ΚΡΟΥΣΕΙΣ ΕΡΩΤΗΣΕΙΣ ΑΣΚΗΣΕΙΣ
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DOPPLER : .1.
, yy, 10 kgm/s. 0,2 s. . ( SI) . 20. . 10. . +20. . +10. . ( SI) . 200. . 100. . +200. . +100.
2. . . . . . . . . 3. () . . . . . , . . .4.
m . t, . m/t. . 2m/t. . m/2t. . . m , . t. . . m. . 2m. . . . m/t. . . m. . 2m. . . . m/t. . . m/t. . 2m/t. . m/2t. . . 2 kg 6 kg , . 8 m/s 2 m/s. , ( SI): . 75 . 64 . 12 . 76
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7. , . . . . . . . .1
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1 2, 10 m/s 15 m/s , . 2 m/s . 15. . 10 . 5. . 10. m1 5 m/s . 1 = 10 m/s 2 = 10 m/s . . . . . . . .m1 = 2 kg m2 = 4 kg
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13. . . . . . . . .14.
m . F , . F. . 2F. . 4F. . F / 4. 15. 2 kg 6 kg , . 8 m/s 2 m/s. To ( S.I) . 75. . 64 . 12 . 76 16. m . . 1/4. . 1/2. . 1/3. . 1 17. 2 . % . 90%. . 10%. . 5%. . 50%.2
18. , . . . . . . . .19.
. ;p p
20. . . . . . . . . 21.
B
. . . , . . . . . 22. . . . . . . . .23.m m1, m2 . m1 A 1 i) ( ) . m1=m2 . m1 >> m2 . m1 > m2 . m1 > m2 . m1 p = p pm1 = pm2 . . . m1 = -m2
1
m2
2=0
2.
m1
1
2
m2
3. ; . . . . . . . , .4.
2 1 , ; ( ) () ( ) ( ) . p = p . = . p + p = 0 . = . = 0 . =
1
2
. p = p . =
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m2 1 2, m1 2 1 . 1 2 , ; . 1 1 . . 1 1 , , . . 1 1 2 2 . . m1 = m2, 1 1 2 2 .
6. , , ; . . . .5
. . . . 7. ;8.
m 0 . 0 = 9m. . ; . 9/10 . . 1/10 . . . . .
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m1 = 3m 1=0 m2 = m. ;
m1
1
m2
2=0
30 . 4 3m 0 . m1 p1 = . 4 . , p1 = p2 . . . . =
10.
m . . . m. m . . 2 2m . . 3 1 2 . m . 2
m2 m1 = 2m m2 = m 1 m1 = 2 1 20 2 = 0 . . ; . . . p1 = p2 . . p1 = p2 . . m1 p1 = -2m0. . m2, 0. 12. m 1 2
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6
. . , ; 2 = 1 + 2 . 2 = 1 + 2 . 1 1 1 2 2 (2m 2 = m 1 + m 2 . ) 2 2 . 2 = 1 + 2 2 2 213.
, m1 = 2 kg, m2 = 3 kg 1 = 5 m/s. , : . = 2 m/ s . = .
m1
1
m2
=
m 1 1 m +m 1 2
m 2 1 . m +m 1 2 ;
=0
14. .15.
, , .
16. .17.
. . . . . . . .
18.
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21. 22.
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24.
25. . . .7
. . . . . . . , .26.
300 Hz. 274 Hz. : . . . . . . . . . . 400 Hz. 410 Hz. : . . . . . . . . . .
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: - .1.
. . . . . . . . . . . 2. 1. 2. . 3. (). 4. . 5.
1 1 2. . ( ). . 2 . 1 . 1 . . 1. . 2. . 3. . 4. 5. .
8
3.
. . ( ). . . . . . 1. . 2. . 3. .
4.
. . , . , 2. . , 3. . , 4. . , 5. 6. 1.
fA = fA fA fA fA fA
+ = + S = S = S = + S + =
fS fS fS fS fS fS
: , , .1.
, ().............................................. . () ....................................... . ().......................... () ...................... . , , .. ........................... .
2.
3.
4. , ........................ . 5. ..6.
... .......................... , .
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1. . ;p1(kg m/s)
2. ; ;3.
30
1 kg p1 = f(t), . , kg; ) 0,5 ) 1 ) 2 ) 5 ) 10 .
10
0
t
4. ; 5. , 1 2 . .6.
7 kgm/s 10 kgm/s, 2 s. ( SI) : . 1,5 . 3 . 0,6 . 2 .
, 600 kg, 144 km/h 1000 m. . [. 960 N] 8. 100 kgm/s. , , . 100 kgm/s . 100 kgm/s . 100 kgm/s .7.
9. , , . , - , .10.
; ; . . ; . ; m1 = 8 kg 1 m2 = 2 kg. m2 ( ) = 256J , m1, ; m2 [. 144 J]10
11.
12.
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m1 = 6 kg m2 = 1 kg. m2 m2 = - 48 J, ; [. 24 kg m/s] 15. m 0 . 0/4. . ; . = M/m ; [. . 5/4m0 . 5/3]14. 16.
m1 = 8 kg m2 = 2 kg , , , . xx, 1 = 10 m/s 2. . 2 , 8 m/s 13 m/s ; . ; . 9,5 m/s; . . [. . 5 m/s . 20 J . 15 J . ] m1 = 1 kg m2 = 1 kg = 8 m. m1 1 = 8 m/s, : ) , ) m2. : g = 10 m/s2. [. 18 N, 3,2 m]
17.
m m mA . = : m B . , =0 . . , mA < mB. . mA < mB. [. . = 1/3, . 1/3 < < 1, . = 1/5] 19. m1 = 1 kg m2 = 9 kg 1 = 60 m/s 2 = 10 m/s . . [. 378 J]18. 20.
m1 = 1 kg m2 = 9 kg. m2 p2 = 45 kgm/s, m1 . [. 25 m/s, 20 m/s] 2 kg 3 3 m/s 4 kg . . [ A. 1 = 3 m/s, 2 = 3 m/s, 300]
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m1 = 2 kg = 5 3 m/s m2. , 2 m2. [. 10 m/s, 1 kg]
1
m1 A
m2
300 300
B
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200 m/s . 600 . . [. 100 m/s, 100 3 m/s, 300]2
m1 = 1 kg m2 = 1 kg , 1 = 10 m/s 2 = 10 3 m/s . . , . . [. . 10 m/s, 300, . 0, 100 J, 100 J] 25. m 0 . 2 = 0 2 , . [. 900] 26. m1 . m2 2 . 20% m m . [. 4] 1 2 27. m = 0,1 kg m1 = 5 kg m2 = 2,9 kg m1 m2 0 . m = 0,1 ( ). . s1 = 18 m s2 = 32 m . 0 . g = 10 m/s2. [. 540 m/s]24. 28.
. m = 2 m/s. 2m . m 2m , = 1/18. : g = 10 m/s2. [. 0,4 m] m1 = 0,1 kg 1 = 300 m/s m2 = 2 kg . = 100 m/s. s = 20 m, : . , . . : g = 10 m/s2. [. , 3900 J]12
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m2 = 4 kg k = 100 N/m m2 m1 k,l0 0 . m1 = 1 kg 0 = 20 m/s m2. : . % m1 , . . . [. 64%, 1,6 m] 1 m = 0,5 kg xx 0. 1 () 2 M = 2 kg. = 45 J. . 0. . 1 2 , 0 = 17 m/s. [. . 15 m/s . 3 m/s, 5 m/s] m1, m2 m2 . m1 m2 1 = 10 m/s 3 m3. : m1 =2m2 = 6m3. [. 20 m/s] . mA/mB : . . /2. 2 1 1 . . [. . , . , . 3 3 3 1 ] 2 M = 2 kg . m = 1 kg 100 m/s . . 40 m/s. . 10000 J , . 3300 J] [. . 3 : m1 = 2 kg, 1 = 4 m/s, m2 = 4 kg = 4 m/s = 4 m/s 2 = 4 m/s. . ; . m = 2 kg m = 4 kg 10-3 s; m . % m1; h 20 4 64 3 64 3 10 N, .1777%.] , [. . m/ s, m/ s . 10 N, 3 3 3 31 2 1 2
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M36.
= 4 kg k = 100 N/m. A h = 5 m m = 1 kg, . . 13
k
y
. . . , m . : g = 10 m/s2. [. . 1,2 m, . 0,8 m] 37. = 3 kg k = 100 N/m . h = 1,6 m m = 1 kg (. ) . . . . . . . . . . g = 10 m/s2. [. . 12 J . 0,3 m . 24,5 J, 0,5 J . 10 N, - 30 N, 30 N]38.
m1 m2 . m1 h = 0,2 m. m1 m2. m2 : . m1 = m2, . m1 = 2m2. : g = 10 m/s2. [. . 2 m/s, . 8/3 m/s]
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, m1 m2 m1 m2 = 10 cm. h . 1 m1 0 60 . . m2 = 2 m1, . . . . . () . . m2 = 100 g; 1 1 13 m , m, . N] g = 10 m/s2. [. .1 m/s, . 1/3 m/s, 2/3 m/s, . 180 45 9 1 2
x
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m m, 2 k m . 2 m m . 0 2 1 2 m 2 1. . % . . . . : m = 1 kg, 0 = 20 m/s, k = 800 N/m. [. . 50% . 0,25 m]m 2
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m = 20 g, = 980 g. = 20 cm. = 100 m/s, = 600 . . [. = 0,75]
l m
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m . . = 10 3 m m/s, m = 100 g, = 900 g = 300. [. 1,5 m/s]
m1 = 2 kg m2 = 4 kg 1 = 4 m/s 2 = 2 m/s 600. : . , 4 3 . . [A. . m/ s , 300 2 , . 3 8 J] 44. , = 1 kg 20 cm. x = + 10 3 cm m M k 0 m = 3 kg 0. x . . . . . 0 1. . 2. . 2 s, s , . 3 m/s, 1. 3 m/s 2. 1 m/s] k = 900 /m [. . m 15 1543.h
m = 1/3 kg h = 0,8 m. M M = 1 kg k = 100 N/m. . k . ; . ; g = 10 m/s2. y 2 [. . 2 m/s, -2 m/s, . 0,2 m, - 20 kg m/s ] 46. = 900 g, m = 100 g, = 20 m/s. . m . m 10 m/s. ; l ; = 20 cm. 5 130 131 m , J, N] m [. . 0,2 m, 18 J, 30 N, . 81 9 945. 15
47. , . i) . 10 cm : mA mA 1 =1 = . . m m 5 B B ii) . , mA m B . 5 8 3 = 0,998, =0,997. [. i) . 00, 900, . 1 = , 2 = , ii) ] 9 9 248.
mA = 8 kg mB = 2 kg = 5 m/s = 8 m/s. 0,2 s. : . . . . . . . p = f(t), 1 s 0,4 s 0,6 s. . [. . 2,4 m/s, . -76,96 J, -58,24 J, . - 104 N, +104 N] = 980 g = 2 m . m = 20 g . . : . . . . . ; . , 49 . g = 10 m/s2. [. . 2 5m/ s . 500 m/s, . . 200 5m/ s ] 50 m = 0,2 kg 0 M = 4,8 kg d1 = 0,2 m. . . . . % . [. . 0,192 m . 96%] 2,75 m 4 m . 10 m. , . 16
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[ 1964]
[. 12 m]
l0 = 1,8 m M = 1,5 kg . l0 A 1200 . k m = 0,5 kg, l 1 . . l = 1 m , 1 m1 = 1 kg k = 72 N/m. . . . : . . . . . . ; . 1 = 0,3. 1 2 . I A = M g = 10 m/s2. 3 [A. A. 5 rad/s, 9 m/s B. . 3/8 m ] 1 = 60 m/s f1. f1 S = 100 m/s. 340 m/s f2 f2 . [. 0,82] S = 80 m/s fS = 400 Hz. A = 50 m/s, ; = 340 m/s. [. . 446 z, . 276 Hz, . 371 Hz]. S s
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s
S
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s
S
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fS = 1000 Hz. = 170 m/s . = 340 m/s, t = 5 s, . [. 5000, 2500]
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450 Hz tS. 510 Hz tA = 25,5 s. . . . tS . = 340 m/s. [. . 40 m/s . 28,9 s] S = 30 m/s fS = 300 Hz. fA . A = 10 m/s . . A = 20 m/s . : = 340 m/s. [. . 338,7 Hz, . 259,46 Hz] , fS = 400 Hz, S = 40 m/s. . =340 m/s. [. 95 z] = = 50 m/s. fS = 350 Hz. . , ; . , ; . = 60m/ s . = 340 m/s. [. . 350 Hz, . 350 Hz, . 338 Hz, 341 Hz] = 510 m , 72 km/h. 405 Hz. 425 Hz. . = 340 m/s. [. 680 m, 630 m] , , 100 Hz. = 340 m/s 16 Hz 20.000 Hz. ; [. 338,3 m/s] fS = 576 Hz R = 10 m = 2 rad/s. L = 20 m . 18
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. . . . , . . , ; . . , ; . = 340 m/s. [. . 544 Hz, 612 Hz . 2/3 s . (2 ) . ( fA = fS = 576 Hz)]63.
450 m S 680 Hz. t = 0 , = 1 m/s2. . fA [0, 20 s]. . 20 . . 600 Hz. = 340 m/s. [. . fA = 680+2t (S.I) . 14.000 . 800 m] * 448 Hz. 80 m . . 2 s . . , 2 s . = 340 m/s, g = 10 m/s2 x2 - 68x + 120 = 0 : x1 = 1,813 x2 = 66,187. [. . 476 Hz . 473,24 Hz] * 1 2 , . 1 x 2 y, . . 1 . 1 2 1 2 . 0 . = 0 1 = 0 2 = 2, = 45 . y 1 x
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2
0 . = 900 1 = 2, = 45 2 = 0. 0 . = 45 . . .
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