ΕΠΑΛ ΦΥΣΙΚΗ λυσεις ασκησεων

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Α λυκειου

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  • ***

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    ATELIER: ART CHOICE / / : Atelier: : : : ' . :

    UAKTIKHN 1

    * iMasrtNitovATUim Ell

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  • . Msc , 5 . , . , . , , - . , , 1 . , , -. , , . . , , . , , I - . , . , .

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    .

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    Y i i o m w . lUlAElAL ) FITCKEYMATQ*

    I1AJ \ U I ' l M l

    ^

    , , -.

    . ... . - .

  • '

    : , , , -, , , -) ' , 2010, : I. , I. , . , . , . - . .

    : , - ' , , 2010, : . , . , . , . , . , . , . , . . .

  • 1.1

    1. , :

    s - 1 2 0 / - ?n / = - = m / s v=30m/s . t 4

    :

    u(m/s)>.

    ..

    s(m)> >:;..

    2. t, :

    s + ^ . s + e . 1.980 + 20 . = t = t = s t = 200s t 10

    3. . : S=E j+E2 S = 1 0 1 0 m + 2 0 - 2 0 m S=500m.

    , - s , - 5 0 , -. = - = = 12,5m t 4

  • .

    4. . I 4 -

    2

    t=0

    - t

    t=0

    (): ( = = >| t ( 1 )

    (): 2 = s -

    s - = 2 (2)

    (1) (2) :

    X+Syl('=V lt + V2t s = ^ ^ 2 ) t t = 1.000 -s t =

    ] + 2 10 + 15 ] x :

    =! t x = 1 0 - 4 0 m x = 4 0 0 m . . :

    s(m).

    40s

    Min/s),

    -15

    10 20 30 40

  • 5. . t, : S., = t SM = t . : Sn - 8 = ( -) d = ( -)1

    d 500 t = = s t = 50s - 3 0 - 2 0

    . : S n =wnt = 30-50m 8 = 1.500m.

    6. x = 1 0 t = , - = 10m/s .

    :

    i'

  • s, :

    1 2 - at, 2

    s = s 2 s i = a t 2 at , 2 = 2 2 2 m - 2 l 2 m s = 3m. 2 2 2

    9. A. To -

    3 0 + 1 0 . : s = 20m s = 400m.

    , . - . - s 400 , . - 40 , . : = = - ^ - m / s = m / s .

    10. = 8+2 = 0 + , u0 = 8 m / s a = 2m/s 2 . :

    1 2 S = S4 - s2 = 0 4 + - a t 4 V 2 1 at,

    s = 0 ( 4 - t 2 ) + ^ - a ( t 4 2 - t 2 2 ) s = 8(4 - 2) + ^ 2(16 - 4) |m

    s = 28m

    11. ( in/s)Ai

    50 I

    30

    () /

    j i -/ ;

    '

  • () 10s - . : s 2 = 10-30m s 2 = 300m. () () t = 10s s = 300m - 2 5 0 m s = 50m.

    . t ' . , -

    : 50 = 30t 10t - 50 = 6t t = 12,5s.

    12. . :

    = + a t 30 = +10 ()

    1 9 1 = u A t + at 200 = 10 + 100 ()

    () () . () : = 3 0 - 1 0 () () :

    200 = (30 - 10) 10 + 50 = 2 m / s 2 . - () :

    = (30 - 10-2)m/s u A = 1 0 m / s .

    13. 0 ,7s 0 , s , =\)0t, = 20 .0 ,7m s , = 14m.

    s = ( 5 0 - 1 4 ) m s = 36m.

    :

    02 2 0 2 smax = = ^ 7 : m Smax = 20m. 2 2 - 10

    s m a x < s .

    14. {( + s)m. = 2 m / s 2 ,

    1 , 1 , u0 = 20m/s. : (, + s) = 0 t + t 70 + 55 = 20t + 2t .

  • t , = -25s t 2 = 5s .

    15. . -.

    : x! = x 2 1 0 t = 4 t 2 4t = 1 0 t =2,5s. .

    ^ / s , 0 = 0 a = 8m/s 2 . :

    ( ) >

    n(ni/s)A

    20

    10

    l>2=/ (t) x

    , r*

    /

    /

    l= '(f)

    2.=; -> L(S)

    "= ' ( 0

    t(s)

    16. . l i s

    3 3 . 9 + 5 9 + 2 2 3 m So) = 81m.

    :

    - S ; m / s = 7,36m / s. t 11

    . 3s

    9 - 0 , = At

    j , 2 m / s~ , = 3m / s , 3s -

    3 2 . , 2 2 - ^ m ' s 2 im / s .

    17. . :

    = 0 - a t -y- = 0 - a t 5 = 10 - 2t t = 2,5s

  • 1 2 s = v0 t - a t s =

    1 1 0 - 2 , 5 - - 2 - 2 , 5 -

    2 , m s = 18,75m.

    >

    . u = D 0 - a t = 0 -

    s t = 5s. n . .

    1 0 : 0 = 0 - a t t = = 2

    () :

    - V . 102 . smax 2 2 2 m S m a" ~ 25m.

    18. . ts, (t - 4)s . :

    1 ] 2 s = t = a 2 ( t - 4) .

    s a 8, :

    t2 = ~ 2 ( ~ l6t2 = 2,5^t2 + 16 - 8 t j -

    t = 20s

    4 * s 4s.

    1,8

    1 9 s = = s a = 1,6 20 m s = 320m.

    . " , m / s )

    - : ua = a , t = l , 6 -20m/s = 3 2 m / s = 2 (t - 4) = 2,5 (20 - 4 ) m / s = 4 0 m / s .

    -

    s : = -t

    320

    20 m / s = 16m / s.

    . = f ( t ) s = f( t ) :

  • 19. . : 0 < t < 5s 0 =10 /5 . : 5s < t < 15s = 2 0 m / s . : 15s < t < 2 0 s -

    2 . , = = 4m / s .

    - - 2 2 - - 4m / s .

    . 0 < t < 5s :

    , - 2 0 - 1 0 , 2 -, , 2 = = = m / s = 2m / s z . At tx t A 5 - 0

    . To - .

    10 + 20 5 + 10 20 + - 20 5 + - 5 20 |m = (75 + 200 + 50 + 50)m = 375m 1, 2 2 2

    : = (75 + 200 + 50 - 5 0 ) m = 25 . -.

    . . . , , - s 375 , -. : = = m / s = 15m / s.

  • 1.2.

    1. :

    F = F j + F 2 = (80 + 60) F = 1 4 0 N .

    : F = F 1 - F 2 = (80 - 60) F = 20.

    2. F :

    F = (20 + 10) -5 F = 25 F = 20 - (10+5) F = 5 F = (20+ 10+5) F = 35

    3. . 2 F = F[ + F2 . F = 4F 2 + F2 F 2 = 2 * F j = 4 F 2 F , = 8 N . - .

    . - - ^ F = F , - F 2 . f F = 3 F 2 - F 2 F2 = 5N F ! = 3F2 F, = 15N 6.

    4. . Hooke : F = KAx. = 20cm F = 80N :

    80 80 = -20cm = = 4 . 20 cm cm

  • , = - :

    (cm) 5 8 10 15 20

    () 20 32 40 60 80

    . :

    so

    10 15 20 Ax(cm)

    .

    20 : - 4 / cm,

    .

    5. , = 0, = , Z F = 0. F 3 - F 2 , :

    F , - F 2 - F 3 = 0 F 3 = F 1 - F 2 = ( 2 2 - 7 ) N F 3 = 1 5 N .

    6. , F, F . : F - B = 0 F = B F = 200 .

    7. S F ZF = 20 ' , - . , .

  • 8. - : At

    = m / s 2 = 2,5m / s 2 . 2

    : F = m a = 1 0 - 2 , 5 N F = 25N.

    9. = 4t = - -

    2 > ' ' = 4 m / s . : I F = m a = 1 .4 Z F = 4 .

    10. :

    1 4 - 1 0 , ? ^ . 2 = = m / s = 2m / s . At 2

    : F = m a = 10-2N F = 20N.

    11. . :

    | 4 2 2 , = - - m / s , = 4m / s m, 1

    F^ 15 2 2 2 = - m / s 2 = 5m / s . m2 3

    . 18m t S j S 2 : S 2 - S, = (18 -10 )m S 2 - S 1 = 8m. :

    2 t2 - a] t2 = 8 5 t2 - 4 t 2 = 8 2 2 1 2 2 2,5 t2 - 2 t2 = 8 t2 = 1 6 t = 4s.

    12 . .

    . 2 0 , 2 - , , 2 . . , = = m / s a , = l m / s t . , m 20

    0 S,. - :

    1 2 1 2 s i = 2 ^ s i = ( )

    0 = a , t , 0 = t, ()

  • 5 2 = = m / s 2 2 = 0,25m / s2

    m 20 -

    t, t 2 = = 1L () 2 2

    2 2 0 t. s2 = = () 22 22

    1 2 t 2 s, + s 2 = soX t j + - i - = soX 2 2 cx 2

    t j 2 + 2 t , 2 = 4 0 t, = 4s.

    F 2

    1 2 1 2 s, = t, = 4 s s, = 8m. 2 1 2 1

    . :

    t. ( 4 ^ = t[ + t2 = t, + = 4 + 77 Is = 2 5 2 V 0,25)

    13. . :

    1 2 2s 48 , 2 s = a t - = m / s a = 3 m / s . 2 t 16

    . I F = m ZF = F 1 + F 2 - F 3 : F , + F 2 - F 3 = m a 6 + 2 - F 3 = l - 3 F 3 = 5N.

    14. Z F = F j - F 2 = 4 0 - 2 0 = 20.

    = m m =

    :

    ; , . , ' 40 2 ' n / 2 = m = = - m / s = 0,6m / s . m 20 ' 3

    , , .

  • 15. :

    , 1 2 - 2 2h . [2h h = g t t = t : 2 8

    t = 2s.

    16. t, :

    2 , _ [2h h ^ 8^ 1 ~ J ~ t = 6s.

    t ' : t' = t - A t t ' = (6 - l ) s = 5s.

    h ' = - g t ' 2 = - 1 0 52 m h ' = 125m. 2 2

    Ah : Ah = h - h ' = (180 - 125)m Ah = 55m.

    17. . :

    F 2 4 , 2 2 F = m a = = m / s = 5m / s . m 4.000

    : 2

    S = - - 0 2 = 2 s 0 = ^ 2 a s

    0 = 2 0 m / s . . :

    0 20 , 0 = = s t0) = 4s. a 5

    . :

    *-

    KM

  • 18. . t.

    1 2 : h = g t t

    t = 3s. - , t ' = t - A t t ' = ( 3 - l ) s t ' = 2s. :

    , h - g '2 / 1 ,2 2 V + - g i 0 = -

    = 4 5 - 5 - 2 m / s 0 = 12,5m / s.

    . :

    30 -am.

    )( m/s)

    I : SAP

    S ) T

    . y ?

    < ' . - ; . ; .. - 5 5

    W Wrfr

    s(m/s)T

  • 1.3

    1. . ^ :

    F2 = F , 2 + F 2 2 = 2 F j 2 Fj =

    F, = F2 = /50 F, = F, = 5/2

    2. F F , :

    f = VF,2+F22

    F = /4 . - F3 F.

    F3 = F = ^4) .

    3. F F j , F2 :

    F = ^Fj2 -t- F,2

    F = . - :

    F 1 0 , 2 - , , 2 = = m / s = I Om / s m 1

    - F - F 2

    : p

    = 6 . 3 - 4

  • 4. . :

    2h g 2 = = t2

    I

    2 - 7 2 2 2 gx = m / s g x = 1,6m / s . 3

    . ) , 3s. 6) : = x = 1 2 - 3 m x = 3 6 m .

    5. . y :

    1 = t

    , =

    ()

    (6)

    . () : uy = g t

    1 2 2 8 '

    2y 2 500 g " g =

    g t ' ()

    ()

    m / s 2 g = 10m / s 2 .

    . (0) , . , , x = 0 1 = 1 5 0 1 0 m = 1 .500m.

    . = 2 = , . -

    : B j - = m , (1) T - B 2 = m 2 a (2). . (1) (2) : , - + - 2 = m[ + m 2 , - 2 = (m, +m 2 )

    30 - 10 m

    , " 1

    m,g a - I"2g a =

    m

    7' m, + m 2 4 s . , .. (1) : = B j - m , = (3-10 - 35) = 1 5 .

  • ..

    7. . . By, : EF = m = m (1).

    . (1) :

    m g = m = g =

    8. . mg . Mg, F .

    . - : F - Mg - mg = ( + m) F = [(1.920 + 80)-2+ 1.920 10 + 80 10] F = 24 .000.

    . : - mg = m a = m a + mg = (80-2 + 80- 10) = 960.

    9. .

    : s = a t 2 = a t. 2

    t :

    1 s = -2 2

    ->2

    s 2

    =

    = 10

    2 10 m / s = 5m / s .

    . : = m = 55 = 25. > : = F - = F - = (30 - 25) = 5.

    . :

    = = ^ = mg 5 10

    = 0,1.

  • 26

    10. . F , . - :

    2

    2s

    = 30-2 0,2

    m / s = 2.250m / s"

    : F = m = 60-2.25GN F = 135.000N.

    11 . = 0, XF = 0 F - T = 0 T = F = 1 2 0 .

    120 = -

    250 = 0 ,48.

    . ' = = 0 . 4 8 6 0 ' = 76 ,8. F' : F = ' F = 76 ,8N

    12. . - .

    . - : B t - ' =rn, (1) ' - = m 2 (2)

    . - (1) (2) ! - = ( m , + m 2 ) = ' = 2 : m , g - ^ = ( m , + m 2 )

    8 10 - 0,25 -12 10 = 12 + :

    m / s

    = 2 5 m / s .

    13. . .

    . : = = By = ^, ; = ^

    = 6

    10 2 ,5. 2

  • . :

    1 1 0 2,5 ZF = m a - = m ^ - = = m / s2

    a = 2 ,5m/s 2 . :

    1 2 1 s = a t = 2,5 m s = 1 ,25m. 2 2 '

    14. .

    2 = 35m/s . : = ,

    R

    , 0,8 R = = m R = 0 , 4m. 2 2

    352 = 7 T T m / s 2 = 3 . 0 6 2 , 5 m / s 2 . ,

    2 15. = R, =

    : = R = - 6.380 103m / s 24 3.600

    u = 4 6 3 m / s . : = 2 4632

    = 0 , 0 3 4 m / s 2 .

    16. :

    = ^ = 2 - 2 3,14 8,5 ^ m / s = 368-10 3 m/s . 2 2

    :

    2 .,2 (368 103)

    = = m / s 2 = 19,6 10 m / s . R 13,8 103

    R 6.380 10 3

    17. :

    780 f = Hz f = 13Hz.

    60

  • : = R = 2 n f R

    = 2 = 2 3,14 13 9 ^ . m / s 2 2

    2 2 O = 2 6 , 9 m / s = = m / s2 = 2 . 1 9 3 m / s 2 .

    R 0,33

    18. , , 25% .

    : Fx ( m a x ) = 0 , 2 5 ( 3) = 0 ,25mg. 2 2

    Fx ( m a x ) = 0 ,25mg = ^ _

    1 = V0.25 gR 13 = 13m/s .

    19. : = 12h= 12-3.600s TQ = 43.200S = l h = 1-3.600 T A = 3 .600s.

    _ 2 t. = _ ^ 1 (1)

    1

    2 . ~ 1 ~ 1 (2). - =

    3 / \ /^\ ' 2 2 . ( I ) (2) 1 1 =

    /

    2t l

    V J

    3

    1 . ( 2t

    \

    3 1 3.600 43.200 / J_ t = 10 ,9min .

    3

    20. t

    d 2 , : t = = s t = 0,005s. - 400

    t . 4

    rad : = = = rad / s = 5 0 rad / s .

    * t 0,005s 0,02

  • 21. . : 7

    = a)(R + h) = (R + h)

    -2 3,14

    (6.400 3 + 6.400 1 0 3 ) m / s u = 5 . 5 8 1 m / s . 4 3.600

    . :

    2 2 3,14 = rad / s = 4,36-10" 4 rad/s . 4 3.600

    22 . . : Fx + Fy = B = m g - 60

    { \ = / 3 10 1 0 - 4 0

    2 = ( - 20/3) = 65,36.

    mi m

    mwm """ ~r ; w S W % S

    . 5s u = a t , .

    Fx = m a = Fx 60 4 0 -

    10 m / s2 a = 2 m / s 2 .

    m m u = a t = 2 -5m/s = 1 0 / 5 . .

    :

    c c c 1 , 2 1 . 2 -S = S5 - S4 = - a t 5 - a t 4

    s = ( 5 2 - U 2 ) = j 2 (52 - 42 jm S = 9m.

  • 23. . > F = F = F = = 0,2 1.000 F = 200.

    . :

    F ' - T ( F ' - T ) g ( 5 0 0 - 2 0 0 ) 1 0 , , = = m / s = 3m / s .

    m 1.000 .

    1 2 [ . : s = a t t = J

    2 t = 4s. :

    = = 34/8 = 1 2 / 5 .

    24. . y : / 3 - 30 = 0 Fx = m g 30 = 1 10 Fx = 5/3 .

    30

    . :

    30 = - m -Q a = g 3 0 = 5 m / s 2 . m

    . 0 = 0,

    1 2 . h 1 2 - 2h : S = at = at t = 2 30 2 \ 30

    t = 2s. = = 52/8 = 10m/s .

    .

    a ' = g 4 5 S ' = -. -45

    , 2h t = r V g 4 5

  • 2h = ^/2gh . - = ' t ' = g 45

    \ g 45

    h , - = 10m/s .

    25. . : F - T = m , a (1)

    T = m 2 a (2) (1) (2) :

    F = (m, + m 2 ) o = 5 l 5 L < 1 = l L 5 2 . |

    F = 20 + 500 ^ . F = g 7 _ 5 R

    . F (2) :

    -, g , = m2 = - = - - = 62 ,5.

    7 F | < ,

  • 2.1

    1. - :

    W = = 4 W = 4-30-50J W = 6000J

    2. . : U = m g h = 1010-20J U = 2.000J.

    . : U = m g x

    :

    I (J)

    20(1(1

    x(m)

    3. :

    2 - WT = 0 ~ = x

    1 2

    mu; 0 1000 152

    - = m = 15m 7500

    4. . :

    1 2 1 2 0 + WB = mu mgh = mu

    u = 20m/s

    h - .

  • 5. ,

    F = F = m g () :

    s h = - = ()

    P = F u () () :

    = mg = 2000 10 W = 10.000W t 120

    6. :

    0 + WB - WT = j ran2 mgh - () = - j 2

    ^()30 - () = 2

    2g(A)30 - 2g(A) = 2 : u = 6 m / s .

    7. . T = F : W T = W F = F x = 40-5J W T = 200J .

    . - :

    WT , t = : t

    WT W x 2 0 0 4 , , L = 1 = - J / s W T = 160J/s

    8. - Q :

    m g h ! + 0 = mgh 2 + 0 + Q Q = mg (h [ - h 2) = 2 10 (20 - 18)J Q = 40J

    :

    Q 40 100 = 100 = 10% nigh, 400

  • 9. F , . : F = = ^ = 0,5 100-

    F = 5 0 0 F.

    : = W F = F x = 5 0 0 10J = 5.000J.

    10. . . : W B = Bh = mgh = 80 10-300 0,2J W B = 48000J .

    . :

    W = 4 0 < * > , i s * . 8 0 J / s t 1 0 - 6 0 t

    11. ....