ΜΕΘΟΔΟΛΟΓΙΑ ΑΣΚΗΣΕΩΝ 1ου ΚΕΦΑΛΑΙΟΥ

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    12-Apr-2017

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    vmarousis.blogspot.com 1

    1o

    1. ( . ) . 2. ,

    . 1 : 0,2 sec ; :

    /2 ( ) , .

    2: . 40 , ; : 2 , 20

    .

    3: ( ) 3 ( U ), 80 . ; . ; : H = 3U ( = 2U = U ) 4

    ,

    3. ,

    . : t1 x1=+0,1m t2 x2 = 0,2m x = 0,3m S= 0,5m.

    4. , , . : x = t , , = max t, , = max t , F = Fmaxt, .

    -x +x

    0 +0,1 +0,2 -0,1 -0,2

    -x

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    vmarousis.blogspot.com 2

    : : x = +2 + >0, x = 1

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    vmarousis.blogspot.com 3

    (1) (2)

    =0 (1)

    =0 (2)

    =1 (1)

    =1 (2)

    =2 (1)

    :

    sec = max (10t+ ) = max(10 + ) = max( ) >0

    sec = max (10t+ ) = max(10 + ) = max( )

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    9. . :

    10. :

    ) . = - 8(2t + /2). = -max(t+0) : = 2 rad/s , max= 8

    2 = 8 = 2m. ) ( 10cm) =10 cm. ) d = 20cm d = 2A = 10cm. ) .. ( ) :

    : E) x , (...)

    11. .... (...) D= m2 :

    x, , , , . (1) :

    . ( , .

    12. . 1. .., = 3U ;

    2. .. ( ) , =3U;

    :

    x = At x

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    vmarousis.blogspot.com 5

    13.

    .

    , :

    14. , +x

    x , , ,

    ( ).

    .

    (1) (2) : 1 = 2 , U1 = U2 ,

    F1 = F2 , 1 = 2 , 1 = 2 .

    -x= - d/2 +x = + d/2 ..

    1

    F1 1 F2 2

    2

    1 2

    - +

    d

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    vmarousis.blogspot.com 6

    15.

    . . . ( k ) , 1/m.

    Hooke : F= k ( ) . F . F = 0 w = F : F = w F F= D x, x . . ( ) .. .

    : =

    : =

    , .... =

    ( ).

    (. 3 )

    (. 4)

    w

    x= k

    F = F

    w

    F F

    x

    (. 1)

    (. 2)

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    vmarousis.blogspot.com 7

    16. .. D

    .

    1 : .. F = 0 .

    2 : x , (F) , . 3 : F, : F = Dx D .

    4 : D

    .

    : ) (. 2) : F = F = k x ( 1). .. F = D x ( 2) . ( 1) ( 2) D = k B) : (. 3) F = 0 w = F w = k (3) ( . 4) :

    F = w F F = w k( F = w k F = k x (4) .. F = D x (2) . (4) (2) D = k

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    17.

    18. :

    4, . , . , . , . ( ), ( ), ( ). = U, , U 0, . ( ) ( ) .

    < 0

    > 0

    -A +A 0

    + -

    = -

    = 0

    = +max

    F = +Fmax K = 0

    U = Umax

    = +

    = 0

    = -max

    F = -Fmax K = 0

    U = Umax

    = 0

    = max = 0

    F = 0 K = Kmax U = 0

    > 0, F>0 < 0, F< 0

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    19. .

    a. . b. . c. ,

    i) , F = 0. ii) , =0.

    iii) , x

    0.

    d. : e. , x

    . f. x = (t+0) , = (t+0), =

    2(t+0)

    20. ...;

    , : F = m, F = m2x

    :

    m = 3 kg = 0,4m

    k = 150 N/m.

    .

    :

    F=w kx0 = mg, x0= mg/k = 0,2m

    x,

    w

    F. Newton

    :

    F + w = m F+w = m2x F = m

    2x w

    D = k = m2,

    :

    F = kx , : F = 150x 30 (S.I.).

    x.

    x0

    x

    W

    W

    F0

    F

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    21.

    .. = 1= 2. D1 = m1

    2 D2 = m2 2,

    D = (m1+ m2) 2. D = D1+D2

    22.

    . : A1= 2A2 T1 = 2T2

    2 = 21

    :

    =

    :

    :

    :

    23. ( ) ( ..).

    m1

    m2

    A1

    A2

    t

    x

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    vmarousis.blogspot.com 11

    .. .

    : .. :

    .. :

    2

    1

    m2

    m1

    (+)

    m1 m2 m1 m2

    1 2 1 2 (+)

    m1 m2

    1 2 (+)

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    .. . . H .. :

    .. .

    m1

    .

    ( ) ( ) ( ) ( V )

    .. . .

    . . . ( . ) : F= 0 g = k . : F = 0 (+m)g = k(+x) .

    2 1

    .. & .

    (+)

    m

    x

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    24. ( )

    m1 ...

    m2 ,

    , :

    ) , .

    ) m1.

    ) ... : F = -D1x F = - m12 x (1)

    , , (1) : F = m1

    2 x m1g = m12 x

    x = (2) : max = m1(g +

    2) . x = + (2) : min = m1(g

    2) (3) . () ,

    : min 0

    (3), m1(g 2) 0 g 2

    , , f .

    25.

    ) :

    .

    ) : F

    . ) :

    ) :

    N = m1(g 2x) (2)

    N

    m1

    m2

    m1g

    g x

    +

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    1. . , .

    2. ( ) . .

    3. . )

    t= 0 (1) . Vmax= E , Q . (2) q= Q i = 0 . q = Q(t) I = I(t) . = Q )

    L C

    E,r L

    (1) (2)

    Q

    --------

    ++++++

    (2)

    ----- C

    ++++ Q

    E,r L

    (1)

    i

    i

    E,r E,r

    L L C C

    i i

    i i

    _ _ _

    + + +

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    .

    . . . . () : t = 0 ,I = +I, q = 0

    I = -I (t+) I = -I = -1 = = rad

    :

    ) t=0 , :

    : t=0 . t = 0 . , . LC , ..

    .

    4. q,i,Q,I, ...

    .

    (1)

    :

    5. q UE UB. UE= 3UB (1) Q . .. :

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    (2)

    (2) q= Q (t) (2) :

    : ,

    : ,

    : : , , .

    6.

    .

    7.

    ) :

    ) :

    ) :

    UE + UB = .

    (1)

    ) :

    VL = VC

    8. : (i) . : i

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    , .

    , , , . :

    (1)

    .

    (1) t = T t = (N+1)T = 0, 1, 2, :

    :

    () .

    1. F = - b, . +1 +1. :

    , .

    (-)

    (+)

    C L i

    (-)

    (+)

    i L C

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    vmarousis.blogspot.com 18

    .

    : 20%. 4 10cm 5 ; : 20% 80% 5= 0,8 4 = 0,8 10 = 8cm.

    2. F= -b k . : 0= 40cm = 2sec

    -1. = 10cm;

    : t=

    t =

    3. F = -b

    1 t1 2 t2 . : t = 0 = 25cm. t1= 20sec 1= 16cm, 2 t2= 30sec ;

    :

    = = = 25

    :

    4.

    :

    5.

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    vmarousis.blogspot.com 19

    ( : F) . :

    1. H

    .

    ,

    2.

    , . . . .

    3. . x = (t + ) , = max (t+0) , = - max(t+0) , F= - b = - b (t+) : = =2f , f .

    :

    : = = 2f , f .

    A o1

    A o

    f o f 1 f 2

    A o2

    f

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    vmarousis.blogspot.com 20

    . :

    4.

    , F= F F= b. . :

    F= F , x = 0.

    5. =.

    > max>Umax .

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    1. ..

    x1= A1(t) x2= A2(t+) : x = A(t+)

    .

    2. , , :

    1 2 x1 x2 x = x1+x2 1 2 = 1+2 1

    2 = 1+2

    1 2 1 2

    1 2

    01 02

    3. D D = m2 .

    ,

    A A2

    A1

    x2

    x

    x1

    t

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    vmarousis.blogspot.com 22

    ,

    , .

    . . 1 2 . , :

    (1)

    (2) (3)

    (1) (2) (3):

    , . = /2 = 90

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    4. ..

    1 : x1= 1t 2 : x2 = 2t : x = x1+x2 = 1t + 2t = . . . . .

    .. , .

    1 2 (1)

    .

    :

    :

    :

    H :

    5. O :

    6. ,

    .

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