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  • .

    7

    , 2013.

  • 2

    7 .

    , 76/23

    . , - , , . ,

    . ,

    , 650-02-310/1/2012-06 4.2.2013. : , 1. : 5000

    CIP - ,

    37.016:53(075.2)(076)

    , ., 1953- 7 : : / . ; [ , , ]. - 1. . - : , 2013 ( : ). - 95 . : . ; 27 cm 5.000.

    ISBN 978-86-89679-00-7

    COBISS.SR-ID 202279180

    3

    ......................................................................................................................................... 3 ......................................................................................................................................... 6 ................................................................................................................................................... 6 ................................................................................................................................................ 8 ..................................................................................................................................................... 9 . ............................................... 20 ................................................................................................................................................... 20 ................................................................................................................................................ 21 ..................................................................................................................................................... 22 ............................................................................................................................ 31 ................................................................................................................................................... 31 ................................................................................................................................................ 31 ..................................................................................................................................................... 32 . ..................................................................................... 39 ................................................................................................................................................... 39 ................................................................................................................................................ 40 ..................................................................................................................................................... 41 ......................................................................................................................... 47 ................................................................................................................................................... 47 ................................................................................................................................................ 48 ..................................................................................................................................................... 49 .......................................................................................................... 53 ............................................................................................... .................................. 54 ....................................................................................................................................... 58 ......................................................... 63 ...................................................................................................... 66 .................................................................................. 73 ........................................................................................ 75 ................................................ 82 ...................................................... 84 ........................................................ 86 .......................................... 89 ...................................................................................................... 91

  • 4

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    , 2012.

    5

  • 6

    7

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    tr0R FgmF

    0mMm

    0

    tr0R

    mMFgm

    mF

    a

  • 70

    . , . .

    ) . . .

    . . .

    . , . . ( ). , . , , . , .

    , , . . , . , , .

    , :

    ,

    F , , M .

    . , .

    gmQ 0

    )(0 agmQ

    MFa

    71

    , . . , . .

    . , a , s t . , .

    . .s1 .

    , , . ,

    ,g100 ,g20 .m/s7.1 2 m1 .s1.1 , .

    . .s1

    : ,g100 ,g20 ,g004 ,g01

    .g20 m1 1.5 .s5.2 .

    , , , .

    , e . .

    trF

    2/2 tsa

  • 72

    . ,mm2 mm1 .

    . . .

    , , . .

    . ( ). ( ). .

    . .

    . . .

    .

    . . .

    .

    s = ( _____ ) mm

    = _________ g = _________ g

    = _________ g

    = _________ g

    km

    1m 1k mmM

    trF

    tm

    2m

    2t0 mmm Mmm 0

    0mt

    srt2sr/2 tsa

    0m

    mFgm

    a tr0

    2

    km 1m

    1k mmM

    tm

    73

    1) ______ g 2) ______ g 3) ______ g

    1) ______ g 2) ______ g 3) ______ g

    1) ______ g 2) ______ g 3) ______ g

    __________ N

    kg][m ( tr0R FgmF ) N][ s][t s][srt

    22

    sr sm2

    tsa

    2R

    sm

    mF

    a

    . .

    ___________________________________________________ .

    1: , , .

    2: , Mm ,R FF F . ,

    .

    3: , .

    2m

    2t0 mmm

    Mmm 0trF

    0tr F gmF 0R

  • 74

    ) . . , , , . , , .

    , . , . , . , :

    .

    , , , . .

    . , . .

    . .

    . . . . .

    . .

    . .

    .

    tm

    0m

    gmgm 0t gmt

    gmgmgmgmF 0t0tR 0t2 mmm

    0t

    0

    2 mmgma

    t2m 0m

    t

    srt2sr/2 tsa

    0t2 mmm gmF 0

    0t

    0

    2 mmgm

    a

    75

    s = ( _____ ) mm

    = _________ g

    = _________ g

    ]s[t ]s[srt

    22sr s

    m2t

    sa

    20 sm

    mgma

    . .

    ___________________________________________________ .

    1: , , 4 .

    2: ( ) . , , . , . , .

    , , , . . 2m/s1 , .

    2

    t2m

    0m

    0t2 mmm

    )(0 agmQ

  • 76

    3

    . . , . , . . , . , .

    , .

    , , :

    .

    . .

    s . . .

    .

    .

    . . .

    2m/s81.9g

    2/2tgs

    22t

    sg

    srt

    2sr

    2t

    sg

    77

    s = ( _____ ) mm

    ]s[t ]s[srt

    22

    sr sm2

    tsg ]s[t ]s[srt

    22sr s

    m2t

    sg

    1

    2

    , . , .

    , m5.0 s3.0 . .

    , . m10 s4.1 . . je m20 s2 .

    , , . . . , . 30 , s1.0 .

    . , .

    .

    .

    2

  • 78

    4

    , N , . ,

    , ,

    gmF tr . 1. . . .

    . . . , ( ).

    . ,

    . .

    . . .

    . .

    , .

    . .

    0m = ________ kg t0 mmm = ________ kg

    NF tr

    QN mgQ

    trFF

    0m

    trF

    sr tr,F

    gmF

    0

    sr tr,

    tm

    t0 mmm

    79

    ]kg[0m ]N[trF ]N[srtr,F gmF

    0

    tr,sr ]kg[)( t0 mm ]N[trF ]N[srtr,F gmmF

    )( t0srtr,

    ,

    ________________ .

    _____________________ .

    2. . . . ,

    . . , . . trF :

    )(tr

    gmF

    .

    . .

    . .

    . .

    .

    1m 2m tr,1F tr,2FgmF 1tr,1 gmF 2tr,2

    )( 1212tr,1tr,2 mmggmgmFF mgF tr

    m

    gmmgm )( t0

    sr tr,F

    )(tr gmfF

  • 80

    . .

    . 0m = ________ kg

    kg][tm kg][m ]N[gm ]N[trF ]N[srtr,F ]N[srtr,tr FF ]N[trF ]N[trF

    :

    : A)( gm = ________ N Atr,F = ________ N

    B: B)( gm = ________ N Btr,F = ________ N

    .______________________________

    )()()( ABAtr,Btr,tr

    gmgm

    FFgm

    F

    81

    . g200 .tm

    . . N1.0 ( ).

    kg][tm 0 100 200 300 400 500

    ]N[trF 0.5 0.9 1.1 1.4 1.8 2,1

    0.5 0.8 1.2 1.4 1.6 2.1

    0.6 0.9 1.3 1.4 1.7 2.1

    . . .

    0m = 0.2 kg

    kg][tm kg][m ]N[gm ]N[trF ]N[srtr,F ]N[srtr,tr FF ]N[trF ]N[trF

    0 0.2 1.96

    0.5

    0.53

    0.03

    0.1 0.5 0.5 0.03

    0.6 0.07

    0.1 0.3 2.94

    0.9

    0.87

    0.03

    0.1 0.9 0.8 0.07

    0.9 0.03

    0.2 0.4 3.92

    1.1

    1.2

    0.1

    0.1 1.2 1.2 0

    1.3 0.1

    0.3 0.5 4.90

    1.4

    1.4

    0

    0.1 1.4 1.4 0

    1.4 0

    0.4 0.6 5.89

    1.8

    1.7

    0.1

    0.1 1.7 1.6 0.1

    1.7 0.1

    0.5 0.7 6.87

    2.2

    2.1

    0.1 0.1 2.1 2.1 0.1

    2.0 0.1

  • 82

    : A)( gm = 2.5 N Atr,F = 0.74 N

    B: B)( gm = 6.5 N Btr,F

    = 1.92 N

    83

    :

    .3.0295.0N5.2N5.6N74.0N92.1

    )()()( ABAtr,Btr,tr

    gmgm

    FFgm

    F

    : . , N1.0 . , . , .

    .N)(0.1 N2.0 , .

    , , , . , , . . , .

    . , . , .

    3. .

    , . pmaxtr, gmF . , ,

    .

    ,

    .

    . 90 ,

    FF - FF

    pmax mgN Nmg /pmax

    nmgN

    n

    pmax mg

    mg

  • 84

    . , . , , ( ).

    :

    lhmax .

    . . h l .

    . . .

    . .

    .mm2

    : : h = ( _____ ) mm

    : l = ( _____ ) mm

    ]mm[h ]mm[srh ]mm[l ]mm[srl sr

    srmax l

    h

    :

    180lhmgmg :: np

    srh srl

    2

    2

    ________cm_______cm_______

    sr

    srmax l

    h

    85

    5

    m V:

    .

    . . , :

    ,

    : , g . .

    ( ) ( ) , . ,

    ,

    .

    , :

    .

    . . . , , .

    Vm

    VgF 0p

    0 V

    Q gmQ

    pFQQ VgQQ 0

    gQQV

    0

    00 QQQ

    QQmg

    30 kg/m1000

  • 86

    . .

    . .

    , , .

    .

    ( ).

    30 m

    kg ]N[Q ]N[Q

    30 m

    kgQQ

    Q

    ___________

    : .

    : 1. .

    , , .

    2. , .

    Q Q

    1 2

    1000

    3

    3321

    mkg___________

    2mkg

    mkg

    2

    87

    6

    , F

    s:

    .

    , ,

    .

    90, .

    . . .

    . 4. ( ), ( ) , .

    . . . , . . .mm2

    : .

    sFA

    sFA ppF

    constv trFF

  • 88

    s . ,

    . .

    , . .

    . .

    .

    ]N[F ]J[sFA ]N[trF ]J[tr sFA

    :

    __________ .

    __________ o .

    F

    89

    7

    : ( ) . , ,

    ( ).

    2.

    ,

    ,

    .

    .

    2,

    .

    ,

    .

    ,

    2.

    . .

    s . s = h. .mm2

    . . .

    constEEE pk

    km

    1m 1k mmM

  • 90

    . ( ). ( ). .

    . . . .

    .

    . .

    .

    .

    .

    , .

    = s = h = ( _____ ) mm

    = _________ g = _________ g

    = _________ g

    = _________ g

    1) ______ g 2) ______ g 3) ______ g

    1) ______ g 2) ______ g 3) ______ g

    1) ______ g 2) ______ g 3) ______ g

    tm

    2m

    2t0 mmm 0m

    tsrt

    2sr/2 tsa

    srsr /2 tstav 0m

    0mMm 0m

    2

    2

    kvmE

    hgmE 0p

    2

    km 1m

    1k mmM

    tm

    2m

    2t0 mmm

    Mmm 0

    91

    ]kg[m ]s[t ]s[srt

    22sr s

    m2t

    sa

    sm2

    srtsv ]J[

    2

    2

    kvm

    E ]J[0p hgmE

    , .

    2

    2

    kvmE .

    ( hgmE 0p ). , .

    _________________________________________________ .

    : , . , : .

    , .

    . , .

    kp EEE

  • 92

    8

    , ,

    . ,

    .

    a , . ,vc .

    ,)( s1v11 ttcmQ .)( 2sv22 ttcmQ , ,)()( 2sv2s1v1 ttcmttcm :

    .

    ,

    .

    .

    .

    .

    ,

    . ,

    .

    .

    .

    , ,

    .

    ,

    . ,

    .

    1m 1t 2m 2t

    st

    21

    2211s mm

    tmtmt

    93

    . .

    50 . m . , .

    .m 2 mmm . .

    .

    . .

    . .

    .

    . .

    srt . . .

    ]kg[m ]kg[m ]kg[2m ]C[1 t ]C[2 t ]kg[m ]kg[1m ]C[s t ]C[rs, t

    , ,

    ____________________________________________________ .

    C60

    2t

    1t

    st

    m mmm 1

  • 94

    9

    : , , . , . ,

    .

    .

    .

    , ,

    .

    , (Kkg

    J4200 ).

    :

    )()( vrvvr ttcmttcm , : ,vm vt ,vc , , ,m c ,

    , rt .

    :

    )()(

    r

    vrvv

    ttmttcm

    c .

    C50

    t

    95

    . .

    . .

    , , , .

    .

    ( ).

    . .m v mmm .

    . vt .

    , . .

    . .

    rt .

    . .

    ]kg[m ]kg[m ]kg[m ]kg[vm ]C[v t ]C[t ]C[r t

    Kkg

    Jc

    m

    t