff va ng~u Ive m = m)Fi) 2
-F;, = iF;, va ngau
~ Ive mn =m (-)
F;, 0
Nhu'v~y thu gQn h~ Ive (if~, ....... ,~) v€ tam Ota duqc h~ Ive
(I
Fi ,I I ;:: . . ' ~
F; ,....... , F;, ) dong qu1 tc;n O va hv nga u Ive phang :
A ,2
(2-9)
Nhu ta da bie"t, h - _,.. ----+ N -
k=l
Tu ke"t qua tren ta c6 djnh Ii:
Bjnh li 2-2: H~ llfc phdng bdt kz tuong duong wfi 1 [lfc va mqt ngdu llfc dr'j,t
tq,i 1 dilm tuy y cung ndm trong mijt phdng tdc d1;tng cua hf llfc. chung duqc
g9i la llfc va ngJu llfc thu g9n. Lvc thu g9n d~t t~i tam thu gQn c6 vec to Ive
bang vec to chinh cua h
- 14
+ Ne'u M 0 = o h9 thu g9n la 1 Ive, chinh la h
- 15
MA= fm)~)=o, MB= fmB(I{)=o, Mc= fmc(I{)=o (2-13)
k=l k=I k=l
Trong trlidng h(lp h~ 11/c ddng qui: Di€u ki~n cfin va du dS h~ Ive can
bang la t6ng hlnh chie'u cac Ive tren 2 trgc to~ de) tri~t tieu
n n
Rx= LFkx = 0,
k=l
RY= LFky = 0
k=I
(2-14)
y
MQTSOVIDTJ A
Vi d111: Qua cfiu d6ng chit tam 0, tr9ng
ht
- 16
y
1. day BC nghieng 30° v6i thanh C
2. day BC thing dung p
Gidi: B
Xet can bang cu.a thanh OA
* Trztdng h(fp BC nghieng.
Ht$ ll.)'c tac dvng g6m: ll.)'c ho~t d9ng P,
sue ding T' hai phan phan ll.)'c ban IS X: va
Y
Yoo i
cI~ p L
~ .Bay la ht$ hfc phing ba't kl nen l~p 1======~B===A-x
du'qc ba phu'ong trlnh can bang: Hlnh 2-6
✓3
IX=X0 -T-=0
2
T
IY=Ya+--P=0
2
Imo(F)= -P.OA + T.OB.sin30° = 0 ( tay don cu.a T la OH= B.sin30°) hay
-P+r.I.1-=o
3 2
KSt qua : T = 3 .P,· X 0 = 3P ✓3 · Y0 = - P
2 ' 2
Trztdng h(fp BC thdng dung
Vl P, T thing dung nen phan ll.)'c ban IS chi c6 thanh ph~n thing dung Ya.
chung ta c6 ht$ h,tc song song va l~p du'qc 2 phuong trlnh can bang
Im 8 (F)= -P.BA-Y,,.OB. = 0 ⇒ P.2 + Y,, = 0
ImJF)=-P.OA+T.OB.=0 ⇒ -P+T. 2 =0
3 p
~ ? 3 p
Ket qua : T =- P ; Yo=--
2 2
Vf dl! 3
Piston A chiu tac dvng cu.a ll.)'c P c6 tri s6 P = 25kN,
thanh truySn B lam vdi duong thing dung g6c a= 14°.
Xac dinh ap h,tc cu.a piston len thanh xi lanh va Ive
tac dvng d9c theo thanh truySn.
Bo qua tr9ng luqng piston va thanh truySn H'inh 2-7
Gidi
Piston can bang dudi tac di.mg cu.a ll.)'c da cho P, phan ll.)'c cu.a xi lanh len
s
piston N va phan ll.)'c cu.a thanh truySn (hlnh ve)
Vie't phu'dng trlnh can bang cho ht$ ta c6
Ix= N -Scos76° = 0 (*)
(**)
- 17
Tu phuong trlnh (**) ta c6
25
s= P O= = 25,8kN thay S vao phu'ong trlnh (*) ta c6
sin 76 0,9703
N = 25,8cos76° = 25,8.0,2493 = 6,4kN
Ap Ive cua piston len thanh xi lanh c6 tri s6 6,4 kN cung phu'ong va ngu'QC
chiSu voi N, con hfc tac dl;lng Ien thanh truySn co tri s6 25,8k:N cung phuong
va ngu'QC chiSu voi s
V{ d¥, 4 B
Day treo v~ t c6 tn;mg Iu'qng P = 80 kN
duqc vift qua rong fQC Ava giu bcH toi D. X
Rong r9c A c6 ban ldnh khong dang k€.
Xac dinh phan Ive cua cac thanh AB va
AC. Bo qua ma sat d rong r9c, tr9ng lu'9ng
C
cua cac thanh va day p
Gidi Hinh 2-8
Xet slf can bang cua rong fQC A. cac Ive tac dl;lng len rong fQC c6: tr9ng Ive
p' sue ding day T( T= p vl bo qua ma sat a rong fQC) va cac phan Ive cua
lien k6t thanh s AB , sAC c6 chi€u gia dinh nhu' hlnh ve. Nho rong fQC c6 ban
kinh khong dang kS ta c6 th€ xem r, P, s AB , s AC la hi$ h;tc ph!ng d6ng qui
Ch9n hi$ trlJc xAy nhu' hlnh ve, ta c6 cac phu'ong trlnh can bang:
LX=Tcos30°-Pcos60°-SAc =0 (*)
LY=-Tsin30° -Psin60° +SAB =0 (**)
Tu' phu'ong trlnh (*) c6
SAC =Tcos30' -Pcos60° =P(cos30° -cos60° )= so( 1:-~) = 29,3kN
Tu phu'ong trlnh (**) c6
SAB= Tsin30° -Psin60° =P(sin30° +sin60° )= s{ ~ + ~) =109,3kN
sAC , sAB
tinh ra dSu la s6 du'ong chung to chi6u gia dinh cua sAC , sAB dung
voi chiSu thtfc
V{ d¥, 5
ogm chiu tac dvng cua cac ngftu Ive c6 mo men ml = 20kNrn rn2 = I5kNrn
rn 3 = lOkNrn. Hay xac djnh phan h;tc cf cac g6i Ava B cua agm
Gidi
Tren dfim chi co cac ng~u Ive tac dl;lng, nen d€ can bang phan Ive a 2 g6i
cfing phai l~p thanh mc)t ng~u h;(c. Phan h;(c NB vuong g6c voi m~t tva va c6
- 18
chiSu gia dinh di len, tu'ong ung phan h;(c ~ phai song song voi N s va c6
chiSu gia dinh di xuo'ng. Theo diSu ki~n can bang (2-13) ta c6:
RAl-m 1 +m 2 -m3 =0
RA= m1 -m2 +m1 = 20-15+10 =375kN
l 4 '
RA c6 dffu + chung to chiSu gia
dinh cua_~ la dung chiSu th-L;L'c,
tuong ung Ji;= 3,75kN va chiSu ve A
tren hlnh cfing dung voi chiSu thl;(c
1=4m
Hlnh 2-8
BAIT!P
1. H~ ll;L'c phiing d6ng qui ( hlnh 2-8) g6m cac ll;L'c c6
tri so' ll;(c: ~ = 50N, F;_ = 32N, J{ = 42N, ~ = 60N. Hay
xac djnh hqp ll;L'c cua h~ Ive d6
H1nh2-8
2. Ong tl'\l d6ng chit c6 tr9ng lu'qng P = 60N d~t tren
mang ABC hoan toan nhan va vuong g6c dB. m~t BC
C
Hlnh 2-9 cua mang lam voi m~t nam ngang g6c a= 60° ( hlnh 2-9).
Hay xac djnh cac phan ll;L'c cua mang len o'ng d 2 diSm
tie'o xuc D va E
3. Day ABC va:t qua rong r9c D c6 dffu C
treo v~t nang tr9ng luqng P=l00N, con dffu A
bu(k vao tu'ong. d diSm B tren day treo v~t
n~ng c6 tr9ng htqng G, duoi tac dvng cua v~t
n~ng day lam voi du'ong thing dung nhung g6c
45°va 60°( hlnh 2-10). Hay xac djnh sue ding
cua do
nguon tai.lieu . vn