Một số phương pháp giải bài tập trắc nghiệm cơ học 12: Phần 1

Phần 1 tài liệu Phương pháp giải bài tập trắc nghiệm cơ học 12 do Trận Trọng Hưng biên soạn cung cấp cho người đọc các phương pháp giải bài tập trắc nghiệm về: Động lực học vật rắn, dao động cơ. Mời các bạn cùng tham khảo nội dung chi tiết.

P H l / d N G PHAP G I A I BAI TAP T R A C N G H I E M C d H Q C 12

I R A N T R Q N G HLfNG

C h j u t r a c h n h i e m xua't b a n

N G U Y E N T H I T H A N H H U C f N G Bien tap : H A I A U

\a ban in : H O N G H A I

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- V i tri cua vat tai moi thcJi diem se diTdc xac

dinh bang goc cp giffa mot mat phang dong

P gan vcti vat va mat phang co dinh PQ (ca hai mat phang nay deu chiJa true quay A Z )

Goc (p goi la toa do goe cija vat

- Dcfn vi cua 9 la radian (rad)

- N e u chon chieu du'dng la chieu quay cua vat thi (p > 0

2 T S c d o g o c

- Toe do goc la dai lu'dng dac trUng cho mu^c do nhanh, cham cua chuyen dong quay

Toe dp goc ttfc thdi: co = — d(p

- Gia toe goc trung binh:

- Gia toe goe tii'e thdi:

Aco Ytb

At dco

Y =

dt

- Ddn vj cua gia toe goe la rad/s^ ' j '

4, Cac phrf<yng t r i n h d o n g hoc cua chuyen d y n g quay

a Chuyen dong quay deu Id chuyen dong quay cd tdc do gdc co khdng ddi

cp = (Po + Mt I, v d i (po la t o a d p goc b a n d a u

b Chuyen dong quay bien ddi deu la chuyen dong quay cd gia tdc gdc y khdng ddi ^ ^ ,

Phuong phip g\i\i tap U&c nghigm Co hpc 12 - I r a n Trqng Hang

CO = 00,, + yt

1 2

9 = cpo + coot +

-2

CO -- cof) = 2Y((P - -(po)

+ Neu co.y > 0 thi chuyen dong quay nhanh dan

+ Neu co.y < 0 thi chuyen dong quay cham dan

5 Van toe va gia toe cac diem tren vat quay

Goi r la khoang each tijf mot diem tren vat ran tdi true quay

,!.oT,

V = co.r

i a Toe do dai v cd do Idn:

b Gia toe:

- Vat ran quay deu: gia toe cua m6i diem tren vat ran la gia toe hu^cfng

tam CO d o Idn a„= — = co-.r V 9

- Vat ran quay khong deu: gia toe a cua moi diem tren vat ran c6 hai

+ Gia toe a cua mot diem tren vat ran

a = a„ +a, co:

CO la toe dogoc (rad/s)

Phu'cfng trinh chuyen dong quay deu: cp - cp,, + co.t

fcpo la toad6gdcvaoliicbandau(t = 0)

[cp la toa dogoc vac luc t

• Goe quay trong th5i gian t: Acp = (p - cpo = co.t

Vay: co = 271.5 = 31,4 (rad/s) Chpn dap an C , : r , : , , - r

Vi du 2 Mot banh xe quay deu vdi toe dp gdc CO = 9,42 rad/s

Trong 20s banh xe quay du'de

A 30 vong B 20 vong C 15 vong : D 60 vong Gdc quay: Acp = cp - cpo = co.t = 9,42.20 = 188,4 (rad) = 188,4

271 (vong)

= 30 (vong) Chpn dap an A

Dang 2 CHUYEN DONG QUAY BIEN DOI DEU

Toe dp gdc vao luc t: co = cO(, + y t coo la toe dp gdc luc ban dau (I - 0) (rad/s)

y la gia toe gdc (rad/s^)

• Gia toe gdc: y = C O - C O ,

Phifdng trmh chuyen dong quay bien doi deu:

Vdi Gdc quay: Acp = cp - cpQ = cogt + ^yt'

cp = cpo +coot + - y t ' cpo la tpa dp gdc ban dau (t = 0)

COQ la toe dp gdc ban dau '

5

PTTOng phi'ip hai t.lp trac'ngnigm l^U IHJf 1^

rran-TTung-mmg-Lien he giffa toe do goc vdi goc quay: co" - cOg = 2yAcp

Vi du 1 Mot banh xe quay nhanh dan deu vdi gia toe goe l,57rad/s" Sau 5s ke

tir luc bat dau quay banh xe dat toe d6

Nen:co = 0 + 1,57.5 = 7,85 (rad/s) ma: lrad/s= — v6ng/s ^ n ' ^ ^ i v T

Nen: co = 7,85 — = 1,25 (vong/s): ta goi do la toe do banh xe n = 1,25 v6ng/s

271 Chon dap an B

Vi du 2 Mot banh xe quay nhanh dan deu Sau 2 phut tijf liie banh xe eo toe do

120 vong/phiit, banh xe dat toe do 840 vong/phiit Gia toe goe eua banh xe la

Vi du 3 Mot banh xe dang quay vdi toe do goe lOrad/s thl bj ham va tiep tuc

4 quay cham dan deu vdi gia toe C O do Idn 2rad/sl Lay 71 = 3,14

Cho den khi banh xe dCfng lai, no da quay du'dc xap xi j ^

A 25 vong B 4 vong C lOOvong D 2 vong

M = 0(khi dirng lai)

COQ = 10 rad/s (luc bftt dau ham)

Nen: Acp = 0 - 1 0 '

2(-2)

1

y = - 2 r a d / s (y < 0 vi quay cham dan)

= 25 (rad) ma 1 rad = — vong

271 Vay: Acp = 25 — = 3,98 ~ 4 (vong) Chon dap an B

rj

+ ar

V

r = co^r: gia to'c hu'dng tam

a, = r.y gia to'c tiep tuyen M

+ Gia toe a hdp vdi ban kinh OM goe a ma: tana = " I

CO

Vi du 1 Mot vat ran dang quay deu vdi toe do 2 v6ng/s thl du'dc tang toe, banh

xe quay nhanh dan deu vdi gia to'c 2rad/s' Toe do dai cua diem M tren vat

r i n each true quay 10cm Sau 5s ke ttf lue tang toe la

A v = 3,158 m/s B v = 5,815 m/s C v = 2,256 m/s D v = 4,374 m/s

Giai ' V '

-Toe do goe ban dau (liic t = 0): coo= 27in = 27t.2 = 47i (rad/s) ""^ /

Toe do goe sau 5s: co = coo + yt = 47i + 2.5 22,56 (rad/s) ; ' ' ' ' ' "

Toe do dai cua diem M : v = co.r = 22,56.0,1 = 2,256 (m/s) ^ * ' Chon dap an C ' '

•4

V I du 3 M o t dTa m a i bat dau quay nhanh dan deu tiT nghi K h i dia quay du-dc

I goc l , 5 r a d thi mot d i e m tren vanh dTa dat gia toe tiep tuyen la 2m/s^, gia toe

-V i du 4, M o t banh xe dang quay nhanh dan d e u v d i gia toe goc Irad/s^ quanh

tarn O Sau thdi gian t ke tiT luc banh xe bat dau quay, d i e m M tren vanh

banh xe c6 vectd gia toe a hdp v d i ban kinh C M goc a = 30° T h d i gian t xap

Lf THUYET VA BAI TAP TRAC NGHIEM

1.1 Chpn cau dung Toe do goe eua vat rin quay

A tinh bang cong thiJc

At 2

B tinh bang ddn vj rad/s

C dae tru'ng cho mu'c do nhanh, cham cua ehuyen dong quay

D du"dng neu vat quay nhanh dan va am neu vat quay cham dan 1.2 Chon cau sai Chuyen dong quay deu c6 " '

A gia toe goc la hhng so" • '

B toe do goe k h o n g doi ' " '

C toa do goc du'de tinh b d i : cp = cpo + cot ' "

D goe quay ti le vdi thdi gian quay 1.3 Chon cau diing V d i mot ehieu du'dng bat k i thi

A toa do goe cp > 0 ' - , •

B vat quay theo ehieu du'dng thi co > 0, vat quay theo chieu a m thi co < 0

C vat quay (co y ;^ 0) theo ehieu du'dng thi coy > 0 ' • ''^

D vat quay nhanh dan thi y > 0 - • '•••y':i 'CH-^y-^'Aiy:

1.4 Chon cau diing K h i vat rjfn quay thi eac d i e m khac nhau tren vat ran (khong nam tren true quay) co cung

A toa dp goe va goe quay ' B goe quay va gia to'c g6c

C to'c dp goc va toe dp (dai) D gia toe goe va gia toe (dai) 1.5 M o t vat rKn quay nhanh dan deu tif nghi, to'c dp goc ti le vcjii

A goc quay B binh phu'dng thdi gian

C Ccin bac hai cua thdi gian D can bac hai eua goc quay 1-6 Chpn cong thiJc diing I > ; • ! ; / l u

• -7 Chpn ehieu diTdng la ehieu quay eua vat ra'n thi

A 0) > 0 B y > 0 C co.y > 0 D co.y < 0

1.8 Chon cau sai khi noi ve chuyen dpng quay cua vat rin

A Gia to'c goc dac trU'ng cho siT bien thien cua toe dp goc d moi thdi diem

B Khi vat ran quay deu thi veetcf van to'c eua mot diem tren vat ran khong

C Gia toe hu'dng tam dae trU'ng cho siT thay doi ve hifctng eua vectd van toe

D Gia toe tie'p tuye'n dac trifng cho su" thay doi ve do Idn c u a veetcf van to'c

1.9 Chon cong thiJc dung , , , i ,

A a„ = V ^ r B a„ = C a = r^w'^ +y- D. a, = r.co

1.10 Vat ran dang quay vcti toe dp 10 vong/phiit Toe dp goc cua vat rftn luc do la

A Q) = - rad/s B co = - rad/s C to = —rad/s D co = - rad/s

3 6 3 2

1.11 DTa mai dat toe dp goc 12,56 rad/s sau 5s ke tij" Itic khdi dpng. DTa mai da

quay dUdc

A lOvong B 20v6ng C 2 vong D 5 vong

1.12 Mot banh xe dang quay vdi toe dp 300 vong/phi'it thl bi ham va sau 6s no

con 120 vong/phiit Ke tijT lile ham banh xe se diJng l a i sau

A 10 vong B 25 vong C 8 vong D 50 vong

1.13 Canh quat dang quay vdi toe dp 300 vong/phiit thi li'ie t = 0 canh quat bat

dau quay cham dan deu va sau 5s canh quat con toe dp 180 vong/phiit Canh

quat se duTng lai vao Itic

A t = 1 5 s B t = 1 0 s C t = 12,5s D t = 7,5s

1.14 Sau thdi gian 10s, toe dp quay cua banh xe tang deu tir 120 vong/phiit len

480 vong/phiit Biet ban kinh banh xe la 20cm, trong thdi gian nay xe da chay

y du^c quang du'dng U j " ' - !

A s = 15,7m B s = 125,6m C s = 31,4m D s = 62,8m

1.15 Mot banh xe bat dau quay tu" nghi vdi gia toe goc 2 rad/s' Biet ban kinh banh

xe la 50cm Sau 4s mot diem tren vanh banh xe dii quay dtfdc mot cung dai

g •« •

A s = 8m B s = 4m C s = - m D 16m

n

1.16 Mot dTa mai bat dau quay cham dan deu va dCfng l a i sau 10s Trong 10s

nay dTa quay du"dc 25 vong, lay TC = 3,14 Dp Idn gia toe goe eua dTa la

A l,57rad/s^ B 3,14rad/s^ C 6,28rad/s^ D 12,56rad/s^

1.17 PhiTdng trinh chuyen dpng quay eua vat ran cho bdi cp = 2t^ + 3t - 6, trong

do t tinh bang giay, cp tinh bang rad Toe dp goc Itic t = 5s la

A CO = 15rad/s B co = 42rad/s C co = 23rad/s D co = 8rad/s

1.18 Canh quat dai 50em quay deu vdi to'c dp 90 vong/phiit To'c dp dai cua dau canh quat la

A v = 18,84 m/s B v = 6,58 m/s C v = 24,32 m/s D v = 12,65 m/s 1.19 Mot dTa mai co ban kinh 20cm bat dau quay nhanh dan deu ttr nghi Sau thdi gian lOs ke tu* liie bat dau quay toe dp dai ciia mot diem tren vanh dTa la 20m/s Gia toe gde quay cua dTa bhng

A y = 5rad/s' B y = 8rad/s^ C y = 18rad/s' D y = 1 Orad/s' 1.20 Mot dTa tron ban kinh 30cm bat dau quay nhanh dan deu tCi" nghi vdi gia toe goc 2rad/s^ Sau 10s thi gia toe ht/dng tarn cua mot diem tren vanh dTa lii

A a„ = 60m/s^ B a„= 120m/s^ C a„= 80m/s^ D a„ = lOOm/s^ 1.21 Dau kirn giay cua dong ho de ban coi nhu" chuyen dpng tron deu tren du'dng tron ban kinh 3cm Toe dp dai va gia to'c dai ciia dau kim xa'p xi bang

A v = 0,314em/s va a = 0,033cm/s' B v = 0,526cm/s vii a =

0,248em/s-C V = 1,224em/s va a = 2,140cm/s' D v 2,568em/s va a = 1,634cm/s'

1.22 Coi chuyen dpng ciia cac dau kim giay va kim phiit la cac chuyen dpng tron deu tren cac du'dng tron vdi ban kinh eua dau kim giay bang — Ian ciia

6 dau kim phut Ti so'gia to'c dai ciia dau kim giay va dau kim phiit

A 60 B 120 C 300 D 360 1.23 Trai Dat coi nhu" hinh eau ban kinh 6400km chuyen dpng tron deu xung quanh true ctia no vdi thdi gian quay moi vong la 24 gid To'c dp dai va gia

toe dai cua mot diem tren xich dap gan bang ii ,m q

A V = 465in/s ; a = 0,0338m/s^ B v = 465m/s; a = 34m/s^ '

C v = 228m/s ; a - 0,0338m/s' D v = 228m/s; a = 34m/s^

1.24 Trai Dat eoi nhu" hinh cau ban kinh 6400km chuyen dpng tron deu xung quanh true ciia no vdi thdi gian quay moi vong la 24 gid To'c dp dai va gia to'c dai cua mot diem tren mat dat d vT dp 60" xa'p xi bang

A a 0,4 yfs m/s^ B a = 0,5N/5 m/s^

C a = 0,4 ^ m/s^ D a = 0,8 ^ m/s^

1.27 M o t thanh cu'ng O A dai I m co the quay d6 dang trong mat phang nam

ngang quanh m o t true qua dau O D a u A dat du'dc to'c do 2m/s sau k h i quay

di/dc goc 30° (ban dau duTng y e n ) , luc do gia to'c dai cua dau A xap x i

A a = 12,3m/s^ B a = 8,6m/s^ C a - 5,5m/s' D a = 9,2m/s'

1.28 M o t dTa compact ( C D ) bat dau quay nhanh dan deu tiT nghi xung quanh tam

O K h i quay du'dc goc — r a d thi vectd gia to'c dai a tai d i e m M tren vat ran

6 hdp v<3i ban k i n h O M goc a bang

1.2 Dap an A A sai v i : trong chuyen dong quay deu gia toe goc y = 0

D diing V I goc quay Acp = cp - cpo = : t i l e v d i thdi gian t - ' ' •"- t " '

1.3 D a p an B

A sai, V I neu chon chieu du'cfng ngu^dc v d i ehieu quay cua vat thi cp < 0

C sai, V I vat quay theo chieu du'dng thi co > 0 nhifng neu la chuyen dpng cham

dan thi y < 0, liic do coy < 0

; D sai, V I neu chieu du'dng ngu'dc v d i chieu quay thi chuyen dong nhanh dan

A sai, V I cac d i e m khac nhau tren vat r ^ n eo toa do goc cp khae nhau

C sai, V I toe do (dai) v = co.r; r khae nhau thi v khae nhau , , < « ;

D sai, V I a = -^a^ + a^ , trong do a„ = co^r va a, = yr khae nhau neu r khae nhau,

luc do a khae nhau

1.5 D a p an D , v d i coo = 0 thi co = yt va co = ^2yAcp , ;

V a y toe do goc co ti le v d i can bac hai cua goc quay Acp (va ti le v d i thdi gian t)

1.6 D a p an C, co = - ^ = cp'(t) ' ' ' ' '

dt :.:

1.7 D a p an A V i vat quay theo chieu du'dng thi co > 0

B sai, V I neu chuyen dong cham dan thi y < 0

C sai, V I CO > 0 va y < 0 (cham dan) thi co.y < 0

D sai, V I CO > 0 va y > 0 (nhanh dan) thi coy > 0

Trong 5s dau: CO] - coo = yti

Tuf luc t = 0 de'n k h i dij'ng (co = 0): 0 - cOo = yh

^ = 5 0 7 t ( r a d ) ^ = 2 5 ( v 6 n g )

271

(1) (2)

(11. ^ 1- ^ 0 t, (2) -COn t

PhLfOng phjp giai b^i tjp trSc nghigm Co hgc 12 - Trgn Trgng Hung

nen: = 5 = 12,5 (s)

671-1071 1.14 Dap an D

2 271

M o i vong quay xe di diTdc: S | = 27I.R = 271.0,2 = 0,471 (m)

Quang du'dng xe da di du'dc trong 10s: s = 50.0,471 = 62,8 (m) ' ' > *'

1.15 D a p a n A

• Goc quay: Acp = - y t ^ = - 2 4 ^ = 1 6 (rad) * S / ; ' :

; } 2 2 ' \ • • "••1 !

• V d i goc quay d tam la Acp thi mot diem tren vanh banh xe se quay mot

cung dai: s = R.Acp = 0,5.16 = 8 (m)

• So phiTdng trinh da cho: cp = 2t^ + 3t - 6

V d i phiTdng trinh tdng quat: cp = ^ y t ^ + cogt + cpo ta du'dc

—y = 2 - > y = 4 rad / s^

COQ = 3 rad/s ^fo

B i e u thiJc tinh toe do goc: co = COQ + y.t = 3 + 4t (rad/s) ?

= ( y t ) l R = (2.10)'.0,3 = 120 (m/s') 1.21 Dap an A

Toe do k i m giay: n = 1 vdng/60s Toe do goc: co = 27tn = 2?: — = — (rad/s)

60 30 Toe do dai: v = coR = ^ 3 « 0,314 (cm/s)

Gia toe dai: a = a,, = co^R =

30 1.22 Dap an C

Goi k i m giay la so" 1 , k i m phut la so 2

• v = coR = (27rn).R, vdi n = 1 v6ng/24 gid =

1

O v/s

a

R 6400.10 J « 0,0338 (m/sO

Phuong ph^p giai bSi t j p Xr&c nghigm Co hpc 12 - TrSn Trpng Hung

To'c do xe cung la to'c do dai v cua

mot diem tren vanh banh xe: v = 18km/h - 5m/s

Cty T N H H M T V D W H Khang Vigt

• Co co' - COQ = 2y.A(p

c o ' - 0 = 2y.Acp=^ ^ = - 1 - ^ - ^ = 73

co^ 2.A(p 2 V3

hay tana = N/3 => a = ^ > ' ) ' „ > ' , ; 1

Bal 2 PHl/CJNG TRJNH DpNG Ll/C HQC C U A VAT RAN QUAY QUANH MOT TRgC CO DjNH

TOM TAT LI THUYET b u;' n

1 Momen Wc dO'i vdi true quay

• Momen cua life F ddi vdi true quay la M = F d

( N m ) ( N ) ( m )

vdi d la khoang each tCf true quay den gia eua li/e F

M > 0 ne'u liJc F eo tac dung lam vat quay theo chieu du'dng (thu'dng la chieu quay eua vat) va M < 0 neu ngiTdc lai

2 Momen quan tinh , • i ( , 1 I

• Momen quan tinh I doi vdi mot true la dai lu'dng dae trifng cho miJe quan tinh cua vat ran trong chuyen dong quay quanh vat ay

• Cong thtfe:

^ 2 m ~: I un'nh

• Ddn vi eua I la kg.m

• Momen quan tinh cua mot so' vat ran dong chat doi vdi true doi xtfng

a Thanh C O tie't dien nho so vdi chieu d a i / : I = —m./^

12

b Vanh tron ban kinh R: I = mR' < i " , n O t '

c DTa tron mone: I = —mR^ , ,,

Phoong phap giai bSi tap trSc nghigm Co h o d 2 - Jr^.n Trqng Hung

' Chon chieu diTdng la chieu quay cua vat thi

+ M > 0 ne'u liTc F c6 tac dung lam vat quay

+ M < 0 neu life F c6 tac dung lam can vat quay

+ M = 0 neu gia cua life F di qua true quay

D 4N.m

y F 2

V i du: Mot rong roc ban kinh 10cm c6 the quay de

dang xung quanh true qua tam O cua no Vat qua

ranh cua rong roc mot doan day khong dan roi tac

dung vao hai dau day hai life cCing hifdng thang diTng

/ xuong dirdi vdi cac do Idn F, = ION, Fj = 6N (Hinh

ve) Momen life tac dung vao rong roc

A l , 6 N m B 0 , 4 N m C 16N.m

Giai

V i F, > F2 nen rong roc se quay theo chieu cua lire Fj , vi vay lUc Fj se c6

momen life M j > 0 con lUc Fj eo momen life M2 < 0 vdi:

M , = F , R = 10.0,1 = 1 (N.m)

M2 = - F 2 R =-6.0,1 = - 0 , 6 (N.m)

Momen Itfe tac dung vao rong roc la: M = M , + M2 = 1 + (-0,6) = 0,4 (N.m)

Chon dap an B ^

D a n g 2 MOMEN QUAN TINH

a Cong thiJc tinh momen quan tinh cua:

- Khoi cau dac: I = - m R ^

b Momen quan tinh luon luon la so' du^dng

c Momen quan tinh eo tinh cong

Vi du 1: Thanh manh dai I m , dong chat va tiet dien deu, khoi \\idng 900g, mot

dau gan, vdi vien bi nho (coi nhU chat diem) kho'i lUdng 200g Momen quan

tinh cua he (thanh va bi) doi vdi true quay qua khoi tam va vuong goe vdi

V i du 2: Trai Da't coi nhiT mot khoi caU dac c6 ban kinh 6400km, kho'i lUdng

rieng la 5,5 lO-* kg/ml Momen quan tinh cua Trai Daft do'i vdi true quay xa'p xi

A I = 4,5.10"kg.m^

C 1 = 4,5.10" kg.m^

B I = 9,9.10" kg.m

D I = 9,9.10" kg.m Giai

2 Momen quan tinh cua hinh cau dac: I = - m R ^ ,

v d i m = V D = - T T R ^ D ; / ?

3 • • nen I = —

= —.7c.(6400.10^)^5,5.10^ = 9,8898 x l O " « 9,9.lO" (kg.m') Chon dap an D

.-Dang 3 P H l / O N Q T R I N H D O N Q L l / C HQC CUA V A T R A N Q U A Y

PhUdng trinh dong life hoc cua vat ran quay quanh mot true c6' dinh la:

M = I.Y

vdi : • • Jivsov ,

• M la to'ng cac momen Itfc tac dung len vat ran (ddn vi la N.m)

• I la momen quan tinh cua vat ran doi vdi true quay (ddn vi la kg.m')

• y la gia to'e goe quay cua vat ran (ddn vi la rad/s')

Vi du 1 Mot dTa tron dong nha't cd ban kinh R = 50em, khoi lUdng m = 1kg DTa

chiu tac dung cua liTe cd phiTdng tiep tuyen vdi vanh dTa, do Idn F = 1,5N Bo qua lye can tac dung len dTa DTa quay xung quanh true di qua tam vdi gia toe goe

A Y = 3rad/s' B 7 = 6rad/s' C y = 5rad/s' D y = 8rad/s'

Giai Phu'dng trinh dong liTc hoc: M = I.y

19

Vi du 2 Mot banh xe c6 momen quan tinh doi vdi true quay eo dinh la 5 kg.ml

Banh xe dang quay deu vdi toe do goc 10 rad/s thi chiu tac dung cua momen

life can c6 do Idn 20N.m Banh xe diTng lai sau khi quay them diTdc xap xi

A 12,5 vong B 4 vong C 2 vong D 25 vong

i • Gia toe goc cua banh xe sau khi ehiu tac dung cua momen life can: '

; i t t M , -20 , , 2 , • • '''^ •

[dau - VI banh xe chuyen dong cham dan] ; ' ; * r

Ap dung: co^ - COQ = 2yA(f> => Acp = CO - C O o

2Y

: ° I l l ^ = 12,5(rad) 2(-4)

12.5

271

( v o n g ) « 2 (vong) Chon dap an C

V I du 3 Mot dTa mai c6 bdn kinh R = 50cm, khoi lifdng M = 10kg dang quay vdfi

toe dp 300 vong/phiit thi bi ham bang dp liTc Q hu^dng vao tam O ep len vanh

dia nhiThinh ve vdi dp Idn Q = lOON lam cho dia quay cham dan roi diTng lai

[ Biet he so ma sat giffa dp liTc Q va vanh dia la = 0,5 Ke tijf liic bi ham cho

den khi diTng lai dia quay di/dc xap xl ;^ -J).)

A 1 vong B 2 vong ;

C 3 vong D 4 vong

• Ap life Q tao ra life ma sat (Fms) tiep xuc vdi vanh dTa c6 dp Idn:

F,„s = ^Q

• Momen life ham: M = -Fms-R = -jaQ.R

(c6 dafu - VI momen nay can chuyen dpng)

:>": • Theo phiTdng trinh dpng liTc hpc cua vat ran quay:

M = I.Y => Y = - vdi I = IMR^ nen Y = =

Cty TIMHH MTV DVVH Khang Vigt

luc dTa dCfng lai: co = 0 nen: -COQ = 2y^.(^ => Acp = - — = cogMR

, , , : M R !.u

vdi COo = 300 v/ph = 5 v/s = lOn rad/s, ta duUc: t: -.5 * ' •, :,{! :•[ >; j

-= CO^)4.0,5.100 271 'Q-Q^^ ^ 2,571^ (rad) = ^ ^ ( v o n g ) « 3,925 (vong) ^ 4 (vong) Chpn dap an D

Vi du 4 Mot rong roc la mot dTa tron c6 momen quan tinh I , ban kinh R quay de dang xung quanh mot true nam ngang qua tarn

O Mot doan day nhe khong eo dan du'dc vat qua ranh rong rpc Mot dau day du'dc treo vat nang khoi lu'dng m, dau kia

du'dc keo bang liTc F lam vat nang m di len Lay gia toe rdi tiT

do cua vat la g Gia toe chuyen dpng cua vat m la

• Gpi T la siJc cdng day treo vat nang m va a la gia , I^i

toe chuyen dong cua vat, ta c6: ni\ut fpii

T - m g = ma =?'T = m(g + a) ( I )

• Rong rpc chiu tac dung hai liTc tiep tuye'n vdi • T

rong roe la siJc cang T va liTc keo F Hai liTc nay m tao nen chuyen dpng quay cua rong rpc nen:

Phuang phap giai bai t$p trSc nghigm Co hqc 12 - Jrin Trpng Hung

Vi d u 5 Rong roc la mot vanh tron c6 momen quan tinh I ,

ban kinh R Vat qua rong roc la doan day nhe khong co

dan, hai dau day treo hai vat nang m, va m2 ma m; > rrij

nhu" hinh vẹ Lay g la gia toe rdi tU" dọ Tha cho hai vat

chuyen dpng Gia toe chuyen dong eua cdc vat la

• Rong roc chiu tac dung cua hai life tiep

tuyen T| va T2 lam cho rong roc quay nen: , ,

1 Neu hai dau day c6 treo hai vat nang thi: Fi = mig; F2 = m2g

2 Néu nipt dau day la vat nSng m con dau kia keo bang krc F thl:

F - m e

Cty T N H H M T V D V V H K r i i g Vigt

C A U H O I V A B A I T A P T R A C N G H I E M

2.1 Dai li/dng nao sau day luon luon la só dÚcJng?

Ạ Momen life B Momen quan tinh

C Gia toe goe : D Toe do goc

2.2 Momen liTc co đn vi la

A N B N/m C N.m " D kg.m 2.3 Mot vat dang chuyen dong quay nhanh dan deụ Sau do thoi tac dung life vao vat thi no ,

Ạ vSn tiep tuc quay nhanh dan deu B quay cham dan deu

C dufng yen D quay deu

2.4 Mot dTa tron co ban kinh R = 20cm, khoi lUdng m - lOOg Momen quan tinh

cua dTa dói vdi true quay di qua tam la

Ạ I = 0,04 kg.m' B I = 0,002kg.m' C I = 0,02kg.m' D I = 0,004kg.m' 2.5 Biet momen quan tinh cua thanh dai /, khoi lúdng m doi vdi true quay di qua mot dau thanh nhif hinh ve diTdc tinh bdi eong thtJe: I = ^ T I ' ' ^

O

Mot thanh OA dai 50em, khoi liTdng 200g phan bó deụ Dau A co gan vien bi nho khoi IiTdng 50g Momen quan tinh cua thanh dói vdi true quay di qua dau O va vuong gdc vdi thanh xáp xi bang

Ạ I = 0,029kg.m' B I = 0,017kg.m' C I = 0,013kg.m' D I = 0,023kg.m' 2.6 Trai Dat coi nhU hinh cau dac co khoi liTdng rieng trung binh la 5520 kg/m^

v i ban kinh trung binh 6400km Momen quan tinh cua Trai Dat doi vdi true quay cua no xáp xi bang

A I = 4,5.10"kg.m' B I = 9 , 9 I 0 " k g m \

C I = 6,8.10'' kg.m' D I = 2,8.1 Ốkg.m' *' ' ' 2.7 Mot dTa tron ban kinh 20cm khoi lúdng 1kg dang quay vdi toe do 120 vong/phiit thi bj liTc ham tiep xuc vdi vanh dTa cd do Idn 1,57N DTa dijrng lai

-Ạ t = 0,6s B t = l , O s C t = l , 2 s D t = 0,8s 2.8 Mot thanh manh chieu dai / khoi liTdng phan bo deu cd the quay xung quanh mot true nam ngang qua dau Ọ Biet momen quan tinh cua thanh doi vdi true

Phuong phAp giii bit tjp trie nghigm Co hqc 12 - Trjn Trgng Hung

O la ^ m ^ ^ (m kho'i lUdng cua thanh) Tha thanh liic no dang nam ngang

L a y gia to'c rdi tiT do la g Gia toe goc cua thanh liic vuTa tha

2.9 M o t thanh manh O A kho'i lifdng phan bo'deu c6 the quay de dang xung quanh

dau O B i e t momen quan tinh cua thanh doi vdi dau O la I = - m / ^ vdi m la

khoi lu-dng va / la chieu dai cua thanh L a y g = 9,8m/sl Thanh du-dc tha nhe

liic thanh dang nam ngang Gia toe dai eua dau thanh A liic vCfa tha la

A 9,8 m/s^ B 4,9 m/s' C 14,7 m/s^ D 18,4 m/s^

2.10 M o t thanh manh O A dai / = 50em, khoi lu'dng m = 200g phan bo deu tren

thanh c6 the quay de dang xung quanh true qua dau O tiong mat phang nhm

ngang B i e t momen quan tinh cua thanh doi v d i dau O tinh bang cong thilc

I = ^ m / ' L i i c thanh dang nam yen ta tac dung vao dau A mot life F c6 do

Idn ION va vuong goc vdi thanh Toe do dai cua dau A li'ie thanh q u e l difdc

goc 60° xa'p XI bang , , = , , , , ,

A 9,4 m/s B 25,7 m/s C 4,3 m/s D 12,5 m/s

2.11 M o t banh xe eo dang vanh tron ban kinh 50em dang quay v d i toe dp goc

lOrad/s thi bi ham l a i Life ham c6 do Idn 2 N , ep len vanh banh xe va hu'dng

ve true quay Life ma sat giiJa life ep va vanh banh xe la 0,2 Sau thdi gian 5s

banh xe dijfng l a i K h o i lifdng banh xe

A 0,4kg B 0,2kg C 1,0kg D 0,8kg

2.12 M o t dia mai quay nhanh dan deu tif nghi B i e t rhng liic nay dTa ehiu tac

dung dong thdi cua momen phat dong va momen can K h i dTa quay du'dc goe

60" thl momen phat dong thoi tac dung, dTa quay cham dan deu r o i difng lai

sau khi quay them du'dc goe 30" Dp Idn momen phat dong M va momen can

M ' ( M va M ' deu du'dng) lien he vdi nhau bang bieu thi'fc , ^

A M = 0 , 5 M ' B M = 1 , 5 M ' C M = 2 , 0 M ' D M = 2 , 5 M '

2.13 M o t rong roc c6 momen qudn tinh doi vdi true quay la I ,

ban k i n h R T r e n ranh rong roc c6 quan mot doan day nhe m *

khong dan, dau day c6 treo vat nang m nhu"hinh ve Vl_y

Tha eho vat chuyen dong G o i g la gia toe rdi tif do j ,

Gia toe ehuyen dong cua vat la , Mn\

Cty TNHH MTV DVVH Khang ViQt

D a = mgR

R" R^

2 14 Rong roc la mot dTa tron kho'i lu'dng 600g M o t doan day nhe khong dan vat qua rong roc, hai vat nang khoi lu'dng

Ian Wdt mi - 300g, m2 = 200g treo d hai dau day nhu' hinh

ve L a y g = 9,8 m/s^ L u c dau giff eho hai vat ngang nhau

roi tha nhe Sau 2s hai vat da each nhau (tinh theo phUdng

2.15- Rdng roc c6 ban kinh 50cm, momen quan tinh d o i vdi true quay la 0,025kg.m' M o t doan day nhe khong dan quan quanh ranh rong roc, mot dau day treo vat nang kho'i lifdng lOOg la'y g = 9,8 m/s^ Tha vat chuyen dong, gia toe goe quay eua rong roe la

rad

G

m

2.16 M o t rong roc c6 momen quan tinh doi vdi true quay la 0,012 k g m ' , ban kinh 20em Vat qua rong roc day nhe khong dan, hai dau day mang hai vat nang kho'i lu'dng Ian lu'dt 500g va 200g nhu' hinh ve; lay g = lOm/sl Luc dau giif hai vat diJng yen Tha nhe eho hai vat chuyen dong, sau 0,5s mot diem tren vanh rong roe da quay vdi toe do goe

A 15,0 rad/s B 6,4 rad/s C 2,7 rad/s

HadNGDANGIAI

2.1 Dap an B '

M o m e n quan tinh I = ^ m j r j ^ luon luon la so difdng

i ,!(!"| 2-2 Dap an C ,

Cong thife tinh momen l i f c l a : M = F.d

V d i F ddn v i la N ; d ddn v i la m nen M cd ddn vj la N m

D 7,5 rad/s

• L u c thoi tac dung life (F = 0) nen M = F.d = 0

• Hdn niJa tru'de do vat dang quay nen sau do vat quay deu

M „

y = y = o

2.4 Dap an B

I = i m R ^ =i.0,1.(0,2)^ = 0 , 0 0 2 (kg.m')

2.5 Dap an A ;,

• M o m e n qudn tinh cua thanh: Ij =^m,./^

• M o m e n quan tinh cua bi: h = m 2

V a y momen quan tinh cua thanh c6 gdn bi la:

i m R ^

2

2 F

mR

• Co: w = coo + y.t

Luc dTa dtfng lai (w = 0):

• Life tac dung vao thanh la trong li/c

mg dat tai trong tarn G cua thanh

• Gia toe dai cua dau A: a = ^/a^ + a^

• Gia toe gdc cua banh xe sau khi ham: y = - C O o

Momen lu'c ham: M = Ly = mR^

Phaong ph^p giil bai t$p trie nghi^m Co hqc 12 - TrSn Trgng Hifng

=:> m R \ = ,.QR ^ m = i i O l = = 0,4 (kg) n ,V^

t R.coo 0,5.10

2.12 Dap an B

• Life CO momen phat dpng: , \ r i ; '

+ co^ = 2y Acp -> y = — — "* ,

n , m , i , 2 R^ 2 *

Sau thdi gian t moi vat di du'dc quang du'Sng s (vat mi di xuo'ng, vat m2 di len)

1 2 vdi: s = - a t ; Luc do Chung each nhau: d = 2s = a.t^ = 1,225.2^ = 4,5 (m) 2.15 Dap an C ,

Gia toe cua cac vat eung la gia toe tiep tuyen cua vanh rong roc:

- M o m e n dong lu'dng cua vat r^n d6'i true quay la [ L = Leo

- Ddn vi cua momen dong lU'dng la: kg.mVs 2- Dinh luat bao toan momen dong lif(/ng

N J u M = 0 thi L = hang so] ^ ^, , ,

~ V a t CO I khong doi thi no khong quay hoSc quay deu

- V a t CO I thay doi thi Ijco, = IjWa

29

huong ph^p giai bjii tgp trSc nghigm Co h9c12 - TrSn Trgng HUng

BAI TAP C d B A N

D a n g 1 M O M E H D O ^ Q L U O r i Q

Cong thifc: L - ICQ Ddn vi cua I la kg.m^; oo la rad/s; L la kg.m^/s

/i du 1 Trai Dat coi nhiT hinh cau dac c6 ban kinh 6400km, khoi liTdng rieng

5 , 5 1 0 \ g W quay deu xung quanh true cua no v d i chu k i 24h M o m e n dong

lUcfng ciia T r a i Da't xap X I bang

V i du 2 M o t banh xe bat dau quay tiT nghi xung quanh true cua no di/di tac dung

cua m o m e n liTc 0,5N.m thi sau 10s banh xe c6 momen dong lu'dng

V i du 3 M o t thanh O A dai 20cm dong chat, tiet dien deu khoi lifdng 600g Hai

dau O va A C O gan hai vien bi nho cung k h o i liTdng 300g Cho thanh quay deu

trong mat phang nam ngang xung quanh mot true thang duTng d i qua dau O

To'c do quay cua dau A la Im/s

Diet momen quan tinh cua thanh d o i v d i

1 2

true quay tinh bang cong thiJc I = -Ml ,

30

Cty TMIIIi MTV DVVH Khang Viet

trong d6 M va / la kho'i lu'dng va chieu dai cua thanh

M o m e n dong lu'dng cua thanh luc dang quay la

A 0,2kgm^/s B l,Okgm^/s C 0,lkg.mVs D 2,0kg.m^/s

Giai

M o m e n dong lu'dng cua thanh: L = I.co, v d i :

• I la momen qudn tinh cua thanh va b i d A d o i v d i true quay (con momen quan tinh cua bi d O bang 0)

Chon dap an C

D a n g 2 D I N H L U A T B A O T O A N M O M E N DOING L U p N G

Neu M = 0 thi L = hang so , , ; ; ; ,

• I khong d o i : vat khong quay hoac quay deu - v , M ;

• I thay d o i : I.co = hang so"

V i du 1 M o t ngu'di dufng d tam cua mat ban xoay, hai tay cam hai qua ta ciing kho'i lu'dng mo = 2kg L u c dau hai tay ngu'di nay dang ngang, hai qua ta each true quay r = 50cm va cho ghe quay vdi toe do U i = 3 vdng/s, sau do ngu'di nay xep tay l a i sat ngu'di Cho rang momen quan tinh cua ngu'di va mat ban do'i v d i true quay khong doi va bang IQ - 2kgm^ Toe dp quay cua mat ban luc xep tay l a i la , • nft''*f,f'

^huong phAp giSi bai t^p trie nghigm Co h9c12 - Iran Irgng Hang

M

Vi d u 2 Thanh cUng O A dai / khoi lifdng M va bi nho khoi liTdng m = — cle

dang trifcJt tren thanh Thanh c6 the quay trong mat phang nam ngang xung

quanh true thang diJng di qua dau O (hinh ve) Diet momen quan tinh cua

thanh doi vdi true quay la I = ^ M / ^

(m)

Luc dau bi 6 A , truyen cho thanh quay deu vdi toe do 10 vong/s De thanh quay

vdi toe do 18 v6ng/s thi can di chuyen nhe nhang bi den each true quay khoang

Ngoai lire tae dung vao thanh (gom trong life cua thanh va bi) deu cung

phifdng thang diJng vdi true quay nen momen ngoai life bang 0, do do:

M

T " " 3 ,

I , = i M / 2 + m x ^ = ^ ( / ^ + x2) coi =27tni;c02 =27^2

V i d u 3 H a i dTa tron D , , D2 c6 khoi lifdng

va ban k i n h Ian liTdt m, = R i = ^ D

dong true quay nhiT hinh ve L u c dau dia —

Di quay vdi toe do n, = 234 vong/p con 6 2 ^ ^

dia D2 ddrng yen M a sat 5 true quay " ' ' ^ ^

C A U HOI T R A C N G H I E M V A BAI TAP

3.1 Chon eong thiJc d i i n g

3.3 N e u l o n g cae m o m e n ngoai liTe tae dung len vat bang 0 thi

A L = 0 B vatdiJng yen C vat quay deu D L = h a n g s o 3.4 N e u tong m o m e n ngoai liTc tae dung l e n vat ran (tu-c ed I k h o n g d d i ) triet tieu thi vat CO

A y = 0 B 7 = hang so C 00 = 0 D co = hang soV 0) 3.5 Ngu'di mua ba le dang quay ngu-di tren dau ngdn chan cai (quanh mot true

th^ng diJng di qua dau ngdn chan) v d i hai tay luc dau x e p sat ngu'di N e u ngirdi ay tiJ tCr dang tay ra thi ho ' ' , - a 1 >•

A lap tu-c dijfng l a i • i ' ' B van quay nhuTcu i i ;

C quay nhanh dan D quay cham dan j - " t ' rv/

3.6 M o t v i e n bi nho k h o i li/dng lOOg quay deu 10 vong trong 2 g i a y va each true quay I m M o m e n dong lu'dng eua bi la

A l,57kg.m^/s B 6,28kg.m^/s C 3,14kg.m^/s D 4,85kg.m^/s 3.7 M o t ngirdi khoi lu'dng 60kg dang difng tren M a t D a t d vT do 45° Coi T r a i

B a t la hinh eau ban kinh 6400km va tiT quay quanh true cua no v d i thdi gian

" l o i vong quay la 24 g i d M o m e n dong lu'dng eua ngu'di d o i vdi true quay cua

T r a i Da'txa'p X I bang

A 89315,6kg.m-/s B 17863Ikg.m'/s C 89,3kg.m'/s D 178,6kg.m'/s

^•8 M o t vat ran bi(t dau quay nhanh dan deu tCr nghi vao liie t = 0 V a o liic t,

momen dong lu'dng ciia vat la L ; thi vao liie t2 = 2t| momen dong lu'dng cua

vat la

33

A ^ B 2L, C ^ D 4L,

2 4

.9 Mot vat ran bat dau quay diTdi tac dung cua momen life c6 do Idn 0,1 N.m thi

CO momen dong luTdng la Ikg.m^/s sau thdi gian ,

A 10s B Is , C 20s D 5s '

.10 Mot dTa tr6n ban kinh 20cm dang quay nhanh dan deu du'di tac dung cua

liTc tie'p xuc vdi vanh dia Trong thdi gian 2s, momen dong lu"cfng cua dia tang

them 5kg.m^/s Dp Idn life tac dung vao vanh dTa la

A 25N B 15,6N C 5,8N D 12,5N

.11 Mot thanh ciJng dai Im, kho'i lufdng 600g phan bo deu tren thanh, hai dau

CO g^n hai bi nho, khoi lifdng moi bi la lOOg Thanh quay deu quanh true di

qua trung diem va vuong goc vdi thanh, toe dp moi bi la lOm/s Momen dpng

lu'dng cua he thanh va hai bi la

C 5kgm^/s D 20kgmVs 4^

.12 Mot ngiTdi khoi lu'dng m (coi nhif cha't diem) dang diJng d mep san hinh

trdn nam ngang khoi luTdng M = 4m c6 the quay de dang xung quanh true

thang diJng Liie dau ngiTdi va san dilng yen Ne'u ngu'di ay chay deu quanh

mep san vdi toe dp goc coo thi san

A van diJng yen

B quay deu vdi toe dp goe 0,5cOo theo chieu ngiTdc vdi ehieu chay cua ngiTdi

C quay deu vdi toe dp goc 0,5coo theo cting ehieu chay cua ngu'di

D quay deu vdi toe dp goc 4CL)O theo ehieu ngiTdc vdi ehieu chay cua ngu'di

.13 Hai dTa tron D , va D2 bKng dong, c6 cung dp day nhu'ng ban kinh Ri = 2R2

C L i n g true thang du'ng Luc dau hai dTa rdi nhau va dang quay cung chieu vdi

cae toe dp n i = 2 vong/s va nz = 4 vong/s thi sau do hai dTa dinh nhau va ciing

quay vdi toe dp

A 8/3v5ng/s B 12/5 v6ng/s C 36/17 v6ng/s D 20/9 v6ng/s

.14 Hai dTa tron D i , D2 c6 khoi liTdng va ban kinh Ian liTdt m i = m2, R, = c6

cung true quay thang dufng Luc dau hai dTa rdi nhau va quay ngiTdc chieu

nhau vdi cae toe dp coi = 4rad/s, 0)2 = 8rad/s sau do du'de tha nhe nhang cho

hai dTa dinh nhau, chung ciing quay vdi toe dp

A 5,6rad/sva ngu'dc ehieu quay cua D | ^ ^ ' ^

B 5,6 rad/s va eijng chieu quay cua P | i '

C 4,0 rad/s va ngiTde ehieu quay cua D i

D 4,0rad/s va ciing chieu quay cua D i '

3.15 Mot van dpng vien triTpt bSng dang du'ng yen va quay, neu hp dang tay ra thi

A quay cham lai VI momen quan tinh giam

B quay cham lai VI momen quan tinh tang

C quay nhanh hdn vi momen quan tinh giam

D quay nhanh hdn VI momen quan tinh tang

HLfdNG D A N GIAI

3.1 Dap an B ' ' 3.2 Dap an C

3.3 D a p a n D ^ ^ , ^, _ ,

C d M = 1 ^ = 0 v i I^ O z z ^ ^ ^ 0 hayy = 0

dt dt (chij y: y = 0 thi CO = 0 hoae co = hang so)

3.5 Dap an D VT trpng life cua ngiTdi song song vdi true quay nen tong momen ngoai lirebangkhong, d o d 6 : I , c O | = l 2 C 0 2 O C 0 2 = i-co, 1 •* •

Khi tir tir dang tay ra thi I2 tang dan nen ©2 giam dan: ngiCdi ay quay cham dan 3.6 Dap an C

L = Leo = (mR^).27tn vdi n = ^ = 5 (v6ng/s)

= (0,1.1 ').27t.5 = 7t = 3,14 (kg.m^/s) 3.7 Dap an A

• Ngu'di each true quay khoang: r = M H = Rcoscp

• Momen quan tinh cua ngu'di do'i vdi true quay:

I = mr^ = m(Reos(p)^

• Momen dpng lu'dng eua ngiTdi:

L = 1(0 = m(Reos(p)l — = 60(6400.eos45°)l

24.3600 -89315,6 (kgm^/s) 3.8 Dap an B

V d i M = F.R nen: A L = F.R.At =^ F = AL

R.At 0,2.2 = 12,5(N) 3.11.Dap a n B

Tong momen ngoai life tac dung len he bang

khong VI ngoai li/c (la trong liTc cua ngu'di va

san) song song vdi true quay cua san nen:

= ^.Ti.Rf d.D (d: do day; D: khoi lUdng rieng)

Ti/dng tif: I2 = ^ n R j d D VI R, = 2R2 I i = 2\l2 = I6I2

• D i n h l u a t b a o t o a n d o n g l i T d n g

L i + L 2 = L

36

Cty TMh ' DVVH Khang Vi§t

I|CO| + I2CO2 = ( I | + I2).C0 CO

I,.n, +I2.n2 16I,.2 + l2.4 36 ^ , ^

=> n = —— — - = = — = — (vong/s)

I , + I 2 I 6 I 2 + I 2 17 3.14 Dap an A

I , + 4 1 , • = -5,6(rad/s) Da'u " - " chu-ng to khi dinh nhau hai dTa cung quay ngU'dc chieu vdi D , , toe

; TOM TAT LI THUYET

Dong nang cua vat ran quay quanh mot true co djnh W , =-.I.co2 vdi:

I la momen quan tinh cua vat (kg.m^)

CO la toe do goc quay cua vat (rad/s) W,, :Jun

^hifong ph^p giai bai tjp UJc nghigm Co hQc12 - Tran Trgng Hung —

BAI TAP C d BAN

Vi d u 1 M o t vat ran quay quanh mot true c6 dinh Goi I va L Ian lu'dt la momen

quan tinh va momen dong lifdng cua vat doi vdi true quay do thi dong nang

Vi du 2 Coi banh xe liJ-a nhiT mot dia tron dong chat 6 ciing thcfi diem banh xe

dang chuyen dong, giiTa dong nang tinh tien W j („> va dong nang quay W j (q,

lien he bang bieu thtjfc

V i du 3, Mot vien bi c6 hinh cau dac khoi lu^dng m ISn khong triTdt vcti toe do V

Dong nang cua vien bi la

A 0,7mV' B 0,2mV' C 0,5mV^ D mV^

G i a i Dong nang cua vien bi liic dang Ian:

Cty TIMHH MTV DVVH Khang Viet

V i du 4 Banh da la mot dia tron c6 khoi lu'dng 100kg ban kinh 50cm Lay TT^ = 10

De banh da dat du^dc to'c do 120 vong/phut tuT nghi trong thdi gian 10s thi cong sua't trung binh cua dong cd cung cap cho banh da la

A 25W B 200W C SOW D lOOW

Gi^i Dinh l i dong nang: A ( n g o a i t o , = W d ( s , „ , ) - W < , « , i t u ) = -Im^ -0 = -W

vdi I = - m R ^

2 (n = 120 vong/phiit = 2 v6ng/s)

co = 27in nen A (ngoai life) ~ 1 i-mR^

.2 (27m)' = mR'.Ttln^ = 100.(0,5)^ 10.2' = 1000 (J)

A(ngoaiivrc)Chinh la cong c u a dong cd nen cong suat dong la:

P = A i ^ = , 0 0 ( W )

t 10 Chon dap an D

V i du 5 M o t qua cau du^dc tha Ian khong tru^dt tiT trang thai nghi d A cua mat phang nghieng vdi do cao A H = h (hinh ve)

Bie't momen quan tinh cua qua cau la I = "•nR^

trong do m va R la khoi lu'dng va ban kinh Toe

do khoi tarn qua cau khi Ian den B la

4.1 D ai liTdng khong phu thuoc vao khoi lu'dng eiia vat la C A U HOI VA BAI TAP TRAC NGHIEM

^ - m o m e n quan tinh B dong nang

^- momen lire D momen dong lu'dng

39

Phuong ph^p giSi b^i tjp trie nghi^m Co hqc 12 - TrSn Trpng HtJng

4.2 M o t vat ran quay quanh true c6' dinh M o m e n dong lifdng t i n g 2 Ian thi dong

A tang 2 Ian B g i a m 2 1 a n C tang 4 Ian D g i a m 4 Ian

4.3 M o t vat ran dang quay quanh true eo djnh v d i momen dong lu'dng la

1 kgm^/s va dong nang la 2J M o m e n quan tinh eua vat la

A 0,25kg.m' B 0,5kg.m^ C l,Okg.m' D l , 5 k g m '

m

4.4 M o t rong roc c6 ban kinh 20em, momen quan tinh 4 1 0 ' \ g m ^ de dang quay

xung quanh m o t true c d dinh qua tam eua no D o a n day manh quan quanh

rong roc, dau kia treo vat nang lOOg (hinh ve) ' :

La'y g - l O m / s l T h i i nhe cho vat nang chuyen dong

tijf nghi Sau Is d o n g nang quay eua rong roc la ^ j „ J

A 2,50J B 1,25J

-C 3,75J D 12,5J

4.5 C o i T r a i D a t nhu" hinh cau dac c6 khoi lu'dng 6.10^^kg tif quay xung quanh

true eua no v d i thdi gian m o i vong quay la 24 g i d

D o n g nang quay eua T r a i D a t xap x i

' A 2,6.10'"'J B 2,6.10" J C 4 , 8 1 0 '' j D.4,8.10'-'j

4.6 M o t cai ong thanh mong dong chat va tiet dien deu Ian khong tru'dt Biet

m o m e n quan tinh eua 6'ng la I = M R ^ trong do M la k h o i lu'dng va R la ban

k i n h eiia tiet d i e n

d eCing m o t thdi d i e m giffa dong nang tjnh tien W(„) va dong nang quay W(q)

CO lien he

A W,„) = 2W (q) B W „ „ = - W , „ C W„„ = 4W, (q) D W(,o = W,q,

4.7 M o t dTa tron ban k i n h 10cm, khoi lu'dng 4kg c6 true quay d tarn dTa Tac

dung m o t life 2 N t i e p xiic v d i vanh dia k h i dTa diJng y e n Sau 6s ke tif luc bat

dau quay, d o n g nang eua dTa la ^'^^'^ ' - i ^

A 18J ) B 9J W ,«, ! C 72J i ,: ^ D 36J

4.8 M o t banh da coi nhu' dTa sat dong chat c6 ban kinh R = I m va khoi lu^dng

M = 5000kg dang diJng y e n M o t dong cd cong suat trung blnh P = lOkW lam

banh da quay L a y = 10 Banh da dat toe do n = 120 vong/phut sau thdi gian

A lOs B 20s C 15s D 30s

4.9 M o t banh xe (coi nhu' dTa tron) kho'i lu'dng M = 20kg Ian khong tru'dt tren

mat phang ngang v d i toe d o eua khoi tam la v = 18km/h

D o n g nang ciia banh xe la

A = 125J B Wa = 250J C Wa = 375J D W,, = 500J

40 • ' • • •

Ciy frjilil M i V DVVH Khang Vigt 4.10 Thanh O A dai / dong chat tiet dien deu c6 the quay dS dang xung quanh true quay qua dau O

Luc dau thanh diJng y e n 6 vj t r i thang diirng M o m e n O

quan tinh eua thanh do'i v d i true quay O la I = - m / ,

trong do m la kho'i lu'dng cua thanh L a y g la gia toe rdi t i / do D e thanh c6 the quay den vi t r i nam ngang ^ ^

Ox thi ta can t r u y e n cho dau A eiia thanh mot van to'c

v theo phu'dng nam ngang c6 do Idn to'i thieu

A N / l O m / s B VSm/s C V6 m/s D Vl5m/s

4.12 M o t hinh tru dac lan khong tru'dt Biet momen quan tinh cua hinh tru do'i vdi

true quay la I - ^ m R ^ , trong do m la khoi lu'dng va R la ban kinh cua tiet dien

hinh tru D o n g nang cua hinh tru la 18J Dong nang quay cua hinh tru la

A 9 J B 12J C 6J D 3J

4.13 Cac canh quat may tao thanh mot vat ran cd momen quan tinh do'i v d i true

quay la I = 2 k g m ' Sau 2s ke tiT liie dong d i e n canh quat quay v d i toe do (0 = 120 vong/phut La'y - 10 Cong sua't trung binh eua quat

A P = 4 0 W B P = 80W C P = 1 6 0 W D P = 6 0 W

4.14 M o t qua cau dac kho'i lu'dng M = 5kg lan khong trufdt tren mat san nhan

nam ngang den va vao tu'dng thang dilng To'c do kho'i t a m cua qua cau ngay trurde va sau khi va cham vao tu'dng la Vi = 5m/s va V2 = 3m/s

Nhiet lu'dng toa ra trong thdi gian va cham la

Phjgng phap giai bai tjp trSc nghijnn Co hQc12 - Jr&n Trpng Hung

Ba dai lifdng tren d e u phu thupc kho'i lifdng m

M o m e n lufc: M = F.d khong phu thuoc nn

Theo dinh luat bao toan c d nang:

- > V > 7 ^ ^ v,.,i„ = 73^7

^ • J l - D a p an A

L a y moc the nang t a i vi t r i ban dau

Theo dinh luat bao toan c d nang:

2 I C O Q + ^ m v p = m g h , v d i h = s.sina

43

Phuong phap giai bai tap trSc nghi^m Co hgc 12 - Iran Trpng Hung

>2 vcti

1 = - m R

5

R

, 1 nen: —

Dong nang tinh tie'n: W(„) = - m v "

Dong nang quay: W(q) = ^Ico^ = ^

2 R = —niv^ 4 Vay: W(,„=2W,q,

Dong nang cua hinh tru: W,, = W(„) + W(q) ^ 3W(q)

<^W,,>=iw,=i.l8 = 6(J)

4.13 Dap an B

Theo dinh li dong nang, cong lam canh quat quay: A = - l o ) ^ - 0

Cong sua't trung binh cua quat: P = — =

t 2.t

vdi (0 = 120 vong/phut = 2 v6ng/s = 4n rad/s, nen: P = •^•^^'^^ = 80 (W)

2.2 4.14 Dap an A "

• Dong nang cua qua cau lan khong tru"cJt:

1

W i = - I ( o " + - m v ' = - (2

215 - m R '

1 2 7 2 + —mv = — m v

2 10

Dp giam dong nang cua qua cau ngay tru'dc va sau khi cham vao tu-dng

chinh la phan nhiet nang da toa ra trong thcJi gian va cham:

1 Td 'c do goc va gia toe gdc trong chuyen dyng quay cua vat ran

a Toe do goc: co = — Ddn vi co la rad/s

C0 = CO0 + Yt :, ••:

co^- COQ =2yA(p ,, , ,.,„ ,, ,

• quay nhanh dan ncu: (oy > 0 r j

• quay cham dan neu: coy < 0 ^ ^

• quay deu neu y = 0 .j, ,

3 V$n t6c va gia tOc cua mpt diem tren vat ran quay ^

b Gia toe: a = ^a^ + a f

• a„ la do Idn gia toe hadng tarn dac tru'ng cho sir thay ddi ve hifdng cua

• a, la gia toe tiep tuyen dac tru'ng cho sif thay ddi ve dp Idn cua v , vdi

a, = r y

4 Phufofng trinh dong lijfc hoc cua vat ran quay quanh mot true

a Momen liTc dd'i vdi true quay: M = F.d Ddn vi cua M la N.m

• M > 0 ne'u vat quay theo chieu du'dng (qui U'dc)

• M < 0 ne'u vat quay theo chieu am

b Momen quan tinh: I = ^ m j r ^ Ddn vi cua I la kg.m^

i ' c- PhiTdng trinh dong life hoe: M = I.y

^- Momen dong lifdng

^- Momen dong lu'dng cua vat ran ddi vdi true quay: L = I.co E)dn vi cua L la kg.mVs

b- Djnh luat bao loan momen dong lu'dng: Ne'u M = 0 thi L = hang so

• I khong ddi: vat quay deu hoac du'ng yen ' '

• I thay ddi: IiCOi = I2CO2

45

6 Dong nang ciia vat ran quay: - —I<B^ • Bcfn vi la J

CAU HOI VA BAI TAP TRAC NGHIEM

5.1 Cac ngoi sao diTdc coi nhu"cac khoi cau bang khi tu" quay quanh minh ma khong

chju tac dung cua ngoai life va c6 the tich co dan To'c dp goc cua ngoi sao

A.khongddi , B.tangdan

C giam dan D liic tang, liic giam

5.2 Mot vien bi dang hinh cau dac ban kinh 10cm kho'i liTcJng 1kg Ian khong

trUdt vdi toe do 5m/s Dong nang cua vien bi la

A 12,5J B.5J C 17,5J D 20J

5.3 Banh xe hinh vanh tron ban kinh 50cm chju tac dung cua hai liTc tao thanh

ngau life, moi li/c ed do Idn ION tiep xiic vcti vanh banh xe Momen dpng

lu^dng cua banh xe sau 10s ke tuf luc bat dau quay la

A 12,5kgm^/s B lOOkgm^/s C SOkgmVs D 37,5kgmVs

5.4 Mot vat ran quay quanh mot true co dinh vdi toe do goc khong doi Mot

diem baft ki co dinh tren vat ran khong nam tren true quay co

A gia toe tiep tuyen bang khong va vectcf gia toe hu-dng tam thay doi

B gia toe tiep tuyen bang khong va vectd gia toe hiTdng tam khong doi

C gia toe tiep tuyen va gia toe hUctng tam khong doi va khac khong

D vectd gia toe (toan phan) khong doi

5.5 Phu-dng trinh chuyen dong quay cua vat ran quanh mot true co dinh la:

(p = 2t^ + 3t - 6, trong do t tinh bang giay, cp tinh bang rad

Toe do dai ciia mot diem tren vat ran caehnruc quay 10cm liic t = 5s la

A 5,2m/s B 4,6m/s C 9,2m/s D 2,3m/s

5.6 Sau thcii gian 10s toe do quay cua banh xe tang deu tiT 120 vong/phiit len

480 vong/phut Biet ban kinh banh xe la 20cm Quang du'cfng banh xe da chav

diTdc trong thdi gian noi tren la

A 31,4m B 62,8m C 45,5m D 82,6m

5.7 Mot dia mai chuyen dong nhanh dan deu vdi gia toe goc y = 2 rad/sl Biet

ban kinh R = 20cm Do Idn gia toe dai ciia mot diem tren vanh dla sau Is ke

tijf luc bat dau quay xap xi

A 0,8m/s^ B 0,4m/s^ C 0,89m/s^ D 0,55m/s^

5.8 Mot vat ran quay nhanh dan deu xung quanh true qua O tren vat ay La)'

- = 0,318 Khi dia quay du^dc goc 60° tiT nghi thi vectd gia toe a tai diem M

co" dinh tren vat ran da hdp vdi ban kinh OM goc 9 xap xi bang

A 9 = 45,8° B 9 = 25,5° C 9 = 64,3° D 9 = 18,5°

46

5.9 Thanh manh OA dki I = 50cm, kho'i lu'dng m = 50g co the quay de dang xung

quanh true qua dau O trong mat phang nam ngang Luc thanh nam yen, tac

dung li/c F CO do Idn F = ION vuong goc vdi thanh Liic thanh quet dufdc goc 60°, toe do dai cua dau A xap XI bang

A v = 22,5m/s B v = 45,7m/s C v = 18,6m/s D v = 34,4m/s 5.10 Thanh OA dong cha't, tiet dien deu co the quay di dang xung quanh dau O trong mat phang thang difng Biet momen quan tinh ciia thanh do'i vdi dau quay O la I = ^m/^, trong do m va / la kho'i lu'dng va ehieu dai cua thanh Thanh dUde tha nhe liic no dang nam ngang Biet gia to'c rdi tiT do la g Gia toe (dai) cua dau A liic vtra tha

A.O B ^ C 2g D ^

5.11 Tac dung len mep ciia dia tron dang dilng yen mot liTc tiep tuyen vdi dia

ed do Idn khong doi thi

A dia quay deu

B gia toe gde ciia dia bang khong «f ?

C to'c do gde cua dia ti le thuan vdi thdi gian quay

D gde quay ciia dia ti le thuan vdi thdi gian quay 5.12 Mot dia tron dong eha't khoi lu'dng 4kg, ban kinh 10cm dang quay deu quanh mot true vuong gde vdi mat dia va di qua tam vdi to'c do 60 vong/phiit

thi bi ham bdi mot liTc tiep xtie vdi mep dia DTa quay eham dan deu va dCfng

lai sau khi quay them dUdc 10 vong nifa Do Idn li/c ham la

A 3,6N B.0,72N C 0,0628N D 6,28N 5.13 Mot dTa tron ed kho'i lu'dng 2mo ban kinh R dang quay quanh true thang diJng qua tam vdi toe do 3 vong/s DTa tron thi? hai eiing true quay vdi dTa

trirdc CO kho'i lu'dng mo va ban kinh R diTde dat nhe nhang len dTa tru'de, hai

dTa Cling quay vdi toe do

A 6 v6ng/s B l,5vdng/s C 4,5 v6ng/s D 2 vong/s 5-14 Mot vat ran dang quay nhanh dan deu quanh mot true co dinh (bo qua li/c can) du'di tae dung cua ngoai liTc Luc t = 0 ngoai liTc triet tieu, ke tiJT dd trd di

vat ran

A van quay nhanh dan do quan tinh B duTng lai

C quay eham dan roi duTng lai D quay deu '

47

Phuong phjp giai bai tap trSc nghiSm Cd hpc - I fan irpng HUng

5.15 Rong roc hinh dia tron k h o i liTdng M = 3kg, ban kinh R = lOcm c6 the quay

de dang xung quanh true O qua tarn V a t day nhe khong dan qua rong roc,

mot dau treo vat m = 500g, dau kia keo bang liTc F ~ 8,2N (hinh ve)

L a y g = l O m / s l K e tCr liic bat dau keo, sau thdi gian

At = 1,253 « J— (s) rong roc quay difdc

A n = 2 vong B n = 3 vong

C n = 1 vong D n = 4 v 6 n g '

5.16 Chpn cau sai

A C h u y e n dong quay cham dan, gia toe goc y c6 the a m hay du'dng

B N e u tong cac momen life tac dung len mot vat ran bang 0 thi tong momen

dpng lu'dng cung bang 0

C D p Ictn momen quan tinh phu thupc vao sir phan bo k h o i liTpng xa hay gan

true quay

D T h a n h phan gia tdc hu^dng tarn dac triTng cho su" thay d o i ve hiTdng cua

vectP van toe

5.17 M o t dia tron ban k i n h 10cm quay nhanh dan deu v d i gia toe goc 100 r a d / s l

D p Idn gia toe ciia mot d i e m tren vanh dia sau 0,1s ke tiT liic bat dau quay la

A a = 1 0 m / s ^ B a = 1073m/s^ C a = 1 0 ^ m / s ^ D a = 20m/s^

5.18 V a t r ^ n quay b i e n d d i deu thi mot d i e m c d dinh tren vat ay eo dp Idn

A tdc dp goc khong ddi B tdc dp dai k h o n g ddi

C gia tdc tiep tuyen khong d d i D gia tdc hu^dng tam khong d d i

5.19 Canh quat m a y dai 0,5m D a u canh quat dat toe dp lOm/s sau 5s ke tu" luc

bat dau quay nhanh dan deu tiT nghi Canh quat da quay du-pc gan

A 50 vong B 25 vong C 8 vong D 5 vong

5.20 Rong rpc c6 ban k i n h 10cm diTpc quan bang doan day nhe khong dan, dau

day treo vat nang Tha nhe vat thi no se chuyen dpng thang bien d d i deu va

sau 0,5s vat di du^pc 25cm Tdc dp goc cua rong rpc k h i vat nang di hdt quang

diCdng noi tren la

I A lOrad/s B 5 rad/s - > M :

' C 20rad/s D 50rad/s ; ; ;

5.21 Chpn cau sai » ' " I

A K h i vat ran quay deu thi gia tdc goc bang khong

B Gia tdc goc cua mot dTa tron dang quay quanh mot true ti le thuan v d i tdnt^

momen ngoai life, ti le nghich v d i k h d i lUpng va ban k i n h cua dia

Cty TNHH MTV DVVH Khang Vigt

C M p i d i e m tren vat ran dang quay c6 cung td^c do goc va gia td^c goc (triT

cac d i e m nam tren true quay)

D K h i vat ran quay thi mot d i e m tren vat ran (khong nam tren true quay) se

ve nen q u i dao tron c6 tam nam tren true quay

5.22 M o t banh da c6 k h d i lu'dng m = 20kg, ban k i n h R = 50cm dang quay vdi tdc

dp 0) = 120 vong/phut thi bj ham lai nhd mot ap life Q vuong goc v d i vanh

banh da nhu" hinh ve ^ ^ Banh da quay cham dan deu va diTng lai sau / \

thdi gian t = 10s M a sat trUdt giiTa dp IiTc Q I O ^'^ 'f<^

vk bdnh da la 0,5 L a y 7t = 3,14

Dp Idn ap IiTc Q la

A Q = 15,70N B Q = 12,56N C Q = 376,82N D Q = 125,60N

5.23 M o t banh xe (coi nhu" vanh tron) kho'i lu'dng m = 200g Ian khong tru'dt tren

mat du'dng nam ngang Trong khi chuyen dpng banh xe x e m nhu' chiu tac

dung mot li/c tiep tuyen vdi vanh cd dp Idn khong ddi F = ION Sau 2s ke tiT liic bat dau chuyen dpng banh xe da d i du'dc

A s = 1 0 0 m B s = 50m C s = 200m D s = 150m 5.24 Chpn cau sai

A M o m e n quan tinh cua vat ran phu thupc vao sir phan b d k h d i lu'dng tren

vat ran xa hay gan true quay

B D d i v d i true quay nhat dinh, momen quan tinh cua mot he vat bang tong momen quan tinh cua cac vat trong he do »

C M o m e n lire tac dung vao vat ran khong d d i , momen quan tinh cua vat ran

ay cang Idn thi sir thay ddi tdc dp goc cua vat cang Idn <

D D d i v d i vat ran cd momen quan tinh khong ddi doi v d i true quay, neu

momen dpng lu'dng cua vat r ^ n ddi v d i true quay do khong d d i thi vat quay deu hoac diTng yen

5-25 X e t mot he thdng g o m :

- Rong rpc la mot dTa tron kho'i lirpng m = 1kg cd the quay de dang xung quanh true qua tam O

- D a y A B khong co dan va nhe Vc^t qua rong rpc

~ Lire keo F tac dung vao dau B de k e o vat nang di l e n v d i F = 2 5 N L a y g

= lOm/s'

S'Jc cSng day d phia treo vat nang M 1^

^ • T = 2 4 N B T = 6 N C T = 1 6 N D T = 1 2 N

49

Phuong phAp giSi bai tjp UJc nghiSm Co hpc 12 - Iran Trpng Hung

5.26 Hai dTa tron c6 momen quan tinh do'i v d i true quay qua tam la I i va h ma

I2 = 2Ii dU"de treo bKng doan day thang diJng qua hai tam nhu" hinh ve

Quay dTa difdi nhieu vong cho doan day O1O2 xoan lai roi giiir yen Tha nhe

dTa du'di thi hai dTa quay v d i toe do goc coi va 0)2 (ifng vdi I i va I2) ma

' A CO2 = 2(01 va ehung quay cung chieu

B (O2 = 2(0] va chiing quay ngu'dc chieu

C (02 = — va chung quay ciing chieu

D (O2 = ^ va chung quay ngu'dc chieu

I2

r - f HUdNG DAN GIAI

5.1 D a p an B • ^nnf ; r

, M = 0 nen Ico = hang so

The tich CO dan - > I : giam dan; (o: tang dan

• V e e t d gia toe hiTdng tam a^^ c6 phu'dng thay d o i (con dp Idn a„ = co^R

khong d o i ) V a y vectd gia toe huTdng tam a„ thay d o i

• V e c t d gia toe: a = a, + a„ = a„ : thay d o i

a, = Y R = 2.0,2 = 0,4 (m/s^)

a = ^ a ^ + a f = VoS^To^ « 0,89 (m/s') 5.8 D a p an B

• L u c viTa tha momen lire do trpng luTe

m g tac dung len thanh: M = mg ^

Gia toe goe cua thanh luc vjjTa tha

PP Gia toe dai cua dau A luc vilfa tha: a = ^^a^ + af ,

G

mg

Phuong phip giii bii tjp trie nghijm Co hQCl2 - Tran Trgng Hung

Acp = - y A t ^ = - 1 6 , ^ 2 2

Gia toe tai mot d i e m tren vat ran quay: a = a n + a , •

Do Idn a = >/af + a f , v d i

Vay: a = VlO^TIo^ = lOv^ (m/s^)

a„ = co^R = (yt) R = (100.0,1)^.0,1 = 1 0 ( m / )

'•• • 53

• Sau thdi gian t b a n h xe da q u a y di/dc goc Acp = — Y t ^ = — ^ — t ^ ,

• M o i diem tren vanh banh xe da quay dU'dc cung co do dai:

C sai vi I cang Idn thi Y = ~p chng nho ->• Aco = co - coo = yt cang nho

D diing vi: L = hhng so -> M = — = 0 y = — = 0: vat quay deu hoac du'ng

Momen dong li/dng cua he (2 dTa) luc chu'a tha dTa du'di bang khong

Theo dinh luat bao toan momen dpng IiTdng:

0 = IiCO] + I2CO2 - > CO2 = - — C 0 | = —!-(0i : da'u tru" chiJng to hai dia quay ngu'dc

chieu vdi toe dp 0)2 = CO,

2

ctuams n D A O D O N G C O

BAI 6 D A O D Q N G D I E U H O A TOM TAT Lf THUYET

1 Dao dpng cd '

- Dao dpng cd la chuyen dpng qua lai vj tri can bang

- Dao dpng tuan hoan la dao dpng cd ma sau nhi?ng khoang thdi gian bang nhau, gpi 1^ chu ki, vat trd lai vi tri cu va theo chieu cu

2 Dao dpng dieu hoa « / : , J t ; ; - ; ,

Dao dpng dieu hoa la dao dpng trong d6 li dp cua vat la mot ham cosin (hay sin) cua thdi gian ,

X = Acos(cot + (p)

• X la l i do cua vat

• A la bien dp dao dpng (A > 0) • >;>

• cot + cp la pha dao dpng tai thdi diem t Ddn vi (cot + cp) la radian (rad)

• CO la tan so'goc, ddn vj la rad/s ,

• cp la pha ban dau, ddn vj la rad

* Chu y : Dao dpng dieu hoa va chuyen dpng

tron deu cd moi lien he nhu* sau: Diem P dao dpng dieu hoa tren doan thang P1P2 luon luon

cd the coi la hinh chieu ctia mot diem M chuyen dpng tron deu tren du'dng tron co dirdng kinh P1P2 len P1P2 ,

3 Chu ki - tan so'-tan so'goc

a Chu ki va tan so':

- Chu ki T cua dao dpng dieu hoa la khoang thdi gian de vat thiTc hien mot dao dpng toan phan Ddn vj chu ki la giay (s)

- Tan so f cua dao dpng dieu hoa la so' dao dpng toan phan thiTc hien dU'dc

trong 1 giay Ddn vi tan so la hec (Hz) vdi: IHz = 1/s

- Lien he giffa chu ki va tan so: T =

Phuong phAp giai bai tap trjc nghi$m Co hpc 12 - TrSn Trgng Hung

4 V a n td'c va gia t6'c c u a vat dao dyng dieu hoa

V a n toe la dao ham eua l i do theo th5i gian: v = x ' = -coAsin(cot + cp)

Gia toe la dao ham eua van toe theo thdi gian:

- CJ v i t r i can bang (x = 0): a = 0, hdp life F = 0. 4 t » ; tf-nu J|;:H ij,

i - Veetcf gia toe a luon luon hiTdng ve vi t r i can bang va do Idn ti le vet

do Idn l i d o , ^

5 Do thj c u a dao dong dieu hoa

D o thi cua l i do x vao thdi gian t la mot du'dng hinh sin

V i du v d i 9 = 0 t h i :

BAI TAP C d BAN Dang 1: DVA V A O PHUONG TRirWl CHUYEN DONG TIM C A C DAI

LUONG D A C TRUNG C U A D A O DONG D I E U H O A

1 Phu'dng trinh ehuyen dong eua vat dao dong dieu hoa: ; i i 1 i'

! -Vi - '' X = Aeos(o)t + cp) •iiii.ii'f i i i i i

• A la b i e n do dao dong (A > 0) -'ht iw' - aU

• CO la tan so goe (ddn vj la rad/s) 'fiinsU

• cot + (p la pha dao dong luc t

• (p la pha ban dau

2 L i e n he giuTa tan so goe, chu k i , tan so: co = ^ = 2nf

3 V a t thiTc hien dao dong d i e u hoa giffa hai d i e m P va Q ma : PQ = 2 A

4 Quang du'dng vat di du'de trong mot dao dong toan phan : S = 4 A

5 T h d i gian thi/c h i e n N dao dong toan phan : At = N T

V i du 1: M o t vat dao dong d i e u hoa vdti phu'dng trinh: x = 5cos

Chu k i va tan so cua dao dong Ian lUdt la '

A S = 5cm B S = 1 0 c m C S = 20cm D S = 4 0 e m

G i a i

Tan so goe: co = 2;: (rad/s) Chu k i : T = — = — = 1 (s)

CO 271

So dao dong toan phan thife hien trong 2s: N = = j - = 2

M o i dao dong toan phan vat di du'de 4 A

V a y quang du'dng vat di diTdc trong 2s la: S = 2.4A = 8A v d i A = 5em

Pha dao dong \h: 5nt

Ldc pha bang — tiJc 5nt - — = — thi: x = 2cos

Vay chon dap an C - u ^ - < •

Phúdng trinh chuyen dong: x = Acos(cot + cp)

+ Luc qua vj tri can b^ng O (x = 0) do Idn van toe ciTc dai: |v| = v„„x = w.A

+ dvi tri bien (x = ±A) thi v = 0 'J ' ^ ' - ^ ^ * ' ''^''^ ^

• Gia toe: a = v' = x " = -côAcos(cot + (p) hay a = x " = -colx

+ Luc qua vj tri can bang O (x = 0 ) : a = 0 ,,,

+ VectcJ gia toe a luon luon hÚdng ve vi tri can bang Ọ

V i du 1: M o t vat dao dpng dieu hoa tren true x'Ox vdi phiTdng trinh chuyen dpng:

= 5^2 cos 27:t +

4J (cm) Luc t = Is vat:

Ạ di theo chieu dúdng vdi dp Idn van toe 3 L 4 cm/s

B di theo chieu am vdi dp Idn van toe 31,4 cm/s

C di theo chieu dúdng vdi dp Idn van toe 5 cm/s

D di theo chieu am vdi dp Idn van toe 5 ^/2 cm/s

Giai

2nt +

-4 Ta c6: X = 5 ^/2 cos

V i du 2: M 6 t vat dao dpng dieu hoa tren doan thang PQ = 4 cm vdi thdi gian tif

i P ^ Q la 0,25s Dp Idn van toe cua vat liie qua trung diem O cua PQ la:

1 = 0 , 2 5 (s) ^ T = 0,5 (s) -> CO = — = — = 47: (rad/s)

2 T 0 , 5

Va PQ = 2A -> A = ^ = - = 2 (cm)

Vay: |vo| = 4TC.2 = STT « 2 5 , 1 2 (cm/s) Chpn dap an D

Vi dv 3: M o t vat dao dpng dieu hoa vdi phúdng trinh chuyen dpng:

x = 5cos 2 0 t

-3 (cm) Vat dat gia toe cUc dai :

Ạ liic qua vi tri can bang vdi dp Idn 20 m/s^

B lue qua li dp ci/c dai vdi dp Idn 20 m/s^

C liic qua li dp ciTc tieu vdi dp Idn 20 m/sl t i ] c • - A - r'

D liic qua vi tri va dp Idn khac vdi ket qua A , B, C :

Giai ,

Gia toe: a = - cộx ; a : max <-> x = - A : li dp eife tieu

Vay : ti,,„, = + or A = + 20\5 = 2000 (em/s^) = 20 (m/s^) Chpn dap an C

= A

-1 du -1: M o t vat dao dpng dieu hoa vdi bien dp -10 cm, chu k i 0,5s Van toe cua

vat liic qua li dp x = 6 cm va di theo chieu am la

Phitong ph^p giai bai t j p trie nghi^m Co hgc 12 - Trcin Trpng HiJng

N e n V = ±47t Vl 0^ - 6^ = ±3271 « ± 100,48 (cm/s)

V i vat d i theo chieu a m nen v < 0, vay : v = -100,48 (cm/s)

Chon dap an B

V i du 2: M o t vat dao dong dieu hoa tren doan thang PQ vdfi chu k i 0,785s L i i c va

qua vi t r i each trung d i e m O cua PQ la 3 cm thi no c6 do Ictn van toe la 32 cm/s

M u o n v i e t phufdng trinh chuyen dpng cua vat dao dpng d i e u hoa ta Ian lu'pt

theo cac budc nhu" sau:

Bu'dc 1: V i e t phu'Png trinh tdng quat: x = Acos((ot + cp)

Bifdc 2: T i m tan so goc co Dung cac eong thiJc c6 lien quan den co nhu":

CO = 271.f = — ; CO = / — (cho con lac 16 x o ) ; co = J - (cho con lac dc

Birdc 4: T i m pha ban dau (p u * ; « '

Thu'dng trong de bai co cho d i e u k i e n (gpi la d i e u k i e n ban dau):

L u c t = 0 (luc ban dau) vat qua v i t r i nao do da biet (tu'c biet x = Xo) va di theo

chieu dUPng hay am (tu'c biet v > 0 hay v < 0)

C h u y : Ne u de cho luc t = 0 ma vat dang d v i tri bien (tu'c x = ± A ) thi ta khong c6

V > 0 hay v < 0 Luc do ta dupc: + A = Acoscp coscp = ±1 cp = 0 hoac cp - 7T

Vi du 1: M o t vat dao dpng d i e u hoa tren doan thang P Q = 6 (cm) v d i thdi gian chuyen dpng tiT P den Q la 0,5 (s) B i e t luc t = 0 vat qua vj t r i can bang O va

di theo chieu dUPng PhifPng trinh chuyen dpng cua vat la

A X = 6cos(27rt + 7t) (cm) s ' / ; : B x = 6cos(27rt) (cm) ' ^

C X = 3cos(27it) (cm) D x = 3cos(27xt + n) (cm)

G i a i Bu'dc 1: Phu'Png trinh chuyen dpng cua vat co dang: x = Acos(cot + cp) Birdc 2: T i m CO P A O A Q

Theo de : - = 0,5 (s) - > T = 1 (s) va co = ^ = Y " = ^ T I (rad/s)

Birdtc 3: T i m A - ''^f^^? • ^ • ' t Theo de: P Q = 6 (cm) hay 2 A = 6 suy ra A = 3 (cm)

Bu'dc 4: T i m cp • ^ Theo de: L u c t = 0 thi X = 0 va V > 0

TUT X = Acos(cot + cp) ta dUPc

Vi du 2: M o t vat dao dpng d i e u hoa v d i chu k i 2s Du'a vat ra k h o i v i t r i can bang

O la 2 cm va liic t = 0 truyen cho no van toe co dp \6n 6,28 em/s hiTdng theo

chieu dUPng thi vat chuyen dpng ve v i t r i can b^ng O Phu'Png trinh chuyen dpng eua vat la: ' - •

Pliiforig pliap giai b.ii lap liSc nriiiiCm Cd hoc 12 - iifin Iionii laiiii

72 ^ (p = — Vay: x = 2 ^/2 cos 7tt + smcp < 0

Chon dap an A

V i d u 3: M o t vSt dao dpng dieu hoa giiJa hai diem P va Q v d i tan so f = 1 Hz

Luc t = 0 vat bat dau dao dpng thi sau do 2,5s vat qua l i dp x = - 5 \/2 cm va

hirdng ra xa vj tri can bKng vdi van toe cd dp Idfn la I O T I ^ cm/s PhiTdng tnnh

chuyen dpng cua vat la

371^

571 (cm)

V i du 4: M o t cha't diem dao dpng dieu hoa tren try x'Ox Liic t = 0 chaft diem qua

li dp X = 73 cm va hudng ve vj tri can bang O vdi gia toe a = -1073 m/s^ Van toe ciTc dai cua vat la 62,8 cm/s Lay i^ = 10 V d i phiTdng trinh chuyen dpng cua vat CO dang x = Acos(cot + cp) thi bien dp A va pha ban dau cp la

X = Acos(cot + cp)

v = -coAsin(cot + cp) Luc t = 0, X = 73 cm va V < 0 (hinh ve)

63

Phuang phap giSi bai tap t d c nghigm Co hpc 12 - I r a n Trong Hang

Nen VB = 2cos(p

V = -coAsincp < 0

coscp = sincp > 0

9 =

T o m l a i : A = 2 cm va cp = - Chon dap an D

6

V i du 5: M o t vat dao dong dieu hoa tren true x'Ox vdi thdi gian tCf liic c6 do Idn

ii do C L f c tieu tdi l i i c c6 li do ciTc tieu ke tiep la At = 0,125 (s) Biet luc vat

qua li do X = - 3 cm thi van toe v = 0 Chpn goc thdi gian (t = 0) la luc vat qua

li do ciTc tieu Phu'dng trinh chuyen dong cua vat la:

A X = 3cos(47tt) (cm) B x = 3cos(16nt) (cm)

C X = 3cos(47it + 7t) (em) D x = 3cos(167ct + Jt) (cm)

Bqdc 1: Phu'dng trinh chuyen dong cua vat c6 dang: x - Acos(cot + 9)

Birdc 2: T i m CO ; • :^;-,l|'fM; u J i H O 4 ' >

+ D o Idn l i do cifc tieu la: x = 0 x = " - A

+ L i do cu'c tieu la: x = - A ,

Theo de: t = 0, X = - A = -3 (cm) (tru^dng hdp x = ±A thi khong kem dieu

kien V > 0 hay v < 0) , «> rr/ri :.i ^'i-y^

Ta diTdc : - A - Acoscp - > coscp = - 1 -> cp = 7t

Vay: x = 3cos(47rt + n) (cm) Chon dap an C

Ghi iiM: V d i phu'dng trinh x - Acos(cot + cp) thi:

a Luc t = 0, X, = + A cp = 0 b Luc t = 0, x = - A - > c p = 7r

c Liie t = Oi i 0 va V > 0 - > cp = d Luc t = 0, x = 0 va v < 0 - x p = + - |

V i d u 6: Hinh ve sau day la do

thi cua li do theo thdi gian t

eua vat dao dong dieu hoa:

CtyTNHH MTV DVVH Khang Viet

C X = 2cos(7it) (cm) D X = 4cos Tit + — i (cm)

2,/

( l i i i i Can ciJ' vao cac gia tri cua t va x cho tren do thi de tlm cac dai hrpng co A,

Do thi cho: Liic t = 0 thi x = 4 (cm) (*) ^ 4 = 4eos(p -> co.scp = I ^ cp =: 0

Vay X = 4eos(2Ttt) (cm) Chon dap an A

Vi du 7: M o t vat dao dong dieu hoa vdi li do x diMc bieu dien bang d6 thj nhir

Do thi cho: A = x,„ax - '0 (cm)

Bu'dc 4: Tim cp

Phi/ang phap bi\ trie nghigm Co hpc 12 - Trgn Trpng Hung

Do ihi cho: Luc t = - s i h i x = 10 cm nen

V i du 8: M o t vat dao dong dieu hoa c6 do thi cua l i do x theo thdi gian t la hinh

sin nhu- hinh ve Phu-cing tnnh chuyen dong cua vat la: ,

V = -coAsin(cot + cp) > 0

N e u vat qua Xo va di theo chieu am thi: , , ,

X() A cos (cot + cp) , ,,

V = -o)Asin(cot + cp) < 0, , f ,: • Bifctc 3: G i a i (1) hoac (2) ta tim diWc t theo k (vcJi k = 0; ± 1 ; ±2; ) Bifcfc 4: Ket hdp v6i dieu kien cua t ta se tim du'dc gia tri k thich hdp va tinh du'ric t

Phaong ph&p giai bai tap tr^c nghigm CO hgc 12 - Trgn Trpng Hung

L a n thi'r hai nen k = 3

The k = 3 vao (*) : I = 3,5 (s) Chon dap an D

M chuyen dong tron deu tren dirdng tron difdng kinh A B , •

2 Cach tinh thdi gian de vat dao dong dieu hoa ttr P - > Q tren doan thang A B (hinh ve)

Bu'dc I : V e dirdng tron dirdng kinh A B , tren do lay hai d i e m M , N cd hlnh chieu tren A B la P va Q

Birdc 2: T i n h gdc M O N = a Bu'dc 3: T h d i gian ,\ de vat dao dong dieu hoa tCr P ~> Q cung la thdi g i ; an chuyen dong Iron deu tren cung M N , thdi gian nay t i le vdi gdc M O N :

At _ a ( r a d ) _ a (do)

T ~ 271 " 360"

Vdi T la chu kl ciia vat dao dong dieu hoa cung la chu kl chuyen dong tron deu

Vi du 1: M o t vat dao dong dieu hoa vdi bien do A, chu k l T Thdi gian be nhat

Bu'dc I : V e dirdng tron du'dng kinh 2A tam la

O, tren do lay hai d i e m M va N sao cho hlnh chieu ciia no tren dirdng kinh la O (vi tri can

Phuang phap g\&\i t}p trac nghigm CO hpc 12 - TrSn Trpng Hung"

Bifdc 3; G o i Al la thdi gian ngan nhat de vat di l i f O - > 1 thl do cung la thdi

gian de vat chuyen dong tron deu tren cung M N v d i :

At_

Vi du 2: M o t vat dao dong dieu hoa tren doan thang A B vdi phu'dng trlnh

chuyen dong: x = 4cos(57it) (cm)

ThcJi gian ngan nha't de vat di tii" ii do x = - 2 v'3 cm den x = 2 cm la:

A At = 0,2s B At = 0,1 s C At = 0,3s D At = 0,5s

Birdc 1: V e du'dng Iron du'dng kinh A B = 8 cm,

i tren do lay hai d i e m M va N sao cho hlnh

; ciiie'u cila no tren A B la P

Bu'dc 3: Thtii gian At be nhat de vat dao dong dieu hoa tiT P ^ Q cung la thdi

gian de \ a t chuyen dong tron deu tren cung M N V d i :

\ du 3: M o t vat dao dong dieu hoa vdi phu'dng trlnh: x = 2 cos3nt (cm) T h d i

sian be nhat giffa hai Ian lien tiep vat qua li do x = 2 cm la:

Theo hlnh ve thl thdi gian be nha't giila hai Ian l i e n tie'p vat qua x = - y j l a

At = 2 - = 1 V d i T = — = 0,4 (s).Vay: A t = — = 0,1 (s) Chon dap an B,

Van toe trung b m h = : —

thdi gian thiTc hien do dai t j - t, At

• Toe dp trung binh:

Quang du'dng di du-dc S

thdi gian thiTc h i e n quang du'dng At

Vi du 1: V a n toe trung binh (v,h) va toe do trung binh ( v ) t r o n g mot chu k l ciia

vat dao dong d i e u hoa vdi bien dp A , chu k l T Ian lu'dt la:

- r - - u - s Is = 4 A , _ 4 A

l o c d o t i u n g b i n h : v = — vOi n c n : v =

At [ A t = T T _ 4 A

2J thl I a n lu'dt thifc h i e n cac bifdc sau:

BUctc 1: N e u l u c d a u ( g o i la to) vat qua vj t i i Xo va d i t h e o c h i e u diTdng t h l :

X Q = Acos((ot|) + (p)

V = - c o A s i n ( a ) t Q + cp) > 0 - > sin(coto + (p) < 0 cos(cot(, + cp) =

X = A c o s (o(tQ + A t ) + cp

B i f d c 3: K h a i t r i e n x va k e t h d p v d i cac b i e u thiJc t r e n se t i n h du'dc x

V I du 1: M o t c h a t d i e m dao d o n g d i e u hoa v d i c h u k l T = 0,2s V a o luc n a o do

chat d i e m qua l i d o x = 3 c m t h l sau l u c do Is no qua l i d o :

c h i e u d i W n g t h l sau l i i c d o - s vat qua II do : ^ • '

A X = 1cm B X = - 1 c m C X « - 2 , 7 c m D x « + 2 , 7 c m

73

Giai

1

C h u k , : T = ^ = l s ; ^ = 8 ^ i ^ ^ ^ ^ T

At khong bang k.T hoac

Bi/dc 1: Goi luc dau la to thi:

D a n g 9 : TINH QUAING DUONG D I Bu'dc 1: Viet lai hai phi/dng trinh x va v:

( * )

X = Acos(cot + (p)

V = -(oA sin (cot + cp) Birdc 2: The t = t, vao (*) de tim x, va v,

Birdc 3: The t = I2 vao (*) de tlm x = X2 va v = V2

Bu'dc 4: Tinh chu ki T va thcti gian vat chuyen dong vdi At = t: - t|

Tim du'dc : At = n.T + Ato vdi n = 0, 1, 2, 3,

74

Pu'dc 5: Tinh quang dUdng di dUdc S

Qufuig dirdng S goiii quang dirt:fng di trong n chu ki la S| = n.4A va quang

(Jirting di S: trong thdi gian Ato con lai: S = S; + S2

Yi dii 1: Mot vat dao dong dieu hoa thang vdi phu'dng trinh: x = 6cos(27tt) (cm)

2 E)o dai quang du'dng ma vat di du'dc tij" luc ti = 0 den liic t2 = — s la:

di chuyen tiT Q (t, = 0) den P roi den I vdi : S = QP + PI = 2.6 + 3 = 15 (cm) Chon dap an D

^ ' 2: Mot vat dao dong dieu hoa thang vdi phu'dng trinh chuyen dong :

= 4cos

2nl 13

(cm) Do dai quang dirdng ma vat di du'dc trong khoang

Pffi gian — s Ke tiT liic t = 0 la

12

A S = 2 cm B S = 18cm C S = 22cm D S = 6 cm

75

Phaong ph^p giii bai tjp trac nghigm Co hpc 12 - TrSn Trgng HJng

Bu'dc 5: Quang du'cJng S di du'dc gom :

- Quang dircfng S| di du'dc trong 1 chu ki dau tien: Si = 1.4A = 4.4 = 16 (cm)

- Quang du'dng S: vat di du'dc trong s la: S2 = 0 1 = 2 (cm)

V a y : S = S|+ S:= 1 8 ( c m ) C h o n d a p a n B • • •

CAU HOI VA BAI TAP TRAC NGHIEM

6.1 Cau nao sau day la sai ?

A V j t i l can bang cua mot vat dao dong thu'dng la vi t r i cua vat khi diJiig yen

B Chuyen dong qua lai vj tri can b;ing goi ia dao dong cd

C Dao dong tuan hoan la dao dong ma sau mot khoang thdi gian vat trd h.ii

vi tri cu

76

^^^^^^^ Cty TNHH MTV DVVH Khang Vi^t

p Dao dong d i e u hoa la dao dong trong do l i do cua vat la mot ham cosin (hay sin) cua thdi gian

6 2 Chu k i T cua vat dao dong dieu hoa la khoang thdi gian de vat qua l i do Xo (da biet) de'n khi t r d l a i l i do x,,

B khoang thdi gian de vat di tii d i e m bien nay den d i e m ' b i e n kia

C khoang thdi gian ngan nha't de vat di tij'diem bien nay den diem bien kia

D khoang thdi gian ngan nhat sau do trang thai dao dong lap lai nhifcfi

6.3 Mot vat dao dong dieu hoa vdi bien do A, chu ki T thi

A thdi gian giCTa hai Ian lien tiep vat c6 do Idn van toe ei/c dai la T

B thdi gian giffa hai Ian lien tiep vat c6 van toe eifc t i e u la T 't'

C quang du'dng be nhat tiT d i e m c6 do Idn l i do cife tieu den d i e m c6 ii do ciTc dai la 2 A

D quang du'dng be nhat giffa hai d i e m khac nhau cung c6 do Idn l i do c\ic dai

la 4 A 6.4 Trong dao dong d i e u hoa ' " ' •

A diem c6 U do ciTc tieu thl van toe ei/c dai > ; ] JI '

B d i e m eo gia toe bang 0 thi do Idn van toe eu'e dai '

C d i e m c6 l i do eife t i e u thi c6 gia toe cifc tieu

D d i e m c6 gia toe cifc dai thi van toe eifc d a i ' ' 6.5 Dao dong dieu hoa la chuyen dong ' H i ' ; hu'iu^ / 1

A bien ddi deu > f - ct'o « 4 ^ ' * ffi.!« * P ' {• '

B cham dan khi tiT d i e m bien ve vj tri can bang O -1 i

C nhanh dan khi tCC vi t r i can bang O di ra d i e m bien i , ^

D CO vectd gia toe a luon luon hu'dng ve v; tri can bang O

6-6 Dao dong dieu hoa c6 vectd gia to'c a i i t

A doi chieu tai v i tri can bang O '"' '

B - d o ' i chieu tai d i e m bien

C cting chieu v d i vectd van toe khi di theo chieu difdng va ngu'de chieu khi

di theo chieu am

D Cling chieu v d i vectd van toe khi di ra khoi vi tri can bang O va ngu'de

chieu v d i vectd van toe khi trd ve vi t r i can bang O

Trong dao dong d i e u hoa thi l i do x

A cung pha vdi van toe v B ngu'de pha vdi van to'c v

^- tre pha hdn van to^e v goc — D sdm pha hdn van to'c v goc —

77

Phuang phip giii bai tjp trie nghijm CO hpc 12 - Trin Trgng Hung

6.8 Trong dao dong d i e u hoa thl do Idn gia to'c a

A t i ie vdi do Idn van toc v , • - :

B t i le ngliicli vdi do Idn van to'c v ' , ,

C tang i<iii do Idn van toc tang va ngiroc lai

D g i a m kiii do Idn van to'c tang va ngifdc l a i

6.9 Cau nao sau day chi/a day du kiii noi ve vat dao dong dieu li5a ?

A V d i mot bien do da cho thl piia la dai lu'dng xac dinh vi tri cua vat

B Chu k l la thdi gian de vat thiTc hien du'dc mot dao dong ,

C T a n so' la so' dao dong loan phan thiTc hien du'dc trong mot giay

D B i e n do dao dong la do lech ciTc dai cua vat ra khoi vj tri can bang

6.10 M o t vat dao dong d i e u hoa vdi phU'dng trinh : x = lOcos 5nl +

-6 (cm)

Trong thdi gian 1,2s vat di du'dc quang di/dng:

A s = 0,3m B s = l , 2 m C s = 0,6m D s = l , 8 m

6.1 1 M o t vat dao dong dieu hoa vdi thdi gian giCTa hai Ian c6 do Idn van toc cifc

dai kc' tie'p la 0,05s va quang du'dng di tirdng dng la 4 cm Tan so va bien do

dao dong la:

A f = l O H z ; A = 2 c m B f = 2 0 H z ; A = 1 cm

C f = 5 Hz ; A = 4 c m D f = 20 Hz ; A = 4 cm

6.12 M o t vat chuyen dong tron deu tren difdng tron du'dng kfnh 10 cm vdi to'c do

1,57 m/s L a y T: = 3,14 Hlnh chicu ciia vat tren mot du'dng kinh ciia du'dng

tron dao dong d i e u hoa v d i bien do va chu k l :

A A = 5cm ; T = 0,4s B A = lOcm ; T = 0,4s

C A = 5cm ; T = 0,2s D A = lOcm ; T = 0,2s

6.13 M o t d i e m dao dong dieu hoa tren doan thang dai 20 cm, thdi gian chuyen

dong cua d i e m a'y ttr dau nay den dau kia la 0,5s Bie't rang d i e m nay la hinh

chieu cua mot vat chuyen dong tron deu tren du'dng tron cd du'dng kinh

doan thang noi tren V a n to'c cua vat la :

A v = - 1 8 , 8 4 cm/s

C v = 25,16 cm/s

B v = 3,46 cm/s

D V = -32,63 cm/s

Cty TNHH MTV DVVH Khang VIgt

5 l 5 M o t vat dao dong dieu hoa vdi phU'dng trinh chuyen dong :

A | v | = 25,72 cm/s /;! B | v | = 100,48 cm/s ,f

C Iv!= 164,86 cm/s D | v | = 82,24 cm/s

6.17 M o t vat dao dong dieu hoa thang T h d i gian giSa 3 Ian lien tie'p qua ciing

mot d i e m la 0,5s vdi quang du'dng di du'dc la 40 cm B i e t lilc t = 0 vat eo van toc ci/c d a i PhU'dng trinh chuyen dong cua vat la:

A X = 5cos(87it + n) (cm) B x = 5cos8nt (cm)

C X = 10eos(4nt + TI) (cm) D x = 10eos4nt (cm) S'i ;

6.18 Du'a vat ra khoi vi t r i can bang O 2 cm ve phia chieu am cua true toa dp x'Ox L u c t = 0 truyen cho vat van toc c6 dp Idn 62,8 cm/s hu'dng ve vi t r i can bang O thl vat se dao dong dieu hoa vdi tan so' f = 5 Hz Phufdng trinh chuyen dong cua vat la :

(cm)

6.19 M o t vat dao dong dieu hoa tren true x ' O x Luc t = 0 vat qua l i dp x = 2>/3

cm hu'dng ve vj t r i can bang O vdi dp idn van toe 12,56 cm/s va dp Idn gia toe

\h 80 V3 cm/s^ L a y 7t = 3,14 va 7t^ » 10 PhU'dng trinh chuyen dong cua vat la:

X = 5cos |^47it J (cm) B x = 4coS 2TCt +

-6 (cm)

47lt

3 (cm)

C X = 5eos 27:t + — (cm) D x = 4cos

V 6y

^•20 V a n to'c cifc dai va gia to'c ciTc dai ciia mot vat dao dong dieu hoa Ian lu'dt

'a 3,14 cm/s va 2 cm/s^ « 0,27i' cm/s' Luc t = 10s vat dang di ra xa vi tri can

'^ng O theo chieu du'dng vdi van to'c c6 dp Idn cm/s

'hiTdng trinh chuyen dong cua vat la : '

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