7/23/2019 Co Ung Dung Chuong 1

1/16

29/08/201414

1

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

7/23/2019 Co Ung Dung Chuong 1

2/16

7/23/2019 Co Ung Dung Chuong 1

3/16

29/08/201414

3

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

7/23/2019 Co Ung Dung Chuong 1

4/16

29/08/201414

4

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

7/23/2019 Co Ung Dung Chuong 1

5/16

29/08/201414

5

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

7/23/2019 Co Ung Dung Chuong 1

6/16

29/08/201414

6

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

7/23/2019 Co Ung Dung Chuong 1

7/16

29/08/201414

7

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

7/23/2019 Co Ung Dung Chuong 1

8/16

29/08/201414

8

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

7/23/2019 Co Ung Dung Chuong 1

9/16

29/08/201414

9

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

7/23/2019 Co Ung Dung Chuong 1

10/16

29/08/201414

10

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

7/23/2019 Co Ung Dung Chuong 1

11/16

29/08/201414

11

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

7/23/2019 Co Ung Dung Chuong 1

12/16

29/08/201414

12

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

7/23/2019 Co Ung Dung Chuong 1

13/16

29/08/201414

13

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

7/23/2019 Co Ung Dung Chuong 1

14/16

29/08/201414

14

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.

7/23/2019 Co Ung Dung Chuong 1

15/16

29/08/201414

15

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

7/23/2019 Co Ung Dung Chuong 1

16/16

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)