co ung dung chuong 1
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Chng I
Nhng
vn c bn
ca tnhhc vt
rn tuyti
B mn C K Thut i hc Bch Khoa Tp.HCM
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1. Cc khi nim c bn
1.2. H tin tnh hc1.3. Lin kt Phn lc lin kt
1.4. iu kin cn bng v cc phng trnh cnbng ca h lc khng gian
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1. Cc khi nim c bn
1.1.1. Vt rn tuyt i
Vt rn tuyt i l mt tp hp v hn cc cht im mkhong cch gia hai cht im bt k lun lun khng i.
1.1.2. Cn bng ca vt rn
Vt rn c gi l cnbng khi v tr ca n khngthay i so vi v tr camt vt no c chnlm chun gi l h quychiu.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.3. Lc
Lc l mt i lng vector c dng o lng stng tc c hc gia cc vt th vi nhau. Ngha l khi thchin s tng tc c hc, cc vt th s truyn cho nhau
nhng lc. Lc l nguyn nhn gy ra s bin i trng thichuyn ng c hc ca vt, l nguyn nhn gy nn ccbin dng ca vt.
a. Khi nim
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.4. Quy i lc phn b trn on thng v lc tptrung tng ng
a. Tng qut
C
BAO
)(xq
xAx
Bx
~x
Cx
a)
Q
D
C
BAO
xDx
b)
( ).
( ) . .
B
A
B
A
x
x
x
D Cx
Q q x dx
x q x x dx Q x
Vi:
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
b. Trng hp ringb1). Lc phn b u
2l
constq
A B
lq.
~
l
C
lqQ .
A B
2lD
C
b2). Lc phn b tam gic:
maxqC
A B32ll
lq .2
1max
~ C
A B32l
lqQ .2
1max
D
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.5. Lc lin kt v lc hot ng. Phn lc lin kt
Lc lin kt: Nhng lc c trng cho tc dng tng h gia
cc vt c lin kt vi nhau qua ch tip xc hnh hc.
Lc hot ng: L nhng lc khng b mt i cng vi lin kt.
Phn lc lin kt: Lc do cc lin kt phn tc dng ln vt.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Lc hot ng
Lc lin kt phn lc linkt
1.1.5. Lc lin kt v lc hot ng. Phn lc lin kt
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.6. Moment
a) Moment ca lc ivi mt im:
Di tc ng ca mt lc vt rn c th chuyn ng tnhtin, chuyn ng quay, hoc va chuyn ng tnh tin va
quay ng thi. Tc dng ca lc lm vt rn quay s cnh gi bi i lng momentca lc.
( )A
m F r F
.Am F M F d
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Cch xc nh chiu vector moment:
1.1.6. Moment
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.6. Moment
??
O
m F
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.6. Moment
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.1.7. Momentb) Moment ca lc i vi mt trc:
( ) ( ')
( ) [ ( )]
O
O
m F m F
m F hch m F
F
'F
r( )om F
A(x,y,z)
O
Moment ca lc Fi vi trc quays c quy c l
i lng dng(+) nu nhn dctheo trc quay tngn ca trc y tathy lc hnh chiuF s c xu hngquay quanh tm Ongc chiu kimng h v ngcli.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.2. H tin tnh hc
Tin 1: Tin v hai lc cn bng
iu kin cn v cho hai h lc cn bng l chng c cngng tc dng, hng ngc chiu nhau v c cng cng .
F
A'F
BF
A'F
B
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Tin 2: Tin thm bt hai lc cn bng
Tc dng ca mt h lc khng thay i nu thm hoc bt hai
lc cn bng.
=> Tc dng ca mt h lc khng thay i khi trt lc trnng tc dng ca n.
1.2. H tin tnh hc
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Tin 3: Tin hnh bnh hnh lc
H hai lc cng t ti mt im tng ng vi mt lc t
ti im t chung v c vector lc bng vector cho hnh bnh
hnh m hai cnh l hai vector biu din hai lc thnh phn.
1 2R F F
1.2. H tin tnh hc
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Tin 4: Tin tc dng v phn tc dng
Lc tc dng v lc phn tc dng gia hai vt c cng ng
tc dng, hng ngc chiu nhau v c cng cng .
A'F
F
'F F
B
1.2. H tin tnh hc
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.2. H tin tnh hc
Tin 5: Tin ha rn
Mt vt bin dng cn bng di tc dng ca mt h lc th
khi ha rn li n vn cn bng.
Tin 6: Tin gii phng lin kt
Vt khng t do (vt chu lin kt) cn bng c th c xem l
vt t do cn bng nu gii phng cc lin kt, thay th tc dng
ca cc lin kt c gii phng bng cc phn lc lin kt
tng ng.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.3. Lin kt Phn lc lin kt
1.3.1. Khi nim
L s chuyn ng c lp m vt rn y c th thc hin ng
thi trong khng gian. V d: chuyn ng ca qut trn v ca
tri t l 2 chuyn ng c lp.
K hiu bc t do ca vt rn l Dof (Degree of freedom).
L vt rn c th thc hin c mi dng chuyn ng trong
khng gian m khng c bt k cn tr no.
1.3.1.1. Vt rn t do hon ton
1.3.1.2. Bc t do ca vt rn
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Xc nh Dof ca vt rn t do hon ton
Trong khng gian hai chiu: 2D
O
S
x
3Dof
: tnh tin thng theophng ngang.
: tnh tin thng theophng ng.
: quay.
1.3. Lin kt Phn lc lin kt
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Trong khng gian 3 chiu: 3D
Ch rng mt chuyn ng c lpbao gm c hai chiu
chuyn ng theo mt phng.
6Dof V
O
z
x
1.3. Lin kt Phn lc lin kt
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.3.1.3. Lin kt
Rng buc ca lin kt (Rlk): L schuyn c lp b mt dolin kt.
Rlk l mt thng s nh gi kh nng cn tr chuyn ng
ca lin kt i vi vt v n c nh ngha bng s chuyn
ng c lp m vt rn b mt i do lin kt y.
L nhng i tng c tc dng hn ch kh nng chuyn ngca vt rn trong khng gian.
1.3. Lin kt Phn lc lin kt
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Bc t do ca h nhiu vt rn c lin kt vi nhau
Khi Dof h> 0: h khng lun cn bng vi mi loi titc ng.
Khi Dof h 0: h lun cn bng vi mi loi ti tc ng.
Kho st mt h thng c hc gm c n vt rn c lin
kt vi nhau bi m lin kt.
Xt mt c htrong khng gian ba chiu (3D):m
lk
h j
j 1
Dof 6n R
Xt mt c h trong khng gian hai chiu (2D): Dofh = 3n -m
lk
j
j 1
R
- Tng cc rng buc ca cc lin kt trong h l:
mlk
jj 1 R
1.3. Lin kt Phn lc lin kt
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.3.1.4. Phn lc lin kt
Phn lc lin kt l nhng lc thuc loi lc th ng (bng).
BP
AP
AR B
R
AB
V
L nhng lc do cc lin k t phn tc dng ln vt
Tnh cht 1: S phn
lc lin kt ca mt loi
lin kt s bng s lm
trn ca rng buc lin
kt y.
Tnh cht
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Cc lin kt thng dng trong c hc
1. Lin kt dy
T C mt phn lc lin kt , s rng buc Rdy= 1
T
: Lc cng dy
Tnh cht 2: V tr t cc phn lc lin kt trng vi v trca cc lin kt y (t ti v tr c lin kt).
Tnh cht 3: Phng ca cc phn lc lin kt s trng
vi phng ca cc chuyn ng c lp b mt i. Tnh cht 4: Chiu ca cc phn lc lin kt s ngc
vi chiu ca cc chuyn ng c lp b mt i.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
2. Lin kt ta nhn
C mt phn lc lin kt , s rng buc Rta= 1
: Phn lc ta
AN
AN
A
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
At
BtAN
BN
B
A
S
tB: tip tuyn ring ca vt ti v tr im B.
, : phn lc php tuyn.AN
BN
tA: tip tuyn ring ca b mt c nh ti im gy A.
2. Lin kt ta nhn
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Ta
2. Lin kt ta nhn
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
3. Lin kt khp bn l
a. Khp bn l cnh (khp bn l ngoi c nh, gi c nh).
Loi lin kt ny c chiu v ln ca cc phn lc linkt cha bit.
y
xA
S
Chiu phn lc d on
Rbl= 2
C 2 phn lclin kt.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
x yF F F
Khp bn l c nh
M hnh lin kt khp bn l trong l thuyt
AA A
xA
yA
A
xA
yA
AA
A
R
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
b. Khp bn ltrt(khp bn l ngoi trt, khp bn l ding, gi di ng)
Rblt= 1
C 1 phn lc lin kt.
Loi lin kt ny ch cho php trt qua li theo phngtrt v quay trong mt phng nhng khng tnh tin thngln, xung theo phng vung gc vi phng trt. trt nh ngi ta lp thm con ln (hnh 1.30).
Chiu v ln phn lccha bit.
V
AN
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
M hnh lin kt khp bn l di ng trong l thuyt
A
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
c. Khp bn l ni
Rbln = 2
C 2 phn lc lin kt tc ng ln tng vt tha tin 4.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
'
'
x x
y y
A A
A A
xyA
'
yA
'
XA
Khp bn l ni
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
V d
Khp BL C nh2RB
Khp BL di ng1RB
Khp BL ni2RB
LK ta1RB
Bc t do ca c h:
3.2 6 0Dof
+ S vt: 2
+ Tng s RB: 6
V d
Gii phng lin kt
xAy
A
xC xD
yD
'
xD
'yD
FN
2Q qa
2yP qa
2xP qa
M
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
4. Lin kt khp cu
Rcu= 3
C 3 phn lclin kt. V
y
x
AA
x
A
A
z
z
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
5. Lin kt ngm phng
yA
xA
AM
Rngm2D= 3
C 3 phn lc lin kt.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
6. Ngm khng gian (ngm 3 chiu )
Rngm3D= 6
C 6 phn lclin kt.
z
yA
xA
zA AxM
A
yM
AMzx
A
Ngm
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
7. Lin kt thanh
Kho st thanh thng hoc cong tha ng thi ba iukin sau:
C trng lng rt b nnc th b qua c.
C hai lin kt hai ucui ca mi thanh thucba loi lin kt sau y:khp cu, khp bn l, tanhn.
Cc thanh khng chu tcng ca lc hocmoment gia thanh.
BR
DR
A
B
C
D
V
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
Nu nhng thanh tha mn ng thi cc iu kin nh trn
c dng lm cc lin kt cho vt rn th chng s c gi
l cc lin kt thanh. Mi lin kt thanh s c mt rng buc
v sinh ra mt phn lc tc ng ln vt. Phn lc ca lin kt
thanh lun c tnh cht nm trn mt ng thng ni lin hai
u c lin kt thanh.
, : B
D
R ABAB CD
R CD
2 lin kt thanh
A: khp cu; B,D: bn l; C: ta nhn.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
V d Lin kt thanh
AR '
AR
CR
C
Khng l Lin kt thanh
xAy
A
'
x
'
yA
xC
yC
os ; sinx A y AA R A R
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
8. - chn.
Dng cc trc quay, trc chu
tc dng ca cc lc t ln trc v
truyn lc ny vo thn my, b my.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bngca h lc khng gian
1.4.1. Thu gn h lc khng gian v tm O
Nu vt rn cn bng vi h 3 lc th h 3 lc y s tha mnng thi 2 iu kin:-ng phng-Hoc ng quy, hoc song song
a. nh l 3 lc
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bngca h lc khng gian
1.4.1. Thu gn h lc khng gian v tm O
C th di di song song mt lc n mt im t mi nm ngoing tc dng c ca n nu ta thm vo trong qu trnh di songsong y mt vector moment bng vector moment ca lc trc khidi di ly i vi tm s c di n.
b. nh l di lc song song
A
B
lA
l A// l BF
F
( )B
M F
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
' "F F F
: Ngu lc Hai lc cng
phng, ngc chiu,bng nhau v ln vc im t khc nhau.
",F F
Moment ca ngu:
. BM F d M F
A
B
lA
l A// l BF
'F
"F
d
A
B
lA
l A// l BF
F
( )BM F
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bngca h lc khng gian
1.4.1. Thu gn h lc khng gian v tm O
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bngca h lc khng gian1.4.2. nh ngha vector chnh
Vector chnh ca mt h nhiu lc l vector tng ca cc vector lctrong h lc y.
1
x jxn
j y jy
j
z jz
R F
R F R F
R F
Vector chnh Thnh phn c bn th nht ca mt h lc
Tnh cht:-i vi 1 h lc xc nh, vect or chnh ca h lc l vector hng
bt bin th nht ca h lc.-Vector chnh ca mt h lc l mt vector t do, c th nm trnng tc dng song song ty trong khng gian tn ti ca h lc.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bng cah lc khng gian
1.4.3. nh ngha vector moment chnh
Vector moment chnh ca mt h lc i vi mt tm l vector tngca cc vector moment tng lc thnh phn trong h ly i vi cngtm y.
1
( ) ( )
( ) ( )
( ) ( )
Ox Ox j x jn
O O Oy Oy j y j
j
Oz Oz j z j
M M F M F
M M M M F M F
M M F M F
Vector moment chnh Thnh phn c bn th hai ca mt h lc
Hnh chiu ca vector Moment chnh ln phng ca vectorchnh l hng s bt bin th 2 ca h lc
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
1.4. iu kin cn bng v cc phng trnh cn bngca h lc khng gian1.4.5. iu kin cn bng ca h lciu kin cn v h lc khng gian cn bng l vector chnhv moment chnh ca h lc i vi mt im bt k phi ng thib trit tiu.
1
1
0
0 0
0( )
( ) 0
( ) 0 ( ) 0
( ) 0
x jx
n
j y jy
j
z jz
j
Ox Ox jn
O O j Oy Oy j
j
Oz Oz j
R F
R F R F
R FF O
M M F
M M F M M F
M M F
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Bi tp 1. Cho Q = 2 kN, F = 10kN, q = 2kN/m, M = 8kN.m, a= 1m, b =2m, = 450, = 600. Xc nh cc phn lc ti A,B.
H c 1 vt (khung).
Ti B c lin kt khp bn l c nh: 2 rng buc.
Ti A c lin kt khp bn l di ng: 1 rng buc.
Dof 3 1 2 1 0 H tnh nh.
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Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
Bi tp 1
yA
x
y
A
M
2 / 3a b
F
Q
yF
xF
Trong :
1
. 32
Q q a b kN
0
0
cos 60 5
sin 60 5 3
x
y
F F kN
F F kN
.Cho Q = 2 kN, F =10kN, q = 2kN/m, M =8kN.m, a = 1m, b =2m,
= 450, = 600. Xc nhcc phn lc ti A, B.
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
Bi tp 1
yA
x
yB
CM
2m Q
yF
xF
1m 2m
2m
DE
2m
Cc phng trnh cn bng:
0
0
0
x
y
B i
F
F
m F
0
0
2 1 . 2 . 2 2 2 3 0
x x
y y y
y x y
B F
B A F Q
M F F Q A
(+)
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Bi tp 2
Cho khung ABCD lin kt vi thanh DF nh khp bn l tiD. Xc nh cc phn lc lin kt ti A, C, D, F?
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Bi tp 2 Gii phng lin kt
xAy
xC xD
yD
'
xD
'
yD
FN
2Q qa
2yP qa
2xP qa
M
0
0
0
x
y
A i
F
F
m F
0
0
0
x
y
D i
F
F
m F
5 n s 3 n s
-
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29/08/201414
16
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
'
xD
'
yD
FN
M
0
0
0
x
y
D i
F
F
m F
Bi tp 2
'
'
2 / 2 0
2 / 2 0
. 0
x F
y F
F
D N
D N
N DF M
'
'
2F
x
y
N qa
D qa
D qa
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied MechanicHochiminh city University of Technology
xyA
xC xD
yD
2Q qa
2yP qa
2xP qa
Bi tp 2
0
0
0
x
y
A i
F
F
m F
0
0
. .2 . .2 .2 0
x x x x
y y y
x x x y
A P C D
A P Q D
P a C a Q a D a D a
2xC qa
3y
qaxA qa
Lu :'
'
x x
y y
D D qa
D D qa
Chng I: Nhng vn c bn ca tnh hc vt rn tuyt i
HCM 06/2014
Applied Mechanic Hochiminh city University of Technology
Bi tp 2
Kt qu '
'
2
2
3
F
x
y
x
x
y
N qa
D qa
D qa
C qa
A qa
A qa
(ngc chiu chn ban u)
(ngc chiu chn ban u)
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