Physics C Lyk Cyprus

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2007

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1: 6 - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - . . . . . . . . . . . . 17 - 1: ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 - 1: ( ) . . . . . . . . . . . . . . . . . . . . . . . . 24 2: - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . - 2: . . . . . . . . . . - : . . . . . . . . . . . . . 3: - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . - 3: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4: - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . 5: - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . 27 27 32 34 37 41 41 51 55 57 57 66 73 73 83 85 86

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2006-2007, , . . , 21 . . . , , . : 1. . 2. , , , , . ,

3. , , . 4. , , . 5. . 6. , . 7. . 8.

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( (6)) ( ) ( ) : , 99345496, cl1@cytanet.com.cy , 99416013, atomic@cytanet.com.cy , . . 99997467 , . . 99567613 , . . 99561131, andemage@cytanet.com.cy , . . 99625517, myrto@pouangare.com , . . 99678058, steliosb@cytanet.com.cy , . . 99416691, p2511958@cytanet.com.cy , . . 99667679, thasmari@cytanet.com.cy 99538083, athanasiadi@cytanet.com.cy 99692097, nicmaths@spidernet.com.cy 99872143, tsalakou@spidernet.com.cy 99451248, phildem@cytanet.com.cy 4

:1. (, , ). , , . 2. . 3. . . 4. . 5. . 6. . 7. .

5

1: (17 ) 1. . 1 km/h; . ; . 2. . . . 3. , ; ; . 4. . ; . , . . .(: P.= 5 kg.m.s-1, )

5. . ; 6. ; 7. . .

6

8. . . 9. , , . 10. . .

; ; ' . 11. 1,2 m/s . (. ). 50 g . ( 0,06 N ) 12. , 5 kg . F . t , . . F = f(t) F = f(x), x . . P E. ; 0 20 s 0 30 s. 7

(: P020 = 200 N s,

P030 = 0 N s ,

E 020 = 4000 J , E 030 = 0 J ). P = f(t) E.= f(t). . 13. 20 g 250 m/s 12 cm . . , i) , ii) ; ( )(: i) F = 5208,5 N, ii) F = 5208,3 N)

. ; 4 (: t 9, 6 10 s ) 14. 0,2 kg 3,2 m . 10-3 s, () , () .(: ) F = 3200 N, ) = 3202 )

15. , 20 m/s, . 75 kg , , 0,2 s. : . ( ) .(: F = 7500 N, )

. .(: = 15000 J)

16. . (i) (ii).

(: i) xKM = 4 m, ii) xKM = 8 m)

8

) (i) (ii); 17. ( 80 kg) (50 kg), . .

. , , , 0 0,5 s. . ; . . 0 0,5 s; t1 = 0, 2 s t2 = 0,5 s ;

(: P.1 = P.2 = 0)

18. 20 g 30 g 30 m/s 10 m/s, . . ) , ) .(: ) VK = 6 m/s, 20 g, ) = -9,6 J )

19. 1 2 2 kg 3kg , , 6 m/s 2 m/s, , . 0,02 s. ) . 1 1 (: u1 = 3, 6 m s , u2 = 4, 4 m s , )

9

) P1 P2 P (, ). ) F1 = f (t ) F2 = f (t ) , F1 F2 ( ) 1 2, .

20. T 1 1 kg, m , t . m. P1(kg.m.s-1)

(: m2 = 2 kg)

21.

1,6 kg. 0,8 kg, , . , , : 0,70 m/s 0,10 m/s 0,30 m/s 0,89 m/s

1 2

0,60 m/s 0,10 m/s

0,37 m/s 0,57 m/s

10

. .

, , . .

. 1 2.

22.

mA L = 8 m mB = 100kg U mB . s1 L S1 = 8,5 m. mA = 60kg . ;

23. 80 kg 4 kg . , 15 g, 600 m/s. : . .(: u. = 2,25 m/s, )

. , , .(: u. = 0,107 m/s, )

. , .(: u. = 0,107 m/s, )

24. ( 226 Ra ), 884 ( 222 Rn ) ( 2 He ). 86

6, 72 1013 J , () , () . ( : mRn 222 u , mHe 4 u ,

1u = 1, 66 1027 kg ).(: ) uRn = 2,56 . 105 m/s, ) Rn = 1,21 . 10-14 J)

11

25. , 100 Kg, 1,5 m/s. . ( ). i. ; . ii. 50Kg; ( 1m/s ) iii. 50Kg , (50Kg). .

= 1,5 m/s

26. 1 4 kg 10 m/s 2 16 kg 4 m/s. 0,02 s. . . , : i) , ii) .(: i) VK = 5,2 m/s, , ii) VK = 1,2 m/s, 2)

. P1 P2 P , . . F1 = f (t ) F2 = f (t ) , F1 F2 ( ) 1 2, .

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27. m1 =1 kg m2 = 3 kg ..u1 = 2 m s u2 = 4 m s

m1=1kg

m2=3kg

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

1 = 7 m s 1 , , 2 = 1 m s 1 , )

. , 10-3 s.(: F1 = 9000 N, , F2 = 9000 N, )

. . () , : . (, , ) . 1 (: = 2,5 m s , ) . , .(: = - 13,5 J)

.

, , . ( ).

28. m=3kg . h1 = 40 m . m 2m m A = m = . 3 3 h2=20 m . h2= 20 m

h1= 40 m

13

: . .(: = 20 m/s)

. . .

.

(: = 10 m/s, )

(: = 300 J)

. , ; 10-2 s.(: F = 12020 N)

29. 1 2 m1 m2, , , . , 1 x1 2 x2.

1

2

. .(: F1 = F2 = K(x1 + x2))

. , . m2 K (: 1 = ( x1 + x2 ) , m1 (m2 + m1 )

2 =

m1 K ( x1 + x2 ) , ) m2 (m1 + m2 )

30. m=30g 1=300m/s M=29,97 Kg .

14

. ) ) ) , K=270 N/m ) =0,1 (: 0,3m/s l=10cm l=3,8 cm )

31. 1 2 m1 m2 . u2 2 . m1 = 0,2 kg, . : P1 = f(t), P2 =f(t), P = f(t) 0 3 s, P1, P2 P , . F1 = f (t )

F2 = f (t ) 0 3 s. ( F , F : 1 2 .)

0

32.

, 9,8kg , (.1), 200g 15m. (.2) ) .

. 1

. 215

) ( ).

16

1

13. . i)

EK = WF 1 0 m0 2 = F x + mg x 2 m0 2 + 2mg x F= 5208,5 N 2xii)

EK = WF

EK ( .) EK ( .) = WF

1 0 m0 2 = F x 2 m0 2 20 103 2502 F= = = 5208,3 N 2x 2 12 102. F 5208 , F . = 0 a t 0 = 0 t m m0 t = 9, 6 104 s F 17. .

17

. . . , . . . 22. = P . = 0 F . = 0 .

0 = m ,0 m a ,0 0 = m ,0 m ( ,0 ) 0 = (m + m ) ,0 m m t = (m + m ) ,0 t m L = (m + m ) x x = m L (m + m )

s = s1 + x = 8,5 +

60 8 = 11,5 m 160

: .

18

29.

. F1 = F2 = K ( x1 + x2 ) . P .

1 K ( x1 + x2 ) 2 2 = 0 , m11 = m22 E . = EK1 + EK2 E . = 1 1 1 K ( x1 + x2 ) 2 = m112 + m22 2 2 2 2 m 2 2 K ( x1 + x2 ) 2 = m112 + m2 1 21 m2

1 = ( x1 + x2 ) 2 =

m2 K , m1 (m2 + m1 )

m11 m1 K = ( x1 + x2 ) m2 m2 (m1 + m2 )

32.

.

1 m0 2 = F d , ( ) 219

:m 0 = (m + M ) VK , 1 1 m 0 2 (m + M ) VK 2 = x F 2 2

m 20 2 1 1 = xF m 0 2 ( m + M ) 2 2 (m + M ) 2 md F = Fx F d m+M M x= d 14, 7 m m+M.

20

1: ( ). , .

. . . (Pasco)

: , ( , m, () , 2m), , 2 -, .

1. DataStudio () . 2. . 3. .

.

4. , (

21

). . , , , . . .

5. . 6. 4. (i)

(ii)

.

7. , , . 8. . . . , , , . , , . .

22

9. . 10. .

23

1 (): ( ). , .

. . . (Science Workshop).

: , ( , m, () , 2m), , -, .

1. - DataStudio , = f(t), () . = f(t), . 2. . 3. .

.

4. , , .

24

DataStudio ( Calculate). , , . .

.

5. , ( ).