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    BAI GING VT LY I CNG 1

    1

    CHNGIV. C NNG V TRNG LC TH

    4.1.CNG V CNG SUT

    4.1.1. Cng

    Gis c F

    khng i, im t ca

    n chuyn di MM ' S

    Cng A do F

    sinh ra:

    A = F.S.cos hayA F.SDthy F.Cos l hnh chiu SF ca F trn MM

    sA F .S (4.1)Cng l i lng v hng, gi trththuc gc Nu im t ca lc F

    chuyn di trn ng cong C D.

    Cng ca lc F

    trong chuyn di v cng nhdS

    l: dA F.dS

    Cng A ca F

    trong chuyn di CD l:

    CDCD

    SdFdAA

    (4.2)

    (4.2) l biu thc tnh cng tng qut.

    4.1.2. Cng sut.

    Cng sut c trng cho sc mnh ca cc my (P).

    Gistrong t, mt lc sinh cng A.

    Ta c:tb

    AP

    t

    (4.3)(4.3) l cng sut trung bnh ca lc trong t.

    tnh cng sut ti tng thi im, ta cho t 0, khi A

    t

    dn ti mtgii hn l cng sut tc thi P

    t

    AP lim

    t 0 hay dAP dt (4.4)

    Cng sut c gi trbng o hm ca cng theo thi gian.

    M

    Hnh 4-1 S

    F M

    F

    M

    M

    F

    dS

    C D

    Hnh 4-2

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    BAI GING VT LY I CNG 1

    2

    Ta cng c th vit cng sut di dng mt biu thc khc:

    Do:dS

    dA F.dS P F. F.vdt

    (4.5)

    Vy, cng sut bng tch phn v hng ca lc tc dng vi vectvn tc

    ca chuyn di.

    4.2. NNG LNG V NH LUT BO TON NNG LNG

    nh ngha:Nng lng l i lng c trng cho mc vn ng ca

    vt cht.

    Ta bit cng l i lng c trng cho qu trnh trao i nng lng gia

    vt ny v vt khc. Ni cch khc: khi mt hthc hin cng th nng lng ca n

    sbin i.Gistrong qu trnh no hbin i ttrng thi 1 sang trng thi2; qu trnh ny hnhn tngoi cng A, ta c bin thin nng lng:

    W2- W1= A (4.6)

    bin thin nng lng ca mt h trong qu trnh no , c gi tr

    bng cng m hnhn c tbn ngoi trong qu trnh .

    - Nu hnhn cng t ngoi A > 0 th nng lng htng.

    - Nu hsinh cng cho bn ngoi A < 0 th nng lng hgim.

    -Nu hc lp, ta c A = 0; W2 = W1= const

    Vy, nng lng khng tmt i m cng khng tsinh ra, nng lng ch

    chuyn thny sang hkhc - nh lut bo ton nng lng:

    Ch :

    + Khng thc mt hsinh cng mi mi m khng nhn thm nng lng t

    mt ngun bn ngoi.

    + ng cvnh cu l mt hsinh cng mi mi m khng nhn nng lng t

    ngun bn ngoi.

    4.3. NG NNG VA CHM

    4.3.1. ng nng

    Xt cht im khi lng m chu tc dng F

    v chuyn di tvtr 1 2.

    Ta c cng ca lc F

    l: A F.dS2

    1

    mdv

    F ma m.dt

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    BAI GING VT LY I CNG 1

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    dv dS v

    A m. dS m. dv m.v.dv m.ddt dt

    2 2 2 2 2

    1 1 1 1 2

    mv mvmv

    A d A

    2 2 22

    2 1

    1

    2 2 2 (4.7)

    T(4.7) biu thc ng nng: dmv

    W 22

    Khi (4.7) thnh: W2- W1= A (4.8)

    nh l ng nng:bin thin ng nng ca mt cht im trong mt

    qung ng no , c gi trbng cng ca ngoi lc tc dng ln cht im

    sinh ra trong qung ng .

    ng nng ca vt rn quay:d

    IW

    22

    ng nng ca vt va quay va tnh tin:d

    I mvW

    2 22 2

    4.3.2. Va chm xuyn tm

    Xt hai qucu c khi lng l m1v m2. Trc khi va chm c: v1

    , v2

    cng

    phng; sau va chm chng c vectvn tc 'v1

    , 'v2

    cng phng nhban u.Ta githit h(m1+ m2) c lp. Ta hy tnh

    'v1v 'v

    2:

    Theo nh lut bo ton ng lng, ng lng ca h trc v sau va

    chm:

    ' 'm v m v m v m v1 1 2 2 1 1 2 2

    (4.9)

    Ta phi tm thm mt phng trnh na i vi 'v1 v 'v2 , mun vy ta xc

    nh iu kin khi va chm gn vi hai bi ton cth

    a. Va chm n hi.

    Do ng nng ca hbo ton, ta c:

    m v' m v' m v m v 2 2 2 21 1 2 2 1 1 2 22 2 2 2

    (4.10)

    T (4.9) v (4.10) ta suy ra:

    1

    v

    dS

    F

    2

    Hnh 4-3

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    BAI GING VT LY I CNG 1

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    MN t(M) t(N)A W W (4.15)V d:

    - Trong trng trng u, cht im c cao h: tW ( h) m.g.h C- Trong in trng, thnng ca in tch q0ti vtr cch q mt on r:

    tqq

    W (r) k C.r

    0

    Tnh cht:

    - Hiu thnng gia hai vtrhon ton xc nh.

    - Trng lc v thnng c hthc:

    MN t( M ) t (N )MN

    A FdS W W

    (4.16)

    Nu cht im dch chuyn theo mt vng kn: 0SdF

    (4.17)

    ngha ca thnng:L dng nng lng c trng cho tng tc.

    V d:

    - Dng thnng ca cht im trong trng trng ca qut l nng lng

    c trng cho tng tc gia qut vi cht im.

    - Thnng ca in tch q0trong in trng Culong ca in tch q l th

    nng tng tc gia q v q0.

    4.4.3. nh lut bo ton cnng trong trng trng

    Khi cht im c khi lng m chuyn ng tM N trong trng lc

    th:

    Ta c: MN t(M) t(N)A W W

    Theo nh l vng nng:

    MN (M) (N)A W W t(M) t(N) (N) (M)W W W W Hay: W+ Wt)N= (W+ Wt)M= const.

    Suy ra: WC= W+ Wt= const (4.18)

    Tng ng nng ca cht im trong trng lc thc gi l cnng ca

    cht im

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    BAI GING VT LY I CNG 1

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    nh lut bo ton cnng:Khi cht im chuyn ng trong trng lc

    thth cnng ca cht im trong trng lc thl i lng bo ton.

    Hqu:v W = W+ Wt= const trong qu trnh chuyn ng ca cht

    im nu Wtng th Wtgim v ngc li.

    Ch :Khi cht im chuyn ng trong trng lc thcn chu tc dng

    ca mt lc khc F

    ( th dms

    F

    )cnng khng bo ton.

    4.5. TRNG HP DN

    4.5.1.nh lut niutn vlc hp dn vtr. ng dng

    Hai cht im khi lng m v m t cch nhau mt khong r sht nhau

    bng nhng lc c phng l ng thng ni hai cht im , c cng t

    lthun vi hai khi lng m v m v tlnghch vi bnh phng khong cchr.

    Biu thc:2

    m.m'F F' G.

    r (4.19)

    Trong : G = 6,67.10-11Nm

    kg

    2

    2gi l hng shp dn

    ng dng:a. Sthay i gia tc trng trng theo cao.

    Xt vt c khi lng m trn mt t:M.m

    P G.R

    0 2 (4.20)

    vi: P0= mg0vM

    g G.R

    0 2gi l gia tc trng trng trn mt t.

    Ti im cch mt t mt cao h, ta c :

    M.mP G. m.g

    R h 2 (4.21)

    Gia tc trng trng cao h:M

    g G.R h

    2 (4.22)

    Do :R

    g g .

    R h

    2

    0

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    BAI GING VT LY I CNG 1

    7

    Ta thy:R h

    R h Rh

    R

    2 2

    2

    11

    1

    Ta chxt vt cao h

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    BAI GING VT LY I CNG 1

    8

    Khi lng ca Mt tri l:. .R'

    M 'T .G

    2 3

    2

    4 (4.27)Thay sv tnh ton, ta c : M = 2.1030(kg)

    4.5.2. Trng hp dn

    * Khi nim trng hp dn.

    - Xung quanh mt vt c khi lng tn ti mt trng hp dn m bt k vt c

    khi lng t trong khng gian ca trng u chu tc dng ca lc hp dn.

    -V d: Trng hp dn ca tri t chnh l trng trng ca n.

    * Bo ton momen ng lng trong trng hp dn.

    Xt cht im khi lng m chuyn ng trong trng hp dn ca cht

    im M cnh ti O. Chn O lm gc to.

    Ta c:dL

    / o(F)dt

    M

    m F

    lun hng vo tm O

    / o(F) 0M v dL

    dt 0

    L Const * Kt lun: Cht im m chuyn ng trong trng hp dn ca mt cht im

    M th momen ng lng ca m c bo ton.

    * Hqu: Cht im m chuyn ng trn quo phng, mt phng quo

    ca cht im vung gc vi vect L .

    * Tnh cht thca trng hp dn.

    C lc F

    tc dng ln cht im m chuyn ng trong trng hp dn ca

    M tA n B. Cng ca F

    trong chuyn di dS

    : dA F.PQ F.PQ.CosNu ta vQH OP th PQ. cos = PH dA F.PHv PQ

    l chuyn di vi phn nn ta t OP r

    OH OQ r dr

    (m)

    F

    L

    O

    (M)

    v

    Hnh 4-4

    B

    rA

    rB

    r +dr

    r

    F

    P

    H

    Q

    A

    O

    Hnh 4-5

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    BAI GING VT LY I CNG 1

    9

    Khi PH OH OP r dr r dr mM

    dA Fdr G dr r

    2

    Cng ca lc F

    di chuyn m tA n B l:

    B B

    A A

    r r

    AB

    B Ar r

    Mm Mm MmA Fdr G dr G G

    r r r 2

    AB

    A B

    Mm MmA G G

    r r

    (4.28)T(17) ta thy trng hp dn ca cht im M l mt trng lc th.

    Thnng ca cht im m ti vtr cch O mt khong cch r l:

    t r

    mMW G C

    r

    * Bo ton cnng trong trng hp dn.

    - Cnng ca cht im m chuyn ng trong trng hp dn c bo ton:

    W = W+ W

    t=

    mv mMG Const

    r

    2

    2

    (4.29)

    - Hqu: khi r tng, thnng tng th ng nng gim v ngc li.

    4.5.3. Chuyn ng trong trng hp dn ca tri t

    Nu tmt im A no trong trng hp dn ca Tri t, ta bn i

    vin n c khi lng m vi vn tc u l v0 th l thuyt v thc nghim

    chng ttutheo trsca v0 c thxy ra cc trng hp sau:

    a)Vin n ri trvTri t.b)Vin n bay vng quanh Tri t theo quo kn hnh elip.

    c)Vin n bay ngy cng xa Tri t.

    *Trsvn tc ban u v0 cn thit bn vin n bay vng quanh Tri t

    theo quo kn hnh elip gi l vn tc vtrcp I.

    * Trsvn tc ban u v0 cn thit bn vin n bay ngy cng xa Tri t

    gi l vn tc vtrcp I.

    * Tnh vn tc vtrcp I.

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    BAI GING VT LY I CNG 1

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    Gismt vin n bay cch mt t khng xa coi bn knh quo

    bng bn knh R ca Tri t:

    Vn tc vIca vin n lin hvi gia tc hng tm

    II

    v

    a g v g RR 2

    0 0 0 (4.30)

    viM

    g GR

    0 2

    tnh vI= 7,9 km/s 8km/s

    Vy, nu v < 8 km/s n ri vTri t

    v > 8 km/s n chuyn ng quanh Tri t theo quo elip.

    * Tnh vn tc vtrcp I I .

    Gisn xut pht tA cch tm Tri t mt khong bng bn knh

    R ca Tri t vi vn tc v0v bay ngy cng xa n .Bo ton cnng p dng cho n:

    mv Mm mv MmG G

    R

    2 2

    0

    2 2

    Domv 2 0

    2nn

    mv mM GMG v

    R R 20

    0

    2