193

1. .

,

.

xOy,

( ).

:

.

2. .

,

0 ,

.

,

,

.

:

y

x

y

G

yG

0G

gG

0G

BG

h

O

x

194

.

, :

,

t,

,

t .

:

(xx): x = 0 = .

x = 0 t

(yy):

2

u g t1

y g t2

= =

H

x = 0 y = g t .

:

( )= + = + 22 2 2x y 0 g t 0 :

= =yx 0

g t

27 ( ) 0 h

t = 0 . N

:

. .

. ,

.

. ,

().

. ,

.

195

. .

: h, o, g.

A

0G

dh

x , :

xx: x = 0 (1) x = 0 t (2) yy: y = g t (3) y = g t2 (4) . (2) (4) .

:

(2) 0

xt

= (5)

(4) 2 2(5)

20 0

1 x 1 xy g y g

2 2 = = =

220

gy x

2(6)

. : (4)

2

1y h h gt

2= = = 2ht g (7)

. At t x x= = , :

(2), (7) = 0 2hx g (8)

196

. d

:

2 2 2 2 2A Ad h x d h x = + = + = +

22 02hd h

g (9)

. y Ayt t = =

(3), (7) Ay Ay2h

g 2ghg

= = (10)

: (10)

2 2A A Ay (1)

(10)Ay

(1)A

= + = +

= =

2A 0

0

2gh

2gh

28 h = 320 m, 0 100m/s,

=30 m/s.

:

i) .

ii) .

i) .

, , 0 h.

. :

xx: x = 0 (1) x = 0 t (2)

yy: y = g t (3) y = t2 (4)

(4) . :

(4)2

1 2h 2 320y h h gt t 64

2 g 10= = = = = t = 8 s

x1:

(2) => x1 = 0 t x1 = 1008 x1 = 800 m

197

,

x2 :

x2 = t x2 = 308 x2 = 240 m

H d, :

d = x1 - x2 d = 800 - 240 d = 560 m ii) .

. d ( ) :

d = x1 + x2 d = 800 + 240 d = 1040 m

G

d x2

0G

d h

x1

198

29 , 7,2 m

3 s.

.

;

.

12 m/s ,

i)

;

ii) ;

A. , :

h = g t2 => g = 2t2h

=> g = 1,6 m/s2

B.

:

xx: x = 0 = . (1) x = 0 t (2) yy: y = g t (3) y = g t2 (4)

i) y = h )4(h = g t2 =>

g2h t = => t = 3 s

ii) (2) => x = 123 => x = 36 m

h

0G

199

3. .

xG

,

.

xG

.

.

t1 t2,

. .

:

,

G

3

G

2

G

1

O

y

x

xG

xG

2

xG

1

O

y

x

200

, .

R

2

= ,

.

, ,

, .

.

:

Fk = m k Fk = m 2

R

4. .

,

.

(...).

.

:

GG

G

G

201

(): ,

.

t :

t =

1 s (1 ).

(f): .

t : = Nft

SI = =11 s 1 zs

(1 Herz).

: 1 kz = 103 Hz, 1 MHz = 106 Hz, 1 GHz = 109 Hz.

N

ft

= , ( = 1)

(t = T), : = 1fT

.

(G ): , ,

S .

,

,

:

= S t

: S=2R

t = T, :

= =2 R 2 R f T

S.I. 1 m/s.

G

S

G

G

G

202

(G ): , ,

.

,

,

t :

t =

: = 2 t = T,

:

= =2 2 f T

SI 1 rad/s (

),

rad () ().

: =180

180 .

:

R K K 2

2R

K

u 2 R f

u R

2 f

F F m au

F mu RaR

= = = = = = = = = =

= = = =

S 2 R

t TN 1ft T

2 t T

1f

T

G

G

G

203

. .

: 1

: . gm GG =

: .

:

, . KFT = : .

2 . ,

(xOx),

.,

(yOy)

.

3 . .

.

ru

mamF2

K)

(r == , ( ).

4

amFx = ,

. ,

.

5 , .

204

30 ( ) , R = 20 cm 10

t = 2 s. :

. .

. .

. . 2 = 10.

. M . :

==210

tN

f f = 5 Hz

:

= Rf 2 = 2 m/s . :

==RR = 10 rad/s

. :

=R

2

k = 200 m/s2

,

,

:

= 0

31 ( ) .

T1 = 2 s T2 = 3 s. t =

0 .

. :

i) .

205

ii) .

. .

.

i) 1, 2

().

, :

1 2 1 2 1 21 2

2 2 2 t t 2 ( )t 2 t 2

/ / = = = = /

2 1 1 2

1 2 1 2 2 1

1 1t 1 t 1 t

= = =

t = 6 s

ii) 1, 2

().

, :

1 2 1 2 1 21 2

2 2 2 t t 2 ( )t 2 t 2

/ /+ = + = + = + = /

1 2 1 2

1 2 1 2 1 2

1 1t 1 t 1 t

+ + = = = +

t = 1,2 s

. ,

, ,

.

1 :

1

t t 2,4,6,8,10,12,...= = (1) 2 :

2

t t 3,6,9,12,15,...= = (2)

1, 2.

(1), (2) t 6,12,18,... = ... 1, 2. t = 6 s.

206

32 ( ) A = 1 m

. .

o60 = , = 2 m/s. ,

. m = 10 kg, g = 10 m/s2.

:

:

+==== AAA222

2

R

m mg T m mg - T m R

m F

= 90

Fy = m y = m mg= m = g = 10 23

= 5 3 m/s2

207

33 ( ) m = 1000 kg R = 100 m,

.

; = 0,4 g =

10 m/s2.

:

( ) ,

.

.

=

=====

==

mgN

mgBN0 B - N0FR

mR

mF

y

22

R

==/=/ gRgRRm

gm 22

= 20 m/s

= 20 m/s,

= mg. .

NG

BG

TG

208

.

1. m R, ,

:

. .

. .

. m2/R.

. .

;

2.

, :

. .

. .

. .

. .

. .

3. m = 4 kg, r = 1 m.

100 , :

. .

. .

. .

. .

4. ,

A , : . ,

.

. .

. TG

, .

.

209

.

;

5. :

. .

. .

. ,

().

.

.

x .

6.

( )

;

x .

7.

;

. .

. .

. .

. .

8. .

, :

210

.

.

. .

. .

. .

( )

9. :

. .

. .

. .

. .

. m/r.

. .

. .

. .

;

10. Luna-Park

. ,

, mg, :

. mg . 2mg . 3mg . 4mg

11. .

. ,

:

. 3/2 . 3/4 . 9/4 . 1/2

211

12. 1m, 2 kg. ,

.

4m/s, (g=10m/s2):

. 0 . 20 . 32 . 52

13. 50 m,

. 0,8.

( km/h)

; g=10m/s2:

. 108 . 36 . 72 . 90

14. 1000 kg, 10 m/s

( ) 100 m.

250 . ;

. .

. .

. .

.

212

. 1. h = 320 m 0 =

60 m/s. :

. .

. .

. .

. .

g = 10 m/s2.

(. 8 s 480 m 100 m/s = 4/3 577 m)

2. 0 = 10 m/s,

t = 1 s:

. .

. .

g = 10 m/s2.

(. 10 2 m/s = 45 10m 5m)

3. 0 = 100 m/s. :

.

.

.

.

g = 10 m/s2.

(. 20 s 40 2 s)

4. 0 = 10 m/s h = 80 m.

. 0 2

x 2 ,

x ;

g = 10 m/s2.

(. 40 m 1 s 2 s)

213

5. h = 20 m 01 = 100 m/s.

d ,

02 = 20 m/s. :

. d

. .

g = 10 m/s2.

(A. 100 m 15 m)

6.

= 30, x1 = 1,6 m.

x2 = 1 m, ,

x3 = 0,5 m.

.

: h = 1,25 m, g = 10 m/s2.

(. 0,75)

. 7. m = 200 g A = 1,5 m,

.

1 min 120 . 2 10: . .

. .

. .

. .

. g = 10 m/s2.

(. 6 m/s 0,5 s 4 rad/s 48 2 )

8. R = 10 m.

= 0,4 rad/s. :

h

x3

x2

x1

30

214

. .

. t = 2 min.

(. 0,2 Hz 5 s 24)

9. = 120. R = 50 m.

100/3 s, :

. .

. .

(. 0,02 rad/s m/s 0,01Hz 100s)

10. R = 2 m.

t = 4 s

. :

. .

. .

(. 0,125 Hz 8 s /4 rad/s /2 m/s)

11. m = 2 kg R = 1 m.

t = 5 s 20 . :

. .

. .

. . (2 = 10).

(. 4 Hz 0,25 s 8 m/s 8 rad/s 640 m/s2 1280 N)

12. m = 0,1 kg R = 0,5 m

. t = 10 s 600 .

(2=10).

(. 7200 N)

13. m = 2 kg R = 1 m.

0,8

m.

g = 10 m/s2 2 = 10.

(. 500)

215

14. ** N .

12 .

/3 ;

(. 12 h 1 h 10,9 min)

.

15. R = 120 3 m.

216 Km/h,

. g = 10 m/s2.

(. 30)

16. R = 90 m = 10 m/s.

;

g = 10 m/s2.

(. = 9)

17. m = 1200 kg,

= 54 km/h. R = 60 m.

,

.

g = 10 m/s2.

(. 4500 0,375)

18. 310R = m, 30 .

.

, .

g = 10 m/s2.

(A. 10 m/s)

19. Luna Park

, .

- 50 kg.

216

R

R = 10 3 m = 30,

.

g = 10 m/s2.

(. 1000 1 rad/s)

20. m = 0,2 kg A = 0,5 m.

R = 0,3 m

(

). g = 10 m/s2, :

. .

. .

. .

. = 60.

(. 1,5 m/s 2,5 N 5/2 z /15 s)

21. m = 1 kg , A = 0,8 m = 80 .

f ;

(A. 5/ Hz)

22. 70 kg "" Luna Park.

"" R = 10 m = 1

m/s,

.

g = 10 m/s2.

(A. 693 707 )

23.

( ), R = 12,5 m,

; -

= 0,8 g = 10 m/s2.

(. 1/2 z)

A

m K R

G

217

24.

. 20 cm

,

50 .

.

g = 10 m/s2 2 = 10.

(. 5/9)

25. 5000 Kg 36

Km/h, . 2

. ( ),

50 m ( ).

45000 N. ;

.

26. R = 1,6 m.

, ;,

g = 10 m/s2.

(. 4 m/s)

218

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