# ΕΠΑΛ ΦΥΣΙΚΗ λυσεις ασκησεων

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Α λυκειου

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• ***

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UAKTIKHN 1

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I1AJ \ U I ' l M l

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: , , , -, , , -) ' , 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

* 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. ....