bai tap co ly thuyet

8/8/2019 Bai Tap Co Ly Thuyet

1/70

CAC BAI TOAN VE HE LC PHANG 1

PHAN A: TNH HOC1. CAC BAI TOAN VE HE LC PHANG1.1. BAI TOAN 1 VAT:

BBAA II 11..11:: Dung lc keoQ nam ngang e keo banh xeong chat trong lngP, ban knh R t mat ng A vt lentren mat ng B. Chieu cao chenh lech gia 2 mat ng

2 R

h (Hnh 1.1). Xac nh phan lc tai A, B. Vi tr so Q naoth banh xe se vt qua bac.

Q

hA

B

Hnh 1.1

Tra li: 33A

N P Q ; 2 33B

N Q . Xe vt qua bac khi3Q P

( Hng dan: xe vt bac khi no ri khoi A:0A N )BBAA II 11..22:: Mot chiec en ng nang 300 N c treo

vao cot nh cac thanh ngang1,2AC m va thanh chong1,5BC m . Bo qua trong lng cac thanh. Tm ng lc1S va

2S trong cac thanh AC va BC. Gia thiet cac iem A, B, C ganban le (Hnh 1.2)

Tra li: 1 400S N ; 2 500S N

A C

B

Hnh 1.2

BBAA II 11..33:: Dam ong chat 4CB m , trong lng5Q kN c gi nam ngang nh ta len cac canh tng tai A

va B. Biet 0,05AB m (Hnh 1.3). Xac nh phan lc tai A va Bneu tai au C cua dam treo vat nang40P kN .

Tra li: 3400A N kN ; 3355B N kN

AC B

PHnh 1.3

BBAA II 11..44:: Thanh AB c gan vao tng nh ban leA va gi nam ngang nh thanh CD; thanh CD co 2 au noiban le vi thanh AB va tran. Goc nghieng gia 2 thanh la 600,trong lng cac thanh khong ang ke. Cho2 ; 1AC CBm m (Hnh 1.4). Tm phan lc tai A va C khi au B chu lc thangng 10P kN .

C B

P

A

D

Hnh 1.4

Tra li: 5 3A X kN ; 5AY kN ; 10 3CDS kN ( Hng dan:CD la lien ket thanh, tai C chu ng lcS CD).


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BAI TAP C HOC LY THUYET BBAA II 11..55:: Cau (xem la ong chat)2AB a , trong lngP nam tren goi co

nh A va goi di ong B. tam caoh co lc gio nam ngang Q. Xac nh phan lA va B trong 2 trng hp:

a.- Goi di ong B di chuyen tren mat phang nam ngang (Hnh 1.5a).b.- Goi di ong B di chuyen tren mat phang nghien goc 300 vi phng ngang

(Hnh 1.5b).

B

Q

Ah B

Q

Ah

30

a.- b.-2a 2a

Hnh 1.5

Tra li: a.- A X Q ; 2 2AP h

Y Q a ; 2 2BP h

N Q a b.- 1

2 3 2 3A

P h X Q

a

;

2 2AP h

Y Qa

;3 3

BP h

N Qa

BBAA II 11..66:: Vom oi xng chu tac dung cuahe lc c thu gon thanh lc400Q kN at taiD va ngau lc1200D M kNm. Trong lng vom

800P kN , cac kch thc10a m ; 2b m ;5h m va 060 (Hnh 1.6). Xac nh phan lc

tai cac goi ta A va B.

QP

ba

A B

h

M

Hnh 1.6Tra li: 697A N kN ; 200B X kN ; 449BY kN

BBAA II 11..77:: Dam ong chat AB trong lngP co au A ta vao goc tng va nen nhan, au Bta vao nen nhan nghieng vi phng ngang goc

. Biet dam nghieng vi phng ngang goc (Hnh 1.7). Tm phan lc tac ong len dam tai Ava B.

P A

B

C

Hnh 1.7

Tra li:

sin cos

2cosA X P

;

cos cos1

2cosAY P

;

cos

2cosB N P


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BBAA II 11..88:: Nhan A long vao tam O nam trong matphang thang ng. Treo vao nhan vat nangP. Mat khac, buocvao nhan si day mem nhe ABC, au C (sau khi vat qua rongroc B at v tr cao nhat cua ng tron) treo vat nangQ (Hnh 1.8). Xac nh goc ng vi v tr can bang cua nhan.

Tra li: arccos2QP

OA

Q

P

B

C

Hnh 1.8

BBAA II 11..99:: Thanh ong chat AB trong lng20P N co truc quay nam ngang A, au B treo vat nang

1 200P N . Cung tai au B buoc si day, au day kia saukhi vat qua rong roc nho D treo vat nang200Q N . Biet

A nam ngang va AD AB(Hnh 1.9). Tm goc nghieng cua thanh khi can bang ong thi tm phan lc tai ban le A.

A

B

Q

P1D

Hnh 1.9

Tra li: sin 0, 5082 ; 172,3A X N ; 321,6AY N

BBAA II 11..1100:: Xac nh phan lc taingam A cua dam nam ngang AB tronglng khong ang ke chu lc nh Hnh

1.10. Tra li: 2,83A X kN ;1,67AY kN ; 5,39Am kNm

A BD

2kNm

4kN 3m 2m

1,5 kN m

Hnh 1.10

BBAA II 11..1111:: Xac nh phan lc tai ngamO cua dam nam ngang OA trong lng khongang ke chu lc nh Hnh 1.11.

Tra li: 2,5O X kN ;13,67OY kN ; 27,02Om kNm

AB

4kNm

5kN 4,5

m 3m

O

4kN m2kN m

Hnh 1.11


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BAI TAP C HOC LY THUYET

BBAA II 11..1122:: LcQ nam ngang at vaoau E cua moc ABCDE b ngam au A va codang nh Hnh 1.12 (AB DEva bang banknh R cua ng tron BCD). Xac nh phanlc ngam A, noi lc cac tiet dien B, C, D.

Tra li:

A

Q

B

C

D

E

R

Hnh 1.12

A X Q ; 0AY ; .Am Q R B X Q ; 0BY ; .Bm Q R

C X Q ; 0CY ; 2Cm QR D X Q ; 0DY ; Dm QR

BBAA II 11..1133:: Xe (A) chay tren2 banh xe D va E cach nhau 2m. Xemang theo can nam ngang5BC m ,au can la gau C ch quang nang

15Q kN (Hnh 1.13). Xac nhtrong lngP cua xe (tac dung trenng trung trc cua DE i qua B)e xe khong lat.

Tra li: 60P kN

(A)

B CD E

Hnh 1.13

BBAA II 11..1144:: Tm be day canthiet cua chan ap e ap khong b latkhi nc mc cao nhat6h m satmat ap. Xet 2 trng hp sau:

a.- Tiet dien ap la tam giac(Hnh 1.14a).

b.- Tiet dien ap la hnh thangco ay nho bang ay ln. Biet trong

lng rieng cua ap la324 kN m vacua nc la 310 kN m (Hnh 1.14b)

a.- b.-

h h

Hnh 1.14

Tra li: a.- 152

a m b.- 1511

a m


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1.2. BAI TOAN HE VAT:BBAA II 11..1155:: Hai thanh AB va CD c gi

nam ngang nh gan cac ban le A va D, ta len muiE va ta len nhau tai B (C). Kch thc cho trenHnh 1.15, bo qua trong lng cac thanh. 2 qua caunam tren thanh co cung trong lngP. Tm phanlc tai A, D, E va lc nen tai B.

A

3a a a a a

B E DC

Hnh 1.15

Tra li: 0A X ; 4AP

Y ; 0D X ; 8DP

Y ; 138E

N P ; 34B

N P

BBAA II 11..1166:: 2 thanh ADva DC c noi ban le vi

nhau tai D va co cac lien ketban le A, goi ta con lan B vaC chu cac lc4P kN va lcphan bo eu tren oan BC vi

AC

P q

8m 2m 5m 5mDB

45

Hnh 1.16cng o phan bo 2 kN q m . Bo qua trong lng cac thanh. Kch thHnh 1.16. Xac nh phan lc tai A, B, C va D.

Tra li: 2,82A X kN ; 4,43AY kN ; 22,26B N kN ;5C N kN ; 0D X ; 5DY kN

BBAA II 11..1177:: Thanh AB c gi thang ng nhlien ket ngam vi nen tai A, chu tac dung cua lcphan bo eu nam ngang doc theo chieu dai thanh vicng o2 kN q m . Thanh CD c gan ban le vaothanh AB tai C va c gi nam ngang nh thanhchong EF (tai E va F cung c gan ban le vao AB vaCD). Tac dung lc10P kN thang ng tai D. Boqua trong lng cac thanh. Cac kch thc cho trenHnh 1.17 ( 0,5l m ).

q D

P

F

E

A

C

B3 l= 1,5 m l

4 l

45

Hnh 1.17Xac nh phan lc tai A, C va cac ng lc trong thanh EF.Tra li: 4A X kN ; 10AY kN ; 24Am kNm

13,33C X kN ; 3,33CY kN ; 18,86EFS kN (chu nen)


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BBAA II 11..1188:: Cho he thanh chu lc va lienket nh Hnh 1.18. Cho5P kN , 30 M kNm,

0,9 kN q m . Xac nh phan lc tai A, B va C.

Tra li: 7,00A X kN ; 2,89AY kN ; 23,75Am kNm ;2,5B X kN ; 2,89BY kN ; 7,21C N kN

P

q

A

B

C

M 5m

4m

4m

4m

Hnh 1.18

BBAA II 11..1199:: Cho he thanh chu lc valien ket nh Hnh 1.19. Cho1 14P kN ;

2 12P kN ; 0,9 kN q m ; 20 M kNm. Xacnh phan lc tai A, B va C.

q P

45

P1 2

2m

M

2 m 2 m 1,5 m 1,5 m45

A

D B C

Hnh 1.19Tra li: 22,57A X kN ; 8,77AY kN ; 48,28Am kNm

12,67B X kN ; 0,67BY kN ; 17,91C N kN

BBAA II 11..2200:: oan ng doc nghienggoc 300 gom 2 oan 60AB m va 20BC m noi vi nhau bang ban le B va c gi bigoi co nh A va 2 cot chong CC va DD. Boqua trong lng dam va cac cot. Tren ngco oan tau AE, trong lng phan bo eu, moimet dai la 20k N. Tm phan lc tai A, ng lccac cot va lc tac dung tng ho tai B. Cho

40 ; 70AD AEm m . (Chieu cao oan tau

khong ang ke) (Hnh 1.20).

q

AD

D

C

C

BE

30

40m

60m

70m

80m

Hnh 1.20Tra li: 0A X ; 225AY kN ; 50CS kN ; 1125DS kN ;

0B X ; 150BY kN


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BBAA II 11..2211:: Thanh ong chat AB trong lngP ganvi nen bang ban le A va ta tren qua cau O, qua cau nayong chat trong lngQ, ta len nen va c gi nh dayAO (noi tam O vi chot ban le A). Biet thanh nghieng 600 vi nen (Hnh 1.21). Tm cac phan lc tai A, D va sc cangday AO.Tra li: 3

4A X P ; 3

4AY P ;

2DP

N Q ;2P

T

A60

O

D

B

Hnh 1.21

BBAA II 11..2222:: Tren ng nam ngang, xe ABtrong lngQ mang can BC trong lngP1 quayc quanh truc B va c gi bi day ED. au Ccua can gan mot rong roc nho kch thc khong ang

ke, mot day mem nhe vat qua rong roc, mot au daybuoc vat nangP, au kia buoc vao A. ChoAE EB BD DC va can nghieng vi phngnam ngang goc 600.

C

D

E 60

B

B '

A

P

A '

Hnh 1.22Tm phan lc tai 2 banh xe Ava B, sc cang day ED va lc tac du

ho tai ban le B, ieu kien e xe khong b lat quanh banh xe B.

Tra li: 12 4 2AQ P P

N ; 15 3

2 4 2BQ

N P P ; 1DET P ;

13

2B X P P ; 13

2BY P P

ieu kien xe khong lat:12P

Q P

BBAA II 11..2233:: Hai thanh 4 , 2AB ACa a trong lngkhong ang ke c ghep cng vi nhau (ngam) A va camsau vao tng (ngam) C. Cho060BAC va AC nam ngang.Tai iem gia va thang goc vi AB tac dung lcQ (Hnh1.23). Tm phan lc tai C va lc tac dung tng ho tai A.

Tra li: 32C

X Q ;2CQ

Y ; Cm Qa ;

32A

X Q ;2AQ

Y ; 2Am Qa

Q

A 60C

B

2a

2a

2a

Hnh 1.23


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BBAA II 11..2244:: Gian gom 7 thanh chu lc nh Hnh 1.24 va c bang goi co nh B va goi diong A. Tm phan lc tai A, B va ng lc trong cacthanh.

Tra li: 0B

X ; 2,75B

Y kN ;4,25A N kN ; 1 1,30S kN ; 2 3,03S kN ;

3 3,50S kN ; 4 2,50S kN ; 5 2,60S kN ;6 1,73S kN ; 7 1,73S kN

2kN

A B

2kN

1kN 2 kN

1 2

3

4

5 67

2m 2m

60

60

60

C

E

D

Hnh 1.24

BBAA II 11..2255:: Xac nh ng lc trong cac thanhva phan lc tai goi ta co nh D va goi ta di ong Ecua gian chu lc nh Hnh 1.25.

Tra li: 1 2S P ; 2S P ; 3S P ;4S P ; 5 2 2S P ; 36S P ; 7 0S ; 3E N P ;

3D X P ; 2DY P

AP

1

2

3

4

5

6

7

D

aa

a

PB E

C

Hnh 1.25

BBAA II 11..2266:: Xac nh phan lctai A va B cung nh ng lc tai cacthanh cua gian phang chu lc nh Hnh 1.26.

Tra li: 1,5A X kN ; 0,75AY kN ;

3,75B N kN ;

1

234

567

89

a =4 m a a

P =1 kN

A

P P

1,5 P

E

D C

BF

a

Hnh 1.26

1 2,50S kN ; 2 1,41S kN ; 3 2,25S kN ; 4 2,80S kN ; 5 1,12S kN ;6 0S ; 7 0S ; 8 1,68S kN ; 9 0S

BBAA II 11..2277:: Cho gian nh Hnh1.27. Xac nh phan lc tai A, B va nglc trong cac thanh 1, 2, 3 va 4.

Tra li: 20A X kN ;30AY kN ; 40B N kN ;

1 56,57S kN ; 2 40S kN ; 3 40S kN ;4 20S kN

1

2

3

4

E

D C

FA B

P = 20 k 4

P = 20 kN 1

P = 20 kN 2 P = 30 kN 3a a a

a

Hnh 1.27


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BBAA II 11..2288:: Hai banh xe 1 va 2ong chat trong lng1 981P N va

12 2

PP ta tren 2 ng oi nghieng

nhan vi cac goc nghieng 600 va 450.Truc cua 2 banh xe c gan ban le vithanh 1 2O O bo qua trong lng. Hoi lctac dung len truc 2 banh xe bang baonhieu e he can bang v tr truc1 2O O lech vi phng ngang goc 150. BietQ nghieng vi phng thang ng goc 600 (Hnh 1.28).

60 45

O2

O1

60

15

1

2Q

Hnh 1.28

Tra li: 262,86Q N

BBAA II 11..2299:: Hai khoi tru ong chat tamC1, C2 trong lng1 10P N , 2 30P N namta len nhau trong mot goc vuong tao bi 2mat OA va OB nghieng 600 va 300 so viphng ngang (Hnh 1.29). Tm goc nghieng cua oan noi 2 tam C1 va C2 khi he can bangcung nh tm lc ep cua 2 khoi tru len nhau.

Tra li: 00 ; 17,3 N N

60

O1

1

O 2

2A

O

B

30

Hnh 1.29

BBAA II 11..3300:: Thanh ong chat OA trong lngP c quayc quanh truc O va ta tai iem gia B cua no len qua caong chat C. Qua cau nay co trong lngQ, ban knh R c treovao truc O nh dayOD R . Biet OD hp vi OA goc 300 (Hnh1.30). Tm goc lech gia OD va ng thang ng khi he canbang.

Tra li: 3tan 4 3PQ P

C

O

B

A

D

30

Hnh 1.30


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BBAA II 11..3311:: Qua cau ong chat trong lngQ c treo vaotran O nh si day OD bang ban knh. Tai O treo si day mem nheOA, au A buoc vat nang trong lngP (Hnh 1.31). Tm goc lechcua si day OD so vi phng thang ng khi he can bang.

Tra li: sin 2P

Q P

C

O

A

D

Hnh 1.31

BBAA II 11..3322:: Thanh ong chat AB chieu dai 8a, trong lngP c gan ban le tai A. Doc theo thanh lap trn con chay O co tronglng 2P, con chay O c treo vao day OD. Biet OD ADa

(Hnh 1.32). Xac nh khoang cach AO khi he can bang, ong thixac nh lc cang day OD, phan lc ban le A va lc tac dung tngho gia con chay va thanh AB.

Tra li: AO a ; 2 3T P ; 3A X P ; 0AY ; 2 N P

OD

C

B

A

Hnh 1.32


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1.3. BAI TOAN MA SAT:BBAA II 11..3333:: Thang ong chat trong lngP ta vao tng

trn thang ng va san khong trn nam ngang. Biet he so ma satrt gia thang va san la f (Hnh 1.33). Phai at thang nghiengmot goc vi san bang bao nhieu e mot ngi trong lngQ co the treo len nh thang.

Tra li:

2

2tan Q P

f Q P

A

C

BP

Q

Hnh 1.33

BBAA II 11..3344:: Vong tron O ban knh R at co nhtrong mat phang thang ng. Thanh ong chat AB co 2 au A,B co the trt tren vong tron O. He so ma sat trt gia 2

thanh va vong tron la f . Biet khoang cach OC t tam vongtron en thanh AB bangb (Hnh 1.34). Xac nh goc hpbi OC va ng knh thang ng cua vong tron khi thanh canbang.

Tra li: 22

2

1cot

f b f

R f

O

A

B

C

b

R

Hnh 1.34

BBAA II 11..3355:: Truc (A) trong

lngQ at tren may trt namngang (B) tao bi 2 mat phangnghieng hp vi nhau goc . Biethe so ma sat trt gia truc vamang la f (Hnh 1.35). Tm lcngangP co the keo trt truc (A).

Tra li: sin

2

f P Q

(A)P

Q

(B) (B)

(A)

Hnh 1.35

BBAA II 11..3366:: Tru ong chat trong lngQ, ban knh R namkep gia 2 thanh ngang OA va OB cung gan ban le vao O. o dOA OB l . Truc cua tru va truc cua ban le O song song va namngang. Tac dung 2 lc ngc chieu nhau va cung bangP tai A va Bep tru lai. Biet he so ma sat gia thanh va tru la . Goc

1 1AOO BOO (Hnh 1.36). Xac nh tr so cuaP e tru canbang.

P

O

P

O1

BA

Hnh 1.36


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BAI TAP C HOC LY THUYET Tra li:

tan : f 2 sin cos sin 2 sin sin cos

QR QRP

l f l f

tan : f 2 sin sin cos

QRP

l f

BBAA II 11..3377:: Thanh ong chat AB co trong lngP, ta len nen khong nhan nam ngang tai A va cgi can bang vi tr nghieng 450 nh day BC buoc vaoB. Biet he so ma sat trt gia thanh va nen la f (Hnh1.37). Tm goc nghieng cua day BC vi phng namngang khi thanh trang thai sap trt.

Tra li: 1

tan 2 f

B

C

A

Hnh 1.37

BBAA II 11..3388:: Gia AB trong lng khongang ke, au B treo vat nangP, au A la ong truchieu dai2b m co the trt doc cot thang ngkhong nhan . Biet he so ma sat trt0,1 f (Hnh1.38). Xac nh khoang cacha gia truc cua cot ti

iem treo B e gia can bang.Tra li: 10

2b

a m f

P

b

a

A B

Hnh 1.38

BBAA II 11..3399:: Khoi tru ong chat trong lngQ namtren 2 gia (A) va (B), bo tr oi xng qua ng thangng i qua tam O cua khoi tru. He so ma sat trt giakhoi tru va gia la f (Hnh 1.39). Tm lc tiep tuyenthang ngP lam khoi tru bat au quay. Vi goc naose xay ra t ham.

P

(A) (B)

O

Hnh 1.39

Tra li: 21 cos

f P Q

f f

ieu kien t ham:2cos 1

f f


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BBAA II 11..4400:: 2 vat (A) va (B) trong lng 100 N va200 N at chong len nhau va at len nen nam ngang . He so ma sat gia (A) va (B) la1 0,5 f va gia (B) va nen la

2 0,2 f . Tac dung vao (A) mot lc60P N nghieng 300 vi phng nam ngang (Hnh 1.40). Hoi cac vat (A) va (B)co b trt khong?

(A )

(B)

P30

Hnh 1.40Tra li: Ca 2 vat (A) va (B) khong trt.BBAA II 11..4411:: Tren mat phang nghieng mot goc 300 so

vi phng ngang, co 2 vat (A) va (B) trong lng 200 N va400 N noi vi nhau bang si day khong dan . Biet he so masat gia (A) va (B) vi mat nghieng la0,5A f va 2 3B f (Hnh 1.41). He co can bang khong? Tm lc cangT cua day

noi va tr so cua cac lc ma sat.

( B )

30 ( A )

Hnh 1.41Tra li: He can bang.86,6AmsF N ; 213,4BmsF N ; 13,4T N BBAA II 11..4422:: Banh xe O co xu hng quay

di tac dung cua ngau lcm. e gi can bang,dung lcQ thang ng at tai au C cua onnam ngang AC quay c quanh truc A e epma ham B vao vanh banh xe. Biet he so ma sat

0,1 f , t so 0,2ABAC . Ban knh banh xe

0,4 R m ; momen 10m kNm (Hnh 1.42).

Q

A

O

B Cm

Hnh 1.42

Xac nh lcQ can thiet e ham banh xe.Tra li: 50Q kN BBAA II 11..4433:: 2 banh xe

O1 va O2 truyen ong chonhau bang day ai. Banh xeO1 co ban knh R1 va chu tacdung cua ngau lcm. Banhxe O2 co 2 tang: tang ngoaimac day ai co ban knh R2,tang trong co ban knhr 2 vacuon vao mot day, au daytreo vat nangP (Hnh 1.43).

P

O

R

r R

m2 O 1

2

2

1

Hnh 1.43Tm lien he giam vaP khi he can bang. Tm sc cang ban auS 0 cua day ai

can thiet e truyen ong. Biet he so ma sat trt gia day ai f ; gocom banh xe O1 la ; tong sc cang 2 nhanh day la 2S o.


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Tra li: ieu kien can bang:21 2

m r P

R R

0 11

2 1

f

f

m eS

R e

BBAA II 11..4444:: Banh xe O ban knh R bo qua trong lng,chu lcQ tac ong vao tam O nghieng xuong di so vi

phng nam ngang so vi phng ngang goc . Biet he so masat trt gia banh xe va mat ng la f , con he so ma sat lanlak (Hnh 1.44). Tm goc nghienge banh xe can bang.

O Q

Hnh 1.44

Tra li: cot min , k f R

BBAA II 11..4455:: Tren ng nam ngang co banh xe ongchat tam O, ban knh R, trong lngP chu ngau lcm va valcQ nh Hnh 1.45. Biet he so ma sat trt f va he so ma satlank . Xac nh tr so momenm va tr so lcQ e banh xe canbang.

Tra li: min . ,

. . . .

k mQ f P P

R R

Q R k P m Q R k P

OQ

m

Hnh 1.45

BBAA II 11..4466:: Tren ng nam ngang co chiec xe 2banh. Cac banh xe A va B ong chat cung trong lngP, banknh R noi vi nhau bang than xe AB (xem nh thanh ongchat) trong lngP1. Gia cac banh xe va mat ng co masat trt he so f va ma sat lan he so k (Hnh 1.46).

B QA

Hnh 1.46

Tm lc nam ngangQ can at vao than xe e xe trang thai sap lan kh

Tra li: 1 12 2k Q P P f P P R

BBAA II 11..4477:: Tam go trong lngP1 at tren 2con lan cung trong lngP va ban knh R, cac con lannam tren mat ng nam ngang. Biet he so ma sat trt

gia tam go va con lan cung nh gia con lan va matng la f ; con he so ma sat lan lak . Trong tam G cuatam go cach cac truc cua con lan laa vab (Hnh 1.47).Xac nh lc nam ngangQ at vao tam go e cac conlan trang thai sap lan khong trt.

A

Q

B

P P

G

a b

P1

Hnh 1.47

Tra li: 1 12 .2k

Q P P f P R


15/70



16/70


2. CAC BAI TOAN VE HE LC KHONG GIANBBAA II 22..11:: Vat nangP c treo vao au

O cua mot gia treo tao bi 3 thanh trong lngkhong ang ke, gan vi nhau va gan vao tngbang cac ban le (Hnh 2.1). Tm ng lc cacthanh.

Tra li: 2OAS P ;2

2OB OCS S P

x y

C

B

O

A P

4545

45

Hnh 2.1

BBAA II 22..22:: e keo vat nangP, ngi tadung ti E va gia 3 chan ABCD e keo rongroc A nh Hnh 2.2. Biet BCD la tam giac euco ng cao DE. Ba chan AB, AC, AD va dayAE nghieng cung 600 vi mat at nam ngang.Tnh ng lc thanh.

Tra li: 2 23 3 3

AB ACS S P

1 2

3 3 3ADS P

C

B

A

P60

D

E

60

Hnh 2.2

BBAA II 22..33:: Cho can cau nh Hnh 2.3. Biet1 ; 1,5AD BD CDm m ; 1CM m ; 4KL m . Trong

lng can cau ke ca oi trong100P kN . Trong tam Gcua can cau nam trong mat phang LMFN va cach MNmot oan 0,5m. Trong lng vat nang30Q kN . Tmphan lc tai 3 banh xe khi mat phang thang ngLMFN song song vi AB.

Tra li: 8,33

A N kN ;78,33

B N kN ;43,33C N kN

Q

C

BAF

N

L

M

D

4 mK

G

0,5 m

Hnh 2.3


17/70

CAC BAI TOAN VE HE LC KHONG GIAN 17

BBAA II 22..44:: Tam trong lng khong ang ke, namngang tren mui nhon tam O cua tam. Tren chu vi cua tamat 3 iem nang trong lng1 1,5P N ; 2 1P N va 3 2P N sao cho tam tron van can bang (Hnh 2.4). Xac nh goc

AOB , AOC Tra li: 075 30 ; 0151

PP

P3

21

C

AB

Hnh 2.4

BBAA II 22..55:: Tam go ong chat hnh vuong ABCDtrong lngP c v tr nam ngang nh 6 thanh boqua trong lng nh Hnh 2.5. Toan hnh co dang khoilap phng. Tm ng lc cac thanh chong.

Tra li: 1 3 4 5

0S S S S ;2 6 2

PS S

A B

CD

4

56

3

1

2

P

Hnh 2.5

BBAA II 22..66:: Tam go ong chat hnh vuongABCD trong lngP c v tr nam ngangnh 6 thanh bo qua trong lng nh Hnh 2.6.Toan hnh co dang khoi lap phng. Tac dung

them lc P doc theo canh CD. Tm ng lc cacthanh chong.

Tra li: 1S P ; 2 2S P ; 332

S P ;

4 2S P ; 5 2S P ; 63

2S P

A B

CD

1

23

456

P

P

Hnh 2.6

BBAA II 22..77:: Xet tam go nh bai BAI 2.5:, themngau lcm nam trong mat phang ABCD theo chieungc kim ong ho (Hnh 2.7). Tm ng lc cac thanh.Cho biet canh tam go laa.

Tra li: 1 2m

Sa

; 2 2P m

Sa

; 3 0S ;

4

mS

a; 5 2

mS

a ; 6 2

PS

A B

CD

4

56

3

12

P

m

Hnh 2.7


18/70


BBAA II 22..88:: Tam go ong chat hnh chnhat ABCD, trong lng 200 N mac vao tngnh goc cau A, ban le B va c gi canbang v tr nam ngang nh day CE nghieng600 vi ng thang ng EA. Biet ngcheo AC lap vi canh AB goc 300 (Hnh 2.8).Tm phan lc tai A, B va lc cang day CE.

Tra li: 50 3A X N ; 150AY N ;100A Z N ; 0B B X Z ; 200T N

DC

BA

E

y

x

z

Hnh 2.8

BBAA II 22..99:: Canh ca ong chat hnh chnhat ABCD, trong lngP co chieu dai2AB a ;chieu rong ADa , co truc quay thang ng ABvi 2 goi cau A va ban le B. Ca c m motgoc bang 1200 vi khuon ca. au D chuQ songsong vi canh di EA cua khuon ca. au C cgi bi day CE (Hnh 2.9). Tm sc cang day CEva phan lc cac o .

Tra li: 7T Q ; 3 48A

X P Q ;

E

B

C

D x

z

yA

Q120

Hnh 2.9

8 2AP Q

Y ; 2A Z P Q ;3

8B X P ;

8BP

Y Q

BBAA II 22..1100:: 2 goi A, B (ban le) truc nam ngang AB mang theo banhxe (C) va trong (F) gan cng vao truc;ban knh banh xe (C) gap 6 lan ban knhtrong (F). Quanh trong cuon day treo vatnangQ; quanh vanh banh xe cung cuonday va au t do sau khi vat qua rongroc co nh (D) treo vat nang60P N .Bo qua kch thc rong roc va cac kchthc khac cho tren Hnh 2.10. Nhanhday gia 2 banh xe va rong roc (D) namtrong mat phang song song vi matphang A xz va nghieng vi phng namngang goc 030 .

B(C) A

P

Q

a=0,5 m 2a=1,0 m 0,5 m

x

z

y(F)

(D)

Hnh 2.10

TmQ va phan lc cac o A, B khi he can bang.Tra li: 360Q N ; 69,28A X N ; 17,32B X N ; 160A Z N ; 230B Z N


19/70


BBAA II 22..1111:: Dam ong chat OC tronglng 1000P N , dai 2m c gi nam ngangnh gan vao ban le cau O va 2 day treo CD vaAB. Dam chu tac dung cua ngau lc ,Q Q nam trong mat phang O xy vi 100Q N ;

20EF cm . Cho 0,5OB m (Hnh 2.11). Tmphan lc tai O va lc cang cac day.

B

D

A x

z

yO

Q

Q' CE

F

30

30

Hnh 2.11

Tra li: 2 405

X Q N ; 2 3 3 935,315 2

Y Q P N ; 5002P

Z N ;4

805B

T Q N ; 1000CT P N

BBAA II 22..1122:: Gian khong giangom 6 thanh, trong lng khong angke. Thanh AB nam ngang, ABCD lahnh ch nhat trong mat phang thangng. Lc 1P kN trong mat phangABCD, goc 045 (Hnh 2.12). Xacnh ng lc trong cac thanh.

B

D

A

C

P

1

23

4

5

6

Hnh 2.12Tra li: 1 2 0,5S S kN ; 3 0,7S kN ; 4 5 0,5S S kN ; 6 1S kN BBAA II 22..1133:: Gian khong gian gom 6 thanh, trong lng

khong ang ke. ABCD nam trong mat phang thang ng vuongoc vi tng. Tai nut A tac dung lc thang ngP , goc 045 (Hnh 2.13). Tm ng lc trong cac thanh.

Tra li:

1 26

PS S ; 3

2

3

PS ; 4 5

3 1

6S S P ; 6 2S P

BD

C

P1

2

3

45

6

A

E

K

F

MN

30

Hnh 2.13

BBAA II 22..1144:: Cot AB cua mot cau truc gi v tr thangng nh lien ket coi tru A va 2 thanh bo qua trong lng BCva BD. Vat c cau co trong lngP treo moc G lien ketvi cot nh day BG va thanh bo qua trong lng GE. BietBE AE. Cac goc can thiet cho tren Hnh 2.14. Tm phanlc tai A, sc cang day BG va ng lc tai thanh GE.

Tra li:

B

D

C

G

E

x

z

y

A

60

60

P

30 60

45

Hnh 2.14


20/70


T P ; 2GES P ;3

2CS P ;

2DP

S ;4AP

X ; 34A

Y P ; 7 34A

Z P

BBAA II 22..1155:: Hai canh cahnh ch nhat ong chat ABCD vaABCD cung trong lngP, cungchieu daiAB A B a ; chieu rongAD A D b c mac ban le A, B,A, B vi nen nam ngang va noi vinhau bang ban le E. AAD tao thanhtam giac eu. Biet

4DE a (Hnh

2.15). Tm phan lc cac ban le. x

z

yO

A ' A

B

C ' C

B ' D ' D

E

Hnh 2.15

Tra li: 38A

Y P ;2AP

Z ; 324B

Y P ;2BP

Z ; 36E

Y P ; 0E Z ;

38A

Y P ;2AP

Z ; 324B

Y P ;2BP

Z

BBAA II 22..1166:: Gia 3chan EABD co dang chop eu,lien ket vi 2 dam conxon namngang song song vi nhaubang cac goi cau. Tai E co

rong roc nho, vat qua no siday, mot au buot vat nangP,au kia quan vao truc cua motti co nh sao cho nhanh daynay nam ngang va song songvi

BD

A

x

z

yO

E

P

l4 l2

Hnh 2.16

AB. Bo qua trong lng cac thanh lam chan gia cung nh trong lng vdam conxon. Cac kch thc khac ghi tren Hnh 2.16. Tm phan lc ngaconxon 2 chan A va B.

Tra li: 26O

X P ; OY P ; 23O Z P ;

6 26 x

m Pl ; 0 ym ;3 2

12 zm Pl


21/70



22/70


23/70

CAC BAI TOAN TM TRONG TAM 23

BBAA II 33..33:: Xac nh trong tam cac tamong chat co hnh dang va kch thc nh Hnh 3.3. Cho 12a cm ; 6 R cm

Tra li: a.- 3 4 ,0 2,23 ;048 6

cma

b.- 14, 1 ;2,976 9

cm cm R R

a.- b.-

xO

a

a

a

2

xO

y

R R2

Hnh 3.3

BBAA II 33..44:: Xac nh trong tam cac tam ong chat co hnh danh Hnh 3.4.

a.- b.-

yO

z

x

a

a

aa

2 a

2 a

a

a

2 aa

2 a

2 a

y

z

x

O

Hnh 3.4

Tra li: a.- 910G G

x y a ; 710G

z a b.- 1314G G G

x y z a

BBAA II 33..55:: Xac nh trong tam cac tam ong chat gii han btren Hnh 3.5.

a.-

y

x

y

xO Oa a

y= x

y=x 2

b.-

y

xO y= sin x

c.-

y

xO

y=x 2

y= x

d.- Hnh 3.5

Tra li: a.- 34G

x a ; 2310G

y a b.- 35G

x a ; 38G

y a

c.-2G

x ;

8G y

d.- 920G G

x y


24/70

BAI TAP C HOC LY THUYET BBAA II 33..66:: Dung cong thc Guyanh xac nh trong tam cua cung

tron thuoc vong tron ban knh R va co goc tai tam02

Tra li: 0sin0

d R

; 0

0

sin23

d R

BBAA II 33..77:: Tm the tch cua khoi hnh xuyen tao nen bi tiet dien:a.- Tam giac vuong can, canh goc vuong banga.b.- Na mat tron ban knhr .

Khi quay quanh truc z vuong goc va cach ay mot oan bang R (Hnh 3.6).

a.-

z

b.-

R

a

a

z

R

r

Hnh 3.6

Tra li: a.-2

23 2a a

V R

; b.- 2 2V r R r


25/70

CAC BAI TOAN TM TRONG TAM 25


26/70


PHAN B: ONG HOC VA ONG LC HO4. CHUYEN ONG CHAT IEM 4.1. ONG HOC IEM:

BBAA II 44..11:: Mot iem chuyen ong theo phng trnh cho trc, tm ptrnh quy ao va ch ra hng chuyen ong.

a.- 3 5 x t ; 4 2 y t b.- 2 x t ; 28 y t c.- 5sin10 x t ; 3cos10 y t d.- 2 3cos5 x t ; 4 sin 5 1 y t

BBAA II 44..22:: Cho phng trnh chuyen ong cua iem, tm quy aoa.- 220 5 x t ; 215 3 y t b.- 24 2 x t t ; 23 1,5 y t t c.- 3cos 5 x t ; 4sin y t d.- 2 x at ; y bt e.- 3 4cos x t ; 2 5sin y t

f.- 5cos x t ; 3 5sin y t

BBAA II 44..33:: Mot au bua ap vao coc, sau o chuyen ong cung vthi gian 0,02s th dng lai. Biet coc nhan sau xuong at 6cm. Hay xac nh van tocban au cua coc, coi rang no chuyen ong cham dan eu.

Tra li: 0 6 mv s

BBAA II 44..44:: Hai 2 iem cung bat au chuyen ong t 1 iem tren voknh 16 R m theo hai chieu ngc nhau. iem th nhat chuyen ong t1 2sin 2

s bt t vib la hang so; con iem th hai co gia toc phap24na t . Khi 2

iem gap nhau th gia toc cua iem th hai bang24 5 m s . Tmb va thi iem gapnhau.

Tra li: 32 6b ; 1t s


27/70

CHUYEN ONG CHAT IEM 27 BBAA II 44..55:: Tau hoa chuyen ong vi van toc au54 km h , trong 30s au no i

c 600m. Coi chuyen ong cua tau la bien oi eu. Xac nh vagiay th 30 neu tau chuyen ong tren ng vong ban knh1000 R m .

Tra li: 25 mv s ; 20,708 ma s

BBAA II 44..66:: Tau hoa chuyen ong cham dan eu tren cung 800 R m va i c quang ng800s m vi van toc au0 54 kmv h , van toc

cuoi 18 kmv h . Xac nh gia toc cua tau tai iem au va iem ccung nh thi gian i c quang ng o.

Tra li: 20 0,308 ma s ; 21 0,129ma

s; 1 80t s

BBAA II 44..77:: Tau hoa ri ga vi chuyen ong nhanh dan eu, sa

van toc72 kmv h . ng tau la mot ng cong co ban knh800 R m . Tm gia toctiep tuyen, gia toc phap tuyen va gia toc toan phan khi tau ri

Tra li: 219

mas

; 229

n mas

; 20,248 ma s

BBAA II 44..88:: Mot vien an chuyen ong trong mat phang thaphng trnh: 300 x t ; 2400 5 y t t (t : giay; x, y: met)

Xac nh:a.- Van toc, gia toc vien an tai thi iem au.b.- o cao va tam xa vien an.c.- Ban knh cong quyao tai thi iem au va iem cao nhat cu

Tra li: a.-2

5000 :

10

mv st ma

s

; b.- maxmax

24000

8000

x m

y m; c.-

1

041667

9000t

t t

m

m

BBAA II 44..99:: Mot iem chuyen ong nhanh daneu len mat phang nghieng AB, sau o cham dan eutren mat ngang va cuoi cung dng lai C. Biet

1AB s ; 2BC s va thi gian iem chuyen ong t Aen C laT (Hnh 4.1). Tm tr so cac gia toca1 vaa2 khi iem chuyen ong tren AB va BC. Luc au A,van toc cua iem bang 0.

B

A

Cs

s

1

2

Hnh 4.1

Tra li: 2

1 21 2

1

2 s sa

s T ;

2

1 22 2

2

2 s sa

s T


28/70

BAI TAP C HOC LY THUYET BBAA II 44..1100:: iem M chuyen ong tren ng tron ban knh8 R m vi tam C

co toa o 8,0 . V tr cua iem tren vong tron c xac nh bang goc knh vect CMcua iem va truc x.

sin2 2

t

a.- Lap phng trnh chuyen ong cua iem dang toa o t nnh van toc, gia toc toan phan cua iem luc au va luc hng cuoi.

b.- Lap phng trnh chuyen ong cua iem dang toa o e c

Tra li: a.- 4 sin2

s t m

;

2

4

2

20 :

2

mv st

mas

b.- 8 8cos sin2 2

x t m ; 8sin sin

2 2 y t m

BBAA II 44..1111:: Tm phng trnh chuyen ong doc quy ao cua iem nphng trnh chuyen ong dang toa o e cac:

a.- 23 5 x t ; 24 3 y t b.- cos x a t ; sin y a t ; z ct

c.- cost

x e t ; sint

y e t ;t

z e d.- 24 cos x a t ; 23 sin y a t

Tra li: a.- 25s t b.- 2 2s a c t c.- 3 1t s e d.- 25 sins a t

BBAA II 44..1122:: Mot iem chuyen ong theo ng inh oc co phn2cos4 x t ; 2sin4 y t ; 2 z t , , : x y z m . Tm ban knh cong cua quy ao.

Tra li: 2,125 constm

BBAA II 44..1133:: C cau tay quay thanh truyen vi60AB OA l cm (Hnh 4.2). Biet4 t . Tm quy

ao iem M cua thanh truyen 3MB l . Tm vantoc, gia toc va ban knh cong quy ao cua iem M taiv tr 0 .

A

B

y

xO

l l3M

l

Hnh 4.2


29/70

CHUYEN ONG CHAT IEM 29

Tra li: Quy ao iem M la ng Elip co phng trnh2 2

2 2 1100 20 x y

Khi 2 2

80

0 : 1600

4

M

M

M

cmv scma

scm

BBAA II 44..1144:: Banh xe lan khong trt theong nam ngang (Hnh 4.3), mot iem tren vanhbanh xe co chuyen ong xicloit vi phng trnh:

20 sin20

1 cos 20

x t t m

y t

y

xOA

MC

Hnh 4.3Tm gia toc va ban knh cong cua iem M. Xac nh gia tr

iem M luc0t .Tra li: 2400 constma s co hng doc MC;2. 4sin10AM t ; 0 0t

BBAA II 44..1155:: Day cap c keo sao cho tai iemA co van toc i xuong khong oi bang6A mv s (Hnh 4.4). Xac nh van toc vat (B) c keo len laham cua toa o thang ng y cua no.

Tra li: 2

163B yv y (B ) A

DC

E

Av

4 m 4 m

y

Hnh 4.4

BBAA II 44..1166:: Neu iem A cua day cap ha xuong vi gia toc22A ma s khi vantoc cua no6A mv s (trong BAI 4.15:). Xac nh van toc va gia toc v(B) tai thi iem khi3 y m

Tra li: 5B mv s ; 27B ma s (chon truc y thang ng xuong d


30/70


BBAA II 44..1177:: e a vatnang A len cao, ngi ta buocday vao no, vat qua rong roc co nh (C) vi gia thiet bo quakch thc va au kia cua daybuoc vao thanh B cua oto. Bietoto chuyen ong ngang vi vantoc khong oi7,2B kmv h (Hnh 4.5). Xac nh van toc vatA khi no len cao c khoangcach 20As m . Biet khi 0Bs

BvB

A30 m

C

sA

sB

Hnh 4.5

th 0As (khi o B trung vi A) hay o dai day bang 60m.

Tra li: 1,6A mvs

BBAA II 44..1188:: Xac nh gia toc vat A khi no len cao c khoang cach20As m (trong BAI 4.17:), neu khi o biet xe co gia toc20,6 m s va van toc2

ms

Tra li: 20,51A ma s (chon truc y thang ng hng len)


31/70


4.2. ONG LC HOC IEM:

4.2.1. Cac bai toan thuan:BBAA II 44..1199:: Mot xe gong co khoi lng 700kg ang chay xuong doc doc

ng ray thang va nghieng mot goc 150

vi phng nam ngang. e gi choeu, ngi ta dung day cap song song vi mat doc. Van toc1,6 m s . Xac nh lc cang day cap luc xe chay eu va khi no b4giay. He so can chuyen ong tong cong la0,015 f va luc ham coi rang xecham dan eu.

Tra li: 1 1677,8T N ; 2 1959,2T N

BBAA II 44..2200:: Mot oan tau hoa khong ke au may co khoi lnhanh dan tren oan ray thang nam ngang. Sau 60 giay ke t luc van toc54 km h . Tnh lc keo cua au may len oan toa cho mcan chuyen ong bang 0,005 trong lng oan tau.

Tra li: 59810k F N

BBAA II 44..2211:: Mot may bay co khoi lng 2000kg bay thang ngang vi gia 25 m s. Lc can cua khong kh hng ngc chieu van toc va t l

toc, co cng o 0,49 N khi van toc at gia tr1m s . Xac nh lc keo cua camay bay khi may bay at van toc200 m s . Biet lc nay hp vi hng bay g

0.

Tra li: 30057k F N

BBAA II 44..2222:: Oto ch hang co khoi lng 6 tan chay xuong van toc21,6 km h . T luc bat au xuong pha en luc dng lai, xng 10m, cho rang luc o oto chay cham dan eu. Tnh lc can

day cap) buoc gi pha, coi rang day cap luon cang.Tra li: 5400T N

BBAA II 44..2233:: Mot cai sang quang thc hien dao ong ieu hoabien o 5 A cm. Tm tan so nho nhat cua sang e cac hat quang basang.

Tra li: 14g rad A s


32/70

BAI TAP C HOC LY THUYET BBAA II 44..2244:: Mot au may tau hoa co khoi lng180 tanm chay qua mot cai

cau vi van toc72 km h . Khi au may chay qua iem chnh gia cau th o vcau la 0,1h m . Hay xac nh ap lc phu len cau tai thi iem o. Gianh mot dam co tiet dien khong oi, co o dai100 L m va au khp co nh. Bo qu

kch thc va trong lng au tau.(Gi y: Ban knh cong cua dam tai iem gia

2

12 L

h )

Tra li: 2

2

128640

mhv N N

L

BBAA II 44..2255:: Mot chiec xe ap i tren mot oan ng cong ban knh10 m vivan toc5 m s . Hay tm goc nghieng cua mat phang oi xng doc cua xe a

phng thang ng, ong thi he so ma sat f nho nhat gia lop xe va mat ng khong b o.Tra li: 014 20 ; 0,255 f

BBAA II 44..2266:: May bay bo nhao thang ng at c van toc1000 km h , sau ongi lai a may bay ra khoi hng bo nhao va vach thanh cung

600 R m trong mat phang thang ng. Trong lng ngi lai la 800 N . Hoi ngi laia ep len ghe ngoi mot lc cc ai bang bao nhieu?

Tra li: max 11300 N N

BBAA II 44..2277:: Cho c cau ieu tiet ly tam nh Hnh 4.6, vat Mco khoi lngm gan vi truc quay bang bang ban le bi 2 thanhAM va BM. Xac nh ng lc trong cac thanh neu bo qua tronglng thanh. Choconst ; AM BM l ; 2AB a

Tra li: 22Aml

S a ga

; 22Bml

S a ga

M

A

B

l

l

2a

Hnh 4.6


33/70


4.2.2. Cac bai toan ngc:BBAA II 44..2288:: Mot hon a ri xuong gieng can khong van toc

6,5s ngi ta nghe thay tieng va ap cua hon a vao ay gieng. la330 m s . Tm chieu sau gieng.

Tra li: 175h m

BBAA II 44..2299:: Mot ngi lai tau ien bang cach m dan ien suat ong c sao cho lc keo tang t le theo thi gian t gia trtang c 1177 N . Tm quang ngs tau i c trong cac ieu kien sau: ktau bang 10 tan; lc ma sat khong oi bang31,96.10 N . Van toc au bang 0.

Tra li: 3

50,01962

3s t m

BBAA II 44..3300:: Mot vat nang nam trong mat phang nghieng v030 . Ngi ta tao cho vat van toc au0 15 mv s hng theo pha i len cua

Biet he so ma sat gia vat va mat nghieng0,1 f . Tm oan ng vat nang en khi dng lai va thi gian vat i c oan ng o.

Tra li: 19,55s m ; 2,61t s

BBAA II 44..3311:: Tm van toc ri ln nhat cua mot qua cau co kho10 kg , banknh 8 R cm, chuyen ong ri trong khong kh chu lc can2cF kSv (trong ov lavan toc ri,S la dien tch hnh chieu cua vat ri tren mat phang thari z; k he so t le la hang so bang2 40,2352 Ns m

Tra li: 144,4 mv s

BBAA II 44..3322::

Mot chiec tau thuy trong lngP chuyen ong thang ngang tthai ngh. Lc ay cua chan vt khong oi bangQ va hng theo hng tau cong. Lc can cua nc co tr so 2 2P R k v

gvik la he so t le;v la van toc tau. T

gia tr cua van toc ti han va bieu thc van toc con tau la hong.

Tra li: 1thQg

vk P

; 11th

t

t

ev t v

e

; 22 thk v


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BAI TAP C HOC LY THUYET BBAA II 44..3333:: Mot chiec tau lan ang nam yen, nhan c mot tai troP th lan

xuong sau theo phng thang ng, khi o co the coi nh lc can cua le vi van toc lan cua con tau R kSv, trong o:k la he so t le;S la dien tch hnhchieu bang cua con tau;v la van toc lan. Biet khoi lng tau lam. Tm bieu thc vantoc cua con tau la ham theo thi gian. Tm khoang thi gianT can thiet e van toc lan

bang 95% gia tr van toc ti han.Tra li: 1

kSt

mPv ekS

; ln20mT

kS

BBAA II 44..3344:: oan tau hoa sau khi at toc o0v th chuyen ong di tac dungcua lc tong hp ma cng o tnh theo mot n v khoi lng cua thc: 2 f v a bv cv , trong o:a, b, c la cac hang so;v la van toc oan tau. Tmbieu thc cuav va tm gia tr ti han cua no.

Tra li:

1

c t

c t

Aev

Ae

, trong o: 00

v A

v

; , la cac nghiem ln,

be cua phng trnh 0 f v

BBAA II 44..3355:: e giam lc truyen vao nen khi vat co khoilngm chu tac dung cua lc 0 sinF F t , ngi ta lap hethong giam chan gom lo xo co o cngc va bo can thuy lc cohe so can (lc can R v ) (Hnh 4.7). Xac nh gia tr lnnhat cua ap lc ong lc ma he thong dao ong truyen vao nentrong che o bnh on.

F

c

Hnh 4.7

Tra li:

4 2 2

max 0 22 2 2 2

4

4

k b N F

k b

; trong o:2 ck

m;

2b

m

BBAA II 44..3366:: Tren san bang co 2 ngi nam 2 au cua si day nam A nang 500 N va ngi B nang 700 N . Neu ngi A keo vao day mot lc nam bang 100 N th si day tac ong vao ngi B lc bang bao nhieu? Tm giangi. Bo qua ma sat.

Tra li: 100A BF F N ; 21,96A ma s ; 21,4Bma

s


35/70


BBAA II 44..3377:: Thang may (E) co khoi lng 500kg va oi trong(A) co khoi lng 150kg. Neu mot dam ong tao ra lc keo khongoi 5kN at vao cap tai B (Hnh 4.8), xac nh van toc cua thang mtai thi iem3t s t khi khi hanh trang thai ngh. Bo qua kholng cac rong roc va cap.

Tra li: 7,23E mv s

B

(A)

(E)

Hnh 4.8

BBAA II 44..3388:: Cung BAI 4.37:, biet sau khi len cao 40m, thang may co van 10 m s . Xac nh lc keo cua cap tai B do mo t tao ra.

Tra li: 4246B N N

BBAA II 44..3399:: Tai trongP c nem len vi van toc ban au0v va nghieng mogoc vi phng nam ngang se chuyen ong di tac dung cuacan khong kh R t le vi bac nhat vi van toc theo luat R kPv , trong o:k -he so tle la hang so. Tm o cao cc aih cua tai trong so vi v tr ban au.

Tra li: 0 02sin 1

ln sin 1v

h kvkg k g

BBAA II 44..4400:: Vat (B) c keo len nh gan vaorong roc ong, rong roc nay bo qua kch thc va macvao day, mot au buoc co nh vao A, au kia vat quarong rocc va keo bang lcF nam ngang. Bo qua khoilng cac rong roc va ma sat (Hnh 4.9).

A

(B)

C

d

y

aB

F

Hnh 4.9Xac nh t so lcF la ham cua khoang cach y e cho gia tocBa la khong o

Cho (B) co khoi lngm vaCA d

Tra li: 2 24

4Bm a g d yF

y

BBAA II 44..4411:: Mot vien bi trong lngP nam v tr thap nhatcua mot ranh co dang ng tron ban knh R at trong mat phangthang ng (Hnh 4.10). Hoi phai truyen cho vien vi van toc ban bang bao nhieu e vien bi co the i het ranh tron. Bo qua ma sa

Tra li: 0 5v gR

O R

v0Hnh 4.10


36/70


BBAA II 44..4422:: Vat M treo tren si day dail. Hay xac nh van tocban au0v nho nhat bang bao nhieu can phai truyen cho M theophng vuong goc vi day e M quay u vong tron (Hnh 4.11).

Tra li: 0 5v gl M0v

0

O lM

Hnh 4.11

BBAA II 44..4433:: Mot chat iem co khoi lngm chuyen ong trong mat phang namngang di tac dung cua lc ay t mot tam O co nh theo luat:2F k mr ; trong o:k la hang so;m la khoi lng chat iem; conr la vect nh v chat c iem tnh ttam O. thi iem au, chat iem 0 ,0M a co van toc0v song song vi truc O y.Xac nh quy ao chat iem.

Tra li: 2 2 2

2 2

0

1 x k y

a v

la ng Hyperbol


37/70



38/70


5. CAC DANG CHUYEN ONG CUA VAT RAN 5.1. CHUYEN ONG QUAY QUANH TRUC CO NH:

BBAA II 55..11:: Vat A chuyen ong trttren mat phang nam nghieng nh si daykhong dan truyen chuyen ong quay chobanh xe kep I, banh xe kep I truyen quay chobanh xe II nh an khp ngoai (Hnh 5.1). Taithi iem khao sat, vat (A) co van tocAv ,gia tocAa .

M

O1

R R1

O 2

R 2 (A )

I

II

Hnh 5.1Xac nh van toc goc banh xe II cung nh van toc, gia toc cua

Tra li: 122

A R

v R R

; 1M A R

v v R

;2

1 12 2

2

2 4M A A

R Ra a v

R R R

BBAA II 55..22:: Khi tat ong c co canh quat cua may bay co van1200 vongphutn va no quay c 80 vong th dng lai. Tm thi gian lu

c en khi canh quat dng. Coi chuyen ong canh quat la quay cham dTra li: 8T s

BBAA II 55..33:: Mot banh a co ban knh2 R m ang ng yen bat au quay vgia toc goc khong oi. Sau 10s cac iem nam tren vanh co van toc100 mv s . Tmvan toc, gia toc tiep tuyen, gia toc phap tuyen cua cac iem tren v

15t s .Tra li: 150 mv s ; 210 ma s

; 211250n ma s

BBAA II 55..44:: Truc A co ban knh10 R cmquayc nh qua canP treo vao mot si day khong danquan vao truc. Biet qua can chuyen ong theo phngtrnh: 2100 x t , trong o: x la khoang cach t qua canen ng nam ngang co nh1OO ( x tnh bangcm; t tnh bangs) (Hnh 5.2). Xac nh van toc goc va giatoc goc cua truc cung nh gia toc toan phana cuaiem tren be mat truc tai thi iemt bat ky.

P

O O 1

x

R

Hnh 5.2

Tra li: 20 rad t s ; 220 rad s ; 4 2200 1 400 cma t s


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CAC DANG CHUYEN ONG CUA VAT RAN 39

BBAA II 55..55:: C cau cua xe ti lam chotai trong B chuyen ong thang ng khi quaytay quaya. Do bo phan ham b hong, tai trongbat thnh lnh ri xuong. Phng trnh chuyenong cua tai B la 25 x t cm (t tnh bangs).Truc O x hng thang ng xuong di. Biet

200d mm , so rang cua banh xe tng ngla: 1 13 z ; 2 39 z ; 3 11 z ; 4 77 z (Hnh5.3). Xac nh van toc va gia toc cua iemau A cua tay quaya co o dai400 mm saukhi he chuyen ong c 2s.

O

A

a z1

z 2

z3

z 4 x

B

d

x

Hnh 5.3

Tra li: 1680A cmv s ; 2705,65A cma s

BBAA II 55..66:: Mot vat quay quanh truc co nh. thi iem khcach truc quay khoang0,5 R m co van toc2 mv s va gia toc toan pha28 3 m s. Tm van toc goc, gia toc goc cua vat. Tm van toc va

truc quay khoang cach0,2r m .Tra li: 4 rad s ; 216 2 rad s ; 0,8B

mv s ; 25,54B ma s

BBAA II 55..77:: Vect gia toc cua 1 iem tren vanh vo lang hp vban knh goc 600, gia toc tiep cua iem cua iem o thi iem ksat 210 3 cma s . Tm gia toc phap cua iem cach truc quay motkhoang 0,5r m . Ban knh vo lang1 R m (Hnh 5.4)

O

a60

Hnh 5.4Tra li: 25n cma s

BBAA II 55..88:: e nhan c s thay oi vantoc goc mot cach chu ky, ngi ta dung 2 banhrang Elip bang nhau e truyen chuyen ong. Cac

truc quay i qua tieu c cua Elip. Truc O1 quay euvi van toc goc270 vongphut. Khoang cach 2 trucquay 501 2O O cm , cac ban truc Elip la25 cm va15 cm (Hnh 5.5). Tm van toc goc cc ai va cctieu cua truc O2.

1O

2O

Hnh 5.5Tra li: 2,max 81 rad s ; 2,min rad s


40/70


BBAA II 55..99:: Cho c cau nh Hnh 5.6.Thanh 1 chuyen ong theo luatsin x a kt ,ban knh cac banh rang la2 3,r r va4r . Banh2 gan cng vi banh 3. Kim gan cng vibanh 4. Tm van toc goc cua kim.

Tra li: 32 4

coskimr

ak kt r r

2

3

4

x(t)

1

Hnh 5.6

BBAA II 55..1100:: Cho ccau nh Hnh 5.7. Vat 1chuyen ong theo luat

22 70 x t ( x

-cm; t-s

),cac banh co ban knh:2 30r cm ; 2 50 R cm;

3 60 R cm.

r R 2

2

12

x

O

3r

M

3

R 3

Hnh 5.7Tm van toc goc, gia toc goc cua banh 3 va van toc, gia toc ie

quay khoang cach3 40r cm ) luc vat 1 di chuyen c mot oan bang 40cm.

Tra li: 3 2,94 rad s ; 23 3,89 rad s ; 118Mcmv s ; 2379M cma s


41/70


5.2. CHUYEN ONG SONG PHANG:BBAA II 55..1111:: Tay quay OA quay eu vi van toc

goc 0 . Viet phng trnh chuyen ong cua thanhtruyen AB va cua iem gia M cua AB. Biet ABl ;OA r va khi 0t th 0 (Hnh 5.8).

A

B

y

xO

r l2

M

l

Hnh 5.8

Tra li: 0

0

0

cos

sin

arcsin sin

A

A

x r t

y r t

r t

l

;0

0

cos cos2

sin sin2

M

M

l x r t

l y r t

BBAA II 55..1122:: Tay quay OA quay nhanh daneu quanh O vi gia toc goc0 , lam banh 2 lankhong trt theo vanh banh 1 co nh. Ban knhcac banh lar va R. Khi 0t th 0 0 va 0 .Viet phng trnh chuyen ong cua banh 2 vaiem M tren vanh banh 2. Biet khi0t th

0M M (Hnh 5.9).

O

A y

x

M 0

M1

2

Rr

Hnh 5.9

Tra li:

20

20

20

cos2

sin2

2

A

A

t x R r

t y R r

t R r r

;

2 20 0

2 20 0

cos cos2 2

sin sin2 2

M

M

t t R r x R r r

r

t t R r y R r r

r

BBAA II 55..1133:: Tay quay OA quay euvi van toc goc0 . Viet phng trnhchuyen ong cua thanh AB va trung iem Mcua no. Biet 1OA O B a ; 1OO AB b (a


42/70


Tra li: 0

0

0

0

cos

sin

sin2arctan

cos

A

A

x a t

y a t

a t b a t

;0

0

cos cos2

sin sin2

M

M

b x a t

b y a t

BBAA II 55..1144:: Banh xe hnh tron co ban knh0,5 R m lan khong trt tren mat phang nghieng. Tai

thi iem khao sat tam A cua banh xe co van toc1A mv s va gia toc 23A ma s (Hnh 5.11). Tm:

Van toc goc banh xe, van toc cac iem C, D, E Gia toc goc banh xe, gia toc cac iem B, C, D

A

B

C

D

E

Hnh 5.11BietBD CE; CE song song mat nghieng.Tra li: 2 rad s ; 2C E mv v s ; 2D mv s

26 rad s ; 22B ma s ; 234C

mas

; 285D ma s

BBAA II 55..1155:: C cau hanh tinh co tay quay OAquay eu vi van toc goc0 lam cho banh I ban knhr lan khong trt theo vanh trong cua banh co nh banknh 3 R r (Hnh 5.12). Tm:

Van toc cac iem C, D, E cua banh I. Gia toc cac iem B, C, D.ChoBD CE

O

E

D

C

B

A

0

I r

R

Hnh 5.12Tra li: 02 2C Ev v r ; 04Dv r

206Ba r ; 202 5Ca r ; 202Da r

BBAA II 55..1166:: a phang ban knh R c cuon bang si day coau B co nh. a ri xuong khong van toc au va m dan day raTam O cua a co van toc:2 3

3v gh , vih la khoang cach tam

a t v tr au en v tr khao sat. Tm van toc, gia toc cac iem Dva E ( DE BD)

ODE

B

h

Hnh 5.13

Tra li: 0Dv ;4

33E

v gh ; 43D

gha

R; 2 24

3Eg

a R h R


43/70


BBAA II 55..1177:: Con lan hai tang co banknh 20 R cmva 10r cm lan khong trttheo mat phang ngang. Tang trong c cuonday va buoc vao vat M sau khi vat qua rongroc co nh. Tm gia toc iem cao nhat D luc

1t s khi M ri xuong vi van toc 3 mv t s (Hnh 5.14).

M

DB

C

O

Hnh 5.14

Tra li: 24 26D ma s ; Da tao vi phng thang ng goc :5

cos26

BBAA II 55..1188:: Vat M ri xuong theo luat22 x t ( x tnh bangm) lam chuyen ong rong roc co nh 2 va rongroc ong 1. Rong roc 1 co ban knh0,2 R m (Hnh 5.15).Tm gia toc cac iem: Tam O, A, B, C, D cua rong roc 1luc 0,5t s AOB COD

Tra li: 22O ma s ; 213Ama

s;

253B ma s; 25C ma s ; 26C

mas

M

2

A

O

D

B

C O

1

Hnh 5.15

BBAA II 55..1199:: Cho c cau tay quay thanh truyenvi tay quay OA dai20a cm quay eu vi van toc

goc0 10 rad s ; thanh truyen AB dai 5a, con chay Bchuyen ong theo phng thang ng (Hnh 5.16).Tm van toc goc, gia toc goc cua thanh truyen AB; giatoc con chay B tai thi iem tay quay va thanh truyenvuong goc vi nhau va goc gia tay quay vi phngnam ngang bang 450.

A

O

45

B

0

Hnh 5.16Tra li: 2AB rad s ; 216AB rad s ; 2565,6B

cmas

BBAA II 55..2200:: Cho c cau 4 khau ban le. Tay quay OA quayeu vi van toc goc0 4 rad s ; 0,5OA r m ; 2AB r ;

2BC r . Tai thi iem 090OAB ; 045ABC , hay tm vantoc goc thanh AB, BC cung nh gia toc goc cua chung (Hnh5.17).

45

O

C

B

A

Hnh 5.17Tra li: 2AB rad s ; 4BC rad s ; 220AB rad s ; 28BC

rad s


44/70


BBAA II 55..2211:: Cho c cau 4 khau ban le ABCD. Cacthanh 2AB CD a ; BC a ; oan AD banga . Tay quay ABquay eu vi van toc goc0 . Tm van toc goc, gia toc goc thanhBC va CD khi goc 090ADC (Hnh 5.18).

Tra li: 083BC ; 053CD ;20209BC

; 20209CD D

C

B

A

Hnh 5.18

BBAA II 55..2222:: Cho c cau nh Hnh 5.19,10AB EF KD cm ; BC 25cm ; DC CE.

Thanh AB co van toc goc khong oi10AB rad s . Khi

090 , 030 , 090 :

hay tm van toc goc va gia toc goc thanh EF.Tra li: 20EF rad s ; 2932,8EF rad s

A

B

=90 =90

CE F

KD

Hnh 5.19

BBAA II 55..2233:: Thanh OA dao ong theo luat sin

6 2t rad

lam cho a (K) quay quanh truc O1. Biet

2 2 241OA O B a cm va luc4t s thanh OA va O1B namngang (Hnh 5.20); 060 . Tm:

Van toc goc va gia toc goc cua a. Van toc va gia toc trung iem M.

A

B

O

O1

(K )

M

Hnh 5.20

Tra li: 2

6Krad

s

; 4

23

72Krad

s

; 22M cmv s ;

4

2

4

2

12

312

M

M

M

x

y

cmas

acma

s

BBAA II 55..2244:: Tay quay OA quay eu vi van toc goc0 3 rad s lam cho a lan khong trt tren ng ngang.

Cho 3OA m ; 1 R m . Luc 060 , 090OAB , tm vantoc cac iem B, M va gia toc cua chung.

Tra li: 6B mv s ; 6 2M mv s ;

218B ma s; 218 10M ma s O

B

A

0

M

Hnh 5.21


45/70


BBAA II 55..2255:: Tay quay OA quay eu vi van toc goc0 lam cho banh II co ban knhr lan khong trt tren vanh I co nhban knh 2 R r . Thanh BD dair gan cng vao banh II, thanhBC noi vi con chay C (Hnh 5.22). Tm gia toc iem B, iem Cva gia toc goc thanh BC luc030 , biet luc o OA va BD namngang.

Tra li: 2021Ba r ; 207 3Ca r ; 207 3

5BC

C

OA 0

BD

I

II

r 2 r

Hnh 5.22

BBAA II 55..2266:: Banh rang ban knh R kepgia 2 thanh kha song song chuyen ongnhanh dan ve cung 1 pha. Luc khao sat, cacthanh co van toc1v , 2v va gia toc1a , 2a (Hnh 5.23). Tm van toc, gia toc tam O vagia toc iem A cua banh rang tiep xuc vithanh kha 1.

B

A

y

x

O

v1 a 1

v2 a 2

Hnh 5.23

Tra li: 1 22O

v vv ; 1 2

2Oa a

a ; 1A xa a ; 21 2

4A yv v

a R

BBAA II 55..2277:: Cho c cau vi sai, tay quay OA co vantoc goc0 , gia toc goc0 ; banh 1 quay cung chieu vitay quay co van toc1 03 ; gia toc goc1 03 . Biet

1 22 2 R R r (Hnh 5.24). Tm van toc goc, gia toc gocbanh 2 va gia toc iem M tren vanh banh 2 AM OA

2

1

A

O1

0 0

1

M

Hnh 5.24Tra li: 2 03 ; 2 03 eu co chieu cung chieu kim

4 2 20 0 0 03 2 5 4Ma r

BBAA II 55..2288:: Cho c cau vi sai, banhdan 1 quay ngc chieu kim ong ho vivan toc goc

0 , gia toc goc

0 . Tay quay

3OA R quay thuan chieu kim ong hovi cung van toc goc va gia toc goc vibanh 1 (Hnh 5.25).

21

BO1

0 0

1

A

M

3

R R

3R

Hnh 5.25Tm van toc va gia toc iem M tren vanh ban

1 3AM OA; R R R

Tra li: 010Mv R ; 2 22 2

0 0 0 03 3Ma R R R R


46/70


6. CAC NH LY TONG QUAT ONG LC HOC6.1. NH LY CHUYEN ONG KHOI TAM:

BBAA II 66..11:: Lang tru tam giac vuong (A) tronglngQ at tren nen nhan nam ngang, tren mat nghiengcua lang tru (A) at lang tru (B), gia thiet mat tiep xucgia 2 lang tru cung nhan. Cac kch thc cho tren Hnh6.1. Hoi (A) i c oan ng bao nhieu neu (B) ihet mat nghieng lang tru A. Cho trong lng (B) laP.

Tra li: a

b

(A)

(B)

Hnh 6.1

Ps a bP Q

di chuyen ngc chieu (B) di chuyen.

BBAA II 66..22:: Xac nh dch chuyen cua can cau noinang tai trong1 2P kN khi thanh vn 8OA m quaymot goc 030 en v tr thang ng. Trong lng cancau2 20P kN (Hnh 6.2). Bo qua sc can cua nc. Lucau he ng yen. Xet 2 trng hp:

a.- Bo qua trong lng thanh vn OA.b.- Coi thanh vn ong chat, trong lng

3 1P kN

O

A

30B

Hnh 6.2

Tra li: a.- 0,36a m ; b.- 0,43s m BBAA II 66..33:: Thanh ong chat AB dai 2l co au B ta

tren nen nhan nam ngang va nghieng mot goc (Hnh 6.3).Xac nh phng trnh quy ao iem A khi thanh ri xuongmat phang ngang.

Tra li: mot phan ng Elip: 2

2 2

cos1

4

2A A x l y

l l

y

xBC

A

Hnh 6.3

BBAA II 66..44:: Hai vat nang (A) va (B) co khoilng la1m va 2m c noi vi nhau bang si daymem nhe khong dan va c at tren cac mat KL vaKE cua lang tru DEKL. Lang tru co khoi lng3m c at tren nen nhan nam ngang (Hnh 6.4). Tm dichuyen cua lang tru khi vat nang (A) trt xuong motoan dais tren mat nghieng KL. Ban au he ng yen.

L

KE

D 60

(B)

(A)

Hnh 6.4


47/70

CAC NH LY TONG QUAT ONG LC HOC 47

Tra li: Lang tru i ngc lai mot oan

1 2

1 2 3

22

m ms

m m m

BBAA II 66..55:: Mot tam ong chat co ABC co hnh dang la mogiac vuong can, canh huyen AB dai 12cm c at thang ng ta nhA tren mat phang nhan nam ngang. Ngi ta tha cho tam phaxuong di tac dung cua trong lng (Hnh 6.5). Xac nh quy M nam gia canh ben BC.

Chu y:trong suot thi gian chuyen ong, nh A luon nam tmat ngang

B

C

A

M

Hnh 6.5

Tra li: Cung Elip: 2 29 2 90M M x y

BBAA II 66..66:: Xac nh ap lc len nen at cua mot may

bm nc luc chay khong tai. Trong lng cua phan co nhgom vo (D) va mong (E) la1P ; tay quay OA daia, ong chatco trong lngP2. Trong lng mang trt (B) cung pttong(C) laP3. Tay quay OA quay eu vi van toc goc . Xemnh cac vat tao nen may la ong chat va oi xng.

O

(B) A

(C)(D)(E)

Hnh 6.6

Tra li: 22 31 2 32

cos2 y

P P N P P P a t

g

BBAA II 66..77:: Mot ong c hi nc at namngang tren mat mong nhan trn. Tay quay OA co chieudair va quay eu vi van toc goc . Thanh truyenAB AO. Coi khoi lng cua cac bo phan chuyenong c thu gon ve 2 khoi lng1m va 2m tap trung au A cua tay quay va trong tam pttong (B). Khoilng vo ong c la3m . Xac nh chuyen ong ngangcua vo ong c. Cho biet ban au pttong (B) v tr xa

nhat ve ben trai.

A

(B)O

Hnh 6.7

Neu ong c c bat vt xuong nen, tm ap lc cua ong cngang cua bulong. Bo qua lc cang ban au cua bulong.

Tra li: 1 21 2 3

2cos 1

m m x t r

m m m

;

21 2

21 2 3 1

2 cos

sin

x

y

N m m r t

N m m m g m r t


48/70


6.2. NH LY BIEN THIEN ONG LNG:BBAA II 66..88:: Mot qua lu phao ang bay vi van toc15 mv s th no va v

thanh hai manh. Manh th nhat co trong lng1 80P N bay ve hng chuyen ong

vi van toc1 25m

v s . Xac nh van toc manh con lai. Biet trong lng qu120P N .

Tra li: 2 5 mv s (theo chieu ngc lai)

BBAA II 66..99:: Mot nong sung ai bac nam ngang trong lng1 110P kN . Tronglng vien an la2 540P N . Van toc vien an luc ra khoi nong sung0 900 mv s .Xac nh van toc giat lui cua nong sung thi iem vien an bay

Tra li: 4,42 m s (hng ngc chieu vien an)

BBAA II 66..1100:: Mot dong nc cphong ra t mot voi co tiet dien

216S cm vi van toc8 mv s vanghieng vi phng ngang mot goc030 .Xac nh ap lc tong cong cua nc lenmat tng thang ng. Bo qua anhhng cua trong lc va xem rang cac hatchat long sau khi ap vao tng chuyenong doc theo tng (Hnh 6.8).

Tra li: 88,7 N N

A

B

30

Hnh 6.8

BBAA II 66..1111:: Xac nh ap lc ong lc tong hplen goi (A) cua dong nc chay trong oan ong attrong mat phang ngang nh Hnh 6.9. ng ong cotiet dien tron, ng knh20d cm . Hai nhanh cuaong hp vi nhau 1 goc 1200. Van toc dong nc chaytrong ong 4 mv s . Bo qua tac dung cua trong lc.

Tra li: 503 R N (A)

120

Hnh 6.9


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BBAA II 66..1122:: Xac nh thanh phan ap lc cua nc song song vtruc oi xng cua canh co nh cua roto tuabin. Cho biet lu ltch cua nc laQ va khoi lng rieng cua no la . Van toc cua ncluc va vao canh tuabin la1v hng song song vi truc oi xng, vantoc cua nc luc ra khoi canh la2v hp vi mat phang oi xng goc (Hnh 6.10).

Tra li: 2 1cos . R v v Q

v1

v2

v2

Hnh 6.10

BBAA II 66..1133:: oan tau nang400P kN en chan doc co o tan 0, 006i ( la goc doc) co van toc1 54 kmv h . He so ma sat (he so ca

hp) khi oan tau chuyen ong bang 0,005. Sau khi tau len doc s, van toc cuno giam xuong con2 45 kmv h . Tm lc keo cua au tau.

Tra li: 2,36F kN


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6.3. NH LY BIEN THIEN MOMEN ONG LNG:BBAA II 66..1144:: Mot si day vat qua rong roc co nh O, bo qua

khoi lng cua chung. Mot ngi nam vao day tai A, con tai B treotai trong co cung trong lng vi ngi. Neu ngi leo len vi vatocv tng oi so vi day th tai trong se chuyen ong nh the nao?(Hnh 6.11).

Tra li: 2B vv (i len)

O

AB

Hnh 6.11

BBAA II 66..1155:: Mot ban tron nam ngang quay khong ma satquanh truc thang ng O z i qua tam O cua ban. Mot ngi tronglngQ i tren ban theo quy ao tron tam O, ban knhr vi vantocu khong oi. Hoi ban quay vi van toc goc bang bao nhieu?

Biet ban la ong chat trong lngP, ban knh R. Tai thi iemban au, ban va ngi co van toc bang 0 (Hnh 6.12).

Tra li: 2 2

2

2Qru

Qr PR (ngc chieu ngi i)

z

uO

Rr

Hnh 6.12

BBAA II 66..1166:: a tron ong chat nam ngang c gan chat vaotruc quay AB thang ng ang quay vi van toc goc0 . Tren banknh cua a, mot chat iem M, khoi lng2m chuyen ong t tamO cua a vi van toc khong oiu. Xac nh van toc goc cua a

theo thi giant cung nhu gia tr cua no khi M i ti vanh a. Bieta co khoi lng1m (Hnh 6.13).

Tra li: 2

102 2 2

1 22m R

m R m u t

KhiOM R : 1 01 22

mm m

uO

A

B

M

~

R

Hnh 6.13

BBAA II 66..1177:: Mot ong nam ngang CD co the quay tdo quanh truc thang ng AB. Ben trong ong co qua cau(xem la chat iem) co khoi lngm va nam cach trucquay mot khoangMC d . Tai mot thi iem nao o, ongc truyen van toc goc0 . Xac nh van toc goc1 cuaong khi qua cau va ri khoi ong. Cho biet momen quantnh cua ong oi vi truc quay la J , chieu dai ongCD L .Bo qua ma sat (Hnh 6.14).

Tra li: 2

1 02

J md J mL

B

A

CM

D

Hnh 6.14


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BBAA II 66..1188:: Sc cang cua nhanh dan va nhanh b dancua ai truyen lam quay banh ai co ban knh20r cm vatrong lng 3,27P N co gia tr tng ng la1 10,1T N ;

2 5,05T N . Momen cua lc can phai bang bao nhieu e

banh ai quay vi gia toc goc21,5rad

s (coi banh ai laa tron ong chat) (Hnh 6.15).Tra li: 1c M Nm

T 2

T 1

r

Hnh 6.15

BBAA II 66..1199:: Qua cau A khoi lngm gan vaoau thanhAB l va gan vi truc quay1 2O O. Ca hethong at trong bnh cha chat long. Lc can cua chatlong tac dung len qua cau ngc vi van toc goc va cogia tr . .c R m ( la he so t le). Biet van toc gocban au cua truc quay la0 (Hnh 6.16). Hay xac nhkhoang thi gianT e van toc goc giam i mot na vatm so vong quayn trong khoang thi gian o. O1

O 2

BA

l

Hnh 6.16

Tra li: ln 2lT

; 04l

n

BBAA II 66..2200:: Ngi ta dung ham tay e hammot banh xe ang quay vi van toc goc0 . TmlcP can thiet phai tac dung au tay ham A ebanh xe dng han sau thi gianT cho trc. Tmxem trong thi gian o, banh xe con quay themc bao nhieu vong. Biet momen quan tnh cuabanh xe oi vi truc quay O1 cua no la J , he so ma sat trt gia ma ham va banh xe la f . Bo quakch thc cua ma ham (Hnh 6.17).

O A

RO1

P

b

a

Hnh 6.17

Tra li: 0 JbP faTR

; 04

T n

BBAA II 66..2211:: Mot vat ran quay quanh mot truc co nh khi ong yen, chu tac dung cua momen quay khong oi bang M va cua momen ca

21 M , trong o: la hang so; la van toc goc cua vat. Momen quan

oi vi truc quay la J . Tm luat bien thien cua van toc goc theo thi gcua van toc goc gii han cua vat.

Tra li: 11

t

t

M et

e

vi 2 M

J

; gh M


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BBAA II 66..2222:: e xac nh momen quan tnh cua mot vatoi vi truc AB qua khoi tam C cua vat, ngi ta treo vatbang 2 thanh AD va BE gan cng vao vat sao cho AB songsong vi DE va cung nam ngang. Hai thanh AD va BE quayc t do quanh truc DE co nh (Hnh 6.18). Sau o chovat dao ong va o chu kyT cua dao ong nay. Biet tronglng vat laP va khoang cach gia AB va DE lah. Bo quatrong lng 2 thanh treo va ma sat o truc. Tnh momen quantnh cua vat oi vi truc AB.

AC

B

ED

Hnh 6.18

Tra li: 2

2CT h

J Phg

BBAA II 66..2233:: a.- Bo phan chnh cua dao ong ke e ghi chan ongngang cua mong may la mot con lac nh Hnh 6.19. v tr thang cua OA, lo xo xoan khong lam viec. Momen tnh cua con lac oi vkhi OA nam ngang la43,6 Ncm , momen quan tnh cua con lac oi vitruc quay la 20,003 J kgm; he so cng cua lo xo xoan la0,98c Ncm .Bo qua moi lc can. Xac nh chu ky cua dao ong be t do cua con quay v tr can bang thang ng.

AO

Hnh 6.19

b.- Gan dao ong ke nay vao mot mong may, gia thiemay dao ong ieu hoa theo phng ngang theo luat: sin60 x a t cm . Biet bien odao ong cng bc cua con lac cua dao ong ke la 60. Xac nh bien oa cua daoong mong may.

Tra li: a.- 0,52T s b.- 6,8a mm


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6.4. NH LY BIEN THIEN ONG NANG:BBAA II 66..2244:: Cho c cau hanh

tinh nh Hnh 6.20. Cac banh rang 1,2, 3 la cac a tron ong chat cungban knhr va khoi lngm.Tay quayOA xem la thanh ong chat va cokhoi lngm1. C cau nam trong matphang nam ngang va tay quay OAchu tac ong cua ngau lc co momenkhong oi M . Banh xe 1 co nh(Hnh 6.20).

a.- Tm van toc goc cua tayquay OA la ham cua goc quay cua

no, biet luc au he ng yen.b.- Tm gia toc goc cua tay

quay.

O

A

B1

2

3

4 r

r

r

r

Hnh 6.20

Tra li: 1

1 3

8 33 M

r m m

; 21

3

2 8 33 M

m m r

BBAA II 66..2255:: Mot ngau lc co momen quaykhong oi M tac dung len tang cua mot truc ti coban knh bang R va co trong lng1P . Quan vao

tang ti mot si day mem nhe va khong dan roibuoc au mut t do cua day vao vat nang (A) cotrong lng2P e keo no len tren mat phangnghieng co goc nghieng so vi mat phang nam

(A)

O

M

Hnh 6.21ngang. He so ma sat trt ong gia vat (A) va mat nghieng la f . Tang ti c xemla truc tron ong chat. Tm bieu thc van toc goc truc ti lano. Luc au he ng yen (Hnh 6.21).

Tra li: 22 1

cos sin2

2

M f P Rg

R P P

BBAA II 66..2266:: Giai lai BAI 6.25: neu ke en trong lng cua dadai day lal, trong lng mot n v chieu dai la p. Tai thi iem au, oan daykhoi ti laa. Bo qua s thay oi ve the nang cua oan day quan va

Tra li: 21 2

2 2 cos sin 2 sin12

2 2

M P R f pR a Rg

R P P pl


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BAI TAP C HOC LY THUYET BBAA II 66..2277:: Mot ti keo gom 2 trong (K1) va (K2) co ban knh R1 va R2 ghep

cng vi nhau va gan vao truc quay nam ngang O1O2, momen quan tnh cua cac trongvi truc quay la J 1 va J 2. Tac dung vao tay quay AB mot ngau lc co momenoi M e keo vat nang (D), trong lngP len tren. Khi trong (K2) quan day th trong(K1) nha day. Bo qua ma sat va trong lng day. Ban au he ng ye

goc cua tay quay AB khi vat (D) c keo len mot oanh (Hnh 6.22).

M A

BO1 O 2

(K ) (K )1 2

C

(D) Hnh 6.22

Tra li:

2 1

2

2 1 1 2 2 1

8 2

4 4

gh M P R R

R R gJ gJ P R R

BBAA II 66..2288:: Vat nangP c treo vao au mot si day mem khong dadail va moi n v dai cua no co trong lng bangq. Day nay c quan vao tang

cua mot truc ti co ban knh R va co momen quan tnh oi vi truc quay la J . Vatnang ri xuong lam quay truc ti. Luc dau oan day treo buong dai m x0 va che ng yen. Bo qua ma sat cua cac o truc quay va chieu day cuthay oi the nang cua phan day quan. Xac nh van toc ri cua vato dai ri c x cua oan day treo.

Tra li:

0 0

2

2P q x x x xv R g

gJ P lq R

BBAA II 66..2299:: Mot si day ong chat dai L co mot

phan nam tren mat ban nhan nam ngang, mot phanbuong t do. Xac nh khoang thi gianT e day rikhoi mat ban, biet rang tai thi iem au, chieu daiphan day buong tha lal va van toc au cua day bang 0(Hnh 6.23).

Tra li: 2 2

ln L L L l

T g l

L l

l

Hnh 6.23


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BBAA II 66..3300:: Mot ong c ien keomot he thong truyen ong dung xch nh Hnh 6.24. He thong lam viec nh sau:luc m may, xch bat au chuyen ongvi gia toca va khi at cmaxv th ginguyen toc o o. ng knh cua trucchnh gan vi ong c bang 2r 1, ngknh 2 rong roc co nh khac la22r va

32r . oi vi truc quay cua chung, momenquan tnh cua truc quay chnh la J 1,momen quan tnh cua cac rong roc la J 2 va J 3. Trong lng vat nang keo len laQ1, vat nang ha xuong laQ2. Trong lngmoi n v dai cua day xch laq va dayxch co o dail. Tnh cong suat cua ongc trong qua trnh m may va trong quatrnh chay bnh onmaxv v .

2O

1O

3O

2Q

1Q

Hnh 6.24

Tra li: 31 2 1 2 1 22 2 21 2 3

may J J J Q Q ql

N a Q Q vr r r g g g

1 2 maxmay,bnh on N Q Q v

BBAA II 66..3311:: Mot con lan ong chat hnh tru tron xoay co ngcm va co khoi lng bang 392kg, chuyen ong lan khong trt tren mat phamot ngi ay. Lc ayP co phng chieu khong oi va hng theo thThanh AO dai 1,5m, o cao cua A so vi nen ngang la 1,2m. Bo qua ma sat o truma sat lan cua mat nen. Xac nh:

a.- Cng oP sao cho khi ngi ay i c 2m th con lan at toc o0,8 m s .Luc au he ng yen. Neu ke en ma sat can lan cua nen v0,5k cm thP co cng o bao nhieu? Lay29,8 mg s .

b.- Sau khi at van toc tren, muon gi cho truc banh xe chucan giam cng oP i bao nhieu?

Tra li: a.- 117,6P N ; b.- 200,2P N , giamP mot lng119,1 N


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BBAA II 66..3322:: Cho c cau hanh tinhnh Hnh 6.25, chuyen ong trong matphang ngang. Banh rang 3 co nh, cacbanh rang 1 va 2 c xem la cac atron ong chat cung be day va cung vatlieu. Biet banh rang 1 quay nhanh gap10 lan tay quay. Bo qua khoi lng tayquay. Momen quan tnh cua banh rang1 oi vi truc O1 la J . Banh rang 1 chutac dung cua ngau lc can M 1 khongoi va tay quay O1O2 chu tac dung cuamomen phat ong M khong oi. Tmgia toc goc tay quay.

Tra li: 1101300

M M

J

O1

2

1

O 2

3

M 1

Hnh 6.25

BBAA II 66..3333:: Cho c cau hanh tinh nh Hnh6.26, chuyen ong trong mat phang ngang. Tayquay OA c xem la thanh ong chat dail, nangP. Hai rong roc ong va co nh cung ban knh,rong roc ong co trong lngQ va c xem laa tron ong chat. Tac dung len tay quay motngau lc co momen khong oi M . Tm gia toc goccua tay quay. Xem nh khong co s trt giarong roc va ai truyen.

M

O

A

l

Hnh 6.26

Tra li: 2

3

3gM

l P Q

BBAA II 66..3344:: Cho hop toc o nh Hnh 6.27. trucdan va truc b dan lien he vi nhau bang cac capbanh rang hanh tinh kep. Truc dan I mang tay quayAB, truc dan IV mang banh rang 4. Cac o truc attren 2 au tay quay mang cap truc banh rang hanh

tinh 2, 3. Cho biet cac ban knh1 2 3 4, , ,r r r r cua cacbanh rang. Momen quan tnh cua truc dan vi cac chitiet gan tren no oi vi truc quay hnh hoc cua nobang1 J . Cap banh rang hanh tinh 2-3 co khoi lngm2 va co trong tam nam tren truc oi xng hnh hoc

1

2 3

4

32

A

B

I IV

Hnh 6.27cua no va co momen quan tnh oi vi truc o la2 J . Momen quan tnh cua truc bdan va cac chi tiet lap vi no oi vi truc quay hnh hoc cua no la4 J . Truc dan chu


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CAC NH LY TONG QUAT ONG LC HOC 57 tac dung cua ngau lc can M 4, gia thiet1 M va 4 M khong oi, bo qua ma sat. Ttoc goc truc dan I.

Tra li:

1 31 4

2 41 2 2

2 1 311 2 1 2 2 4

2 2 4

1

2 2 1 1

r r M M

r r

r r r J m r r J J r r r

BBAA II 66..3355:: Giai lai bai toan tren vi gia thiet1 const M ; 24 4 M a va ginguyen cac gia thiet khac.

at: 2 2

2 1 311 2 1 2 2 4

2 2 4

2 2 1 1r r r

J J m r r J J r r r

Tm gia tr van toc goc0

1 trong che o bnh on va tm bieu thc 1 1 t .Ban au he ng yen.

Tra li:

31

31

2

0 011 1 13 2

1;

1

ak M t

J

ak M t

J

M et

ak e

vi 1 32 4

1r r

k r r

BBAA II 66..3366:: Mot hnh non tron xoay ong chat chuyen ong tren mot mat phang khong nhan va nghieng vi mat phang n . Chieu

dai oan ng sinh banga va goc m cua non la 2 . Lap phng trnh vi phachuyen ong cua non.Ch dan:lay thong so nh v cua hnh non tren mat phang n gia

ng sinh tiep xuc vi ng doc chnh cua mat phang nghien

Tra li: 2

sinsin 0

1cos

5

g

a


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BBAA II 66..3377:: Cho c he nh Hnh 6.28. Vat nang (A) cokhoi lng1m ri thang ng, keo theo vat nang (B) co khoilng 2m trt len theo cot thang ng CD. Bo qua ma sat.Lap phng trnh vi phan chuyen ong cua c he.

Tra li:

2 2 2 2 21 2

3 22 2 2 2 2 221 1 2 0

a h m h m a h h

m a hh m gh a h m g a h

(h la oan dch chuyen cua (B) so vi O)

O

(A)

(B)

Ca

Hnh 6.28

BBAA II 66..3388:: Vat nang (A) trong lngP c keo len t trangthai ng yen nh ti (B) co ban knh R, trong lngQ va chu tacdung cua ngau lc co momen 20 M M , trong o:0 M , lacac hang so, la van toc goc cua ti. Biet ban knh quan tnh cuati oi vi truc quay O la (Hnh 6.29). Tm van toc goc gii hancua ti quay va van toc goc cua qua trnh chuyen tiep cua no ttrang thai au ng yen.

O M

(B)

(A)

Hnh 6.29

Tra li: 0gh M PR

; 11

t

gh t

et

e

vi 0

2 2

2 g M PR

PR Q


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60/70


7. NGUYEN LY DI CHUYEN KHA DBBAA II 77..11:: Cho c cau may ep nh

hnh ve (Hnh 7.1). Ngau lc tac dung volang co momen bang M . nh truc vt ccat ren ngc chieu ma cac con chay B vaC ong thi tien gan hoac lui xa nhau. v tr c cau ma BD va OD tao vi ngthang ng lan lt goc va , xac nhlc epS tac dung vao vat chu ep (K).Biet bc truc vt lah, bo qua ma sat vatrong lng cac chi tiet.

Tra li: sin .sin cos

M Q

h

C B

E D

O

A

(K)

Hnh 7.1

BBAA II 77..22:: Cho c cau ham tau ien nh hnh ve(Hnh 7.2). Tm he thc giaa, b, c e di tac dung cualcQ hng theo phng nam ngang tai E, hai ma hamA va B tac dung vao hai banh xe C va D cac lc bangnhau. Tm gia tr cua lc ma hamP tac dung len banhxe. Bo qua trong lng cac thanh va xem banh xe ngyen.

Tra li: b ac a b c ; 2a bP Qb

AC B D

E

c

b

a

Q

Hnh 7.2

BBAA II 77..33:: C cau e nang banh xe maycay la mot c cau bon khau ban OCBO1. Khau BCgan chat vi a ma tam la iem B. Tai iem Acua a co at lc ngangS hng theo tiep tuyenva tai ban le B tac dung lc thang ng R . Chieudai cac thanh 1BC l ; 21BO l ; cac kch thckhac cho tren hnh ve (Hnh 7.3) 1 2, , , H L .Xac nh quan he giaS va R khi c cau can bang v tr nh hnh ve. Bo qua trong lng cac thanhva a cung nh ma sat ban le.

Tra li: 1 12 2

sin

sinl L

S Rl H

O

O

B

AC

R

S

H

L

1

1

2

Hnh 7.3


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NGUYEN LY DI CHUYEN KHA D 61

BBAA II 77..44:: Choc cau may kch nh hnh ve (Hnh 7.4).Chuyen ong cua tayquayOA R qua cacbanh rang 1, 2, 3, 4, 5c truyen sang thanhkha cua kch. Tm lcP can at vuong gocvi tay quay tai mut Ae kch can bang khilc nang 4710Q N .Cho ban knh cac banhrang:1 3r cm ;

54 23

RP

AO1

C

Q

Hnh 7.4

2 12r cm ; 3 4r cm ; 4 16r cm ; 5 3r cm ; 18 R cm

Tra li: 1 3 52 4

49,1r r r

P N r r R

CO1 O 2

(A)(B)

E

(D)

r 2

IP

r 1

R

Hnh 7.5

BBAA II 77..55::

Truc keo vi sai co 2 tang gan chat vi nhau chuyequay CI R . Vat nang D trong lngQ c treo vao rong roc E. Khi quay tCI e keo D th nhanh day trai nha ra khoi tang (A) va nhanh d(B). Ban knh cac tang lan lt la1r va2r 1 2r r (Hnh 7.5).

Tm cng o lcP can at vuong goc vi tay quay tai I e he 7050Q N ; 2 12r cm ; 1 10r cm ; 60 R cm

Tra li: 2 1 117,52

r r P Q N

R


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BBAA II 77..66:: Cho c cau tay quaythanh truyen nam trong mat phang thangng (Hnh 7.6). Xac nh momen M tacdung len tay quay OA khi no nghieng viphng nam ngang goc e can bang vitong ap lcF cua hi len xy lanh. Tay

F

A

BO M

Hnh 7.6quay va thanh truyen coi la cac thanh ong chat cung chieu dail va trong lngP. Boqua ma sat.

Tra li: cos 2 sin M P F l

BBAA II 77..77:: Cho c he c bieu dien nh hnh ve (Hnh 7.7). Day mem nhe khong danc buoc vao vat (A), vong qua rong roc co nh(C), rong roc ong (D), rong roc co nh (E), cuoicung buoc vao vat nang (B). Tai truc rong roc(D) treo vat nang (K) co trong lngQ. Biet 2 vat(A), (B) co trong lng1 2,P P .

(C)(A)

(B)

(K)

(E)

(D)

Hnh 7.7

Tm quan he gia cac lc va xac nh he so ma sat trt f gia vat (A) va matnam ngang e he can bang.

Tra li: 22Q P ; 21 12

Q P f

P P

BBAA II 77..88:: Cung nh bai toan tren (BAI 7.7:) nhng vat A trt trennghieng nghieng vi phng nam ngang goc060 ; 1 2P P P

Tra li: 2Q P ; 2 3 f

BBAA II 77..99:: Cho c he bieu dien nh hnhve (Hnh 7.8). Day mem nhe khong dan buocvao vat (A), vong qua rong roc (O), rong rocong (O1), vong lai rong roc co nh (O) va cuoicung buoc vao vat (B). Tai tam rong roc (O1) buoc vat nang (C) co trong lngQ, con (A) va(B) co trong lng1 2,P P va trt tren cac matphang nghieng nghieng vi phng ngang cac

(A)

(B)

(C)

(O )1

(O)

Hnh 7.8goc va . Bo qua khoi lng cac rong roc va ma sat. Tm quan he gi1 2&P P viQ e he can bang.

Tra li: 1 2sinQ

P ; 2 2sin

QP


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BBAA II 77..1100:: Cho he dam nh hnh ve (Hnh7.9). Tm phan lc tai ngam A va goi ta con lanB. Cho 3a m , 2b m ; 4c m ; 34,9.10 N q m

Tra li: 0A X ; 314,7.10AY N ;344.10A M Nm; 344.10B N N

AB

CD

cba

q

Hnh 7.9

BBAA II 77..1111:: Tm phan lc tai banle A, goi ta con lan B va D (Hnh 7.10).Cho 2a m , 3b m ; 1c m ; 2d m ;

30 M kNm; 10F kN ; 030 Tra li: 3,85D N kN ;

31,67B

N kN ; 1,92 X kN A

; 25A

Y kN

A B C D

cba

F

d M

Hnh 7.10

BBAA II 77..1122:: He 3 thanh AB, BC, va CD noi vinhau bang hai ban le B va C, gan xuong at bang ban leA va ngam D. Cho 2BC CD a ; BK KC; CL LD.Goc nghieng cua thanh AB so vi nen ngang la060 .Tai K tac dung lc1P thang ng va tai L tac dung lc

2P nam ngang (Hnh 7.11). Bo qua ma sat tai cac ban le.Tm phan lc tai ngam D.

P2

P1

C

B

A D

K

L =60

Hnh 7.11

Tra li: 1 23

8D X P P ; 1

5

8DY P ; 1 2

3

4D M P P a

BBAA II 77..1133:: Cho c cau tay quay canlac nh hnh ve (Hnh 7.12). Tm quan hegia cac lcP vaQ e he can bang tai v trgocCOK . ChoOC R ; OK l ; ongthi tm phan lc tai ranh trt K.

Tra li: 2cos

PlQ

R ;

tan X P K ; 2tan M Pl K P

O

Q

AC

K

R

B

l

Hnh 7.12


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BBAA II 77..1144:: Hai dan (I) va (II) c noivi nhau bang ban le D va c noi vao ban leC nh 2 thanh III va IV. Tai A va B dan ta vaocac goi di ong. Tac dung len dan lcP thangng cach goi A mot oan banga theo ngngang. Tm phan lc tai goi B. Bo qua ma sat(Hnh 7.13).

C

AD

(I) (II)

B

III IV

Pa

Hnh 7.13Gi y: Khi giai s dung tam van toc tc thi C1, C2 cua 2 phan dan.

Tra li: a R Pd

2B

1

DCDC ; d la canh tay on cuaB R oi vi C2.


65/70



66/70


8. NGUYEN LY ALAMBEBBAA II 88..11:: Mot qua cau nho co trong lngP c treo

vao toa xe chuyen ong thang vi gia toc khong oia. Daytreo lech vi ng thang ng goc va v tr can bangtng oi vi toa xe. Xac nh gia toca cua toa xe (Hnh 8.1).

Tra li: tana g

a

O

Hnh 8.1

BBAA II 88..22:: Tren oanng ray ABC nam trong matphang thang ng ngi ra tha

mot xe goong nho (xem la chatiem) tai A vi van toc aubang 0. trong lng xe laP,ban knh oan ray vong tron la R (Hnh 8.2).

Tm ap lc phap tuyen

RE D

O

B

(C)

2 A

h

Hnh 8.2 N cua xe len ray trong oan vong tron o. Tm o caoh toi thieu e xe chay het oanray quan tron.

Tra li: 2

2 3cosh

N P R

, trong o la goc cua ban knh OB viban knh nh v cua xe tren vong tron;2,5h R

BBAA II 88..33:: Cung bai toan tren (BAI 8.2:) vi vong tron co oaxng vi ng thang ng qua tam vong tron vi goc m 2 . Tm o cao1h can thiete xe vt qua quang h DE va tiep tuc chuyen ong theo vong tron xe chuyen ong theo quy ao Parabol).

Tra li: 11

1 cos 2cosh R


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NGUYEN LY ALAMBE 67

BBAA II 88..44:: Ti may c at tren damnam ngang nh hnh ve (Hnh 8.3). Cho khoangcach gia 2 goi CD la 8m, 3AC m . Tikeo vat nang (B) co khoi lng la 2 tan chaylen thang ng nhanh dan eu vi gia toc

20,5 ma s . Tm ap lc phu do lc quan tnhcua vat nang (B) gay ra tren hai goi .

C D

Ba

A

O

3m8m

Hnh 8.3

Tra li: 625 N va375 N

BBAA II 88..55:: Xe o to co khoi lngm chay tren ng ngang vi gia w.Trong tam cua xe cach mat ngh va theo phng ngang cach truc banh banh sau nhng oana vab a b . Bo qua momen quan tnh cua cac bavi truc quay cua chung. Tm ap lc phap tuyen cua cap banhlen mat ng. Vi trang thai chuyen ong nao cua xe th 2 agia tr.

Tra li: 1m gb wh

N a b

(banh trc); 2m ga wh

N a b

(banh sau)

1 2 N N khi xe chay cham dan eu vi gia toc2a b

w gh

BB

AA

II

88..66:: au may xe la chay eu

tren mot oan ng ray thang ngang vi vantoc72 km h . Xac nh ap lc phu len ray do tacdung quan tnh cua thanh AB gay ra. Khoilng AB la 200kg c phan bo eu docthanh.

A B

OO1 2

Hnh 8.4

Tay quay co o dai0,3r m , ban knh vanh lan cua banh xe1 R m . Gia thiet cabanh xe lan khong trt tren ray (Hnh 8.4).

Tra li: Ap lc la ham ieu hoa theo thi gian va co3max 24.10 N N


68/70


BBAA II 88..77:: Vat (A) trong lng1P ha xuongtheo mat nghieng (D) truyen chuyen ong cho vatnang (B) trong lng2P nh mot si day khongtrong lng, khong dan, vong qua rong roc co nhO. Goc cua mat nghieng vi phng ngang la .Bo qua ma sat va khoi lng rong roc O. Xac nhap lc cua mat ben (D) len mo E (Hnh 8.5).

Tra li: 1 2 11 2

sincos

P P N P

P P

(A)(B)

(D)

O

(E)

Hnh 8.5

BBAA II 88..88:: Tren mot truc nam ngang AB,ta lap hai thanh cung chieu dail vuong goc vitruc va nam trong 2 mat phang vuong goc vinhau. au cuoi moi thanh gan cac qua cau Dva E, moi qua cau co khoi lngm. Xac nh aplc ong lc cua truc AB len cac goi A va B khitruc quay eu vi van toc . Cac thanh co v tr

E

O

D

BA

y

x

2a 2a 2a

l

l

const

Hnh 8.6nh tren Hnh 8.6. Cac qua cau coi nh chat iem, khoi lng cac thaqua.

Tra li: 253A B

N N ml

BBAA II 88..99:: Thanh AB dai 2l c gan chat vao trucquay thang ng DC quay eu vi van toc goc

OA OB l . Thanh lech vi truc quay mot goc . Haiau thanh gan cac vat nang cung trong lngP. ChoOC a ; OD b . Bo qua trong lng thanh va va kchthc cac vat nang. Hay xac nh phan lc tai cac o Cva D khi thanh AB nam trong mat phang O yz(Hnh 8.7).

Tra li: 0C D X X ;

2 2 sin2lY Y P

g a b C D ; 2D Z P D

B

A

z

xO

bai tap co ly thuyet

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