23i_Olympiada_Fysikis_G'_Lykeiou_A_Fasi_Lyseis.pdf

1

1 (15 ) () :

, .

= 0 (1,5 .)

() (i) m

, , r .

,

2mrI = (1 .) (ii) ,

, .

,

=

=n

1i

2ii rmI (1 .)

() :

( ). (

). .

(1,5 .)

23

( )

, 18 , 2009

0 = =

23 ( )

2

. () .

xmMRmxMRLL =+= 22122 21)

21(

2922

2)

492

2( 1

2

1

22 RMMRRMMR =+

9189

12

1

22 RMMRMRMR =+

=918

8 12 RMMR R14 = (4 .)

() ( )

+=+= 21

222

1 492

21

21

21 RMMRE

185 21

2

MRE = (2 .)

+=+=+=9

16169

2214

21

21

21

21 21

22

122

122

1222

2 MRMRRMMRmE

925 21

2

MRE = (2 .)

() ===18

4518

59

25 2122

122

12

MRMRMREEE 2

5 212MRE = (2 .)

2 (15 ) . .

, , , . . . , . (4 .)

( )0F = .

.. PP = (1 .) . ()

l . ... : 1=2 += 2120 2

121 mmgm l= lg2201 = ll gg 2101 lg81 = (2 .)

1

2R=x

2

A B

0

A

B

l 1

2 +

23 ( )

3

() .

(0.5 .) =+== 221 28)( mgmmmmPP l lg22 = (2,5 .)

() ,

2 2 , , ( 3). ....

==++=++

=

hgghgg

hmgmghmmmg

EE

2422

)(21

21 2

22

2

3..2..

llll

ll

(5 .) 3 (20 ) () 1: ,

Blower, & , , , 2 - , , .. .

2: , Blower, & , , , 2 , , .. . (4 .)

()

3 .

===

A

AAA

kgms

mP

2,011,0

2,01

smA /55,0= = 0BP smB /0=

===

A

AAA

kgms

mP

2,003,0

2,01

smA /15,0=

1 ( 1)

2 ( 2)

h

A

B

l

A

B

l 2

3

l2=h

-0,04-0,02

00,020,040,06

0,080,1

0,12

0,140,16

0 0,2 0,4 0,6 0,8 1

t (s)

P (k

gms-1

)

PA

PB

3

23 ( )

4

=== BBBBB kgmsmP 4,014,04,0 1 smB /35,0= (4 .) ( 0,5 . ) () 1. 11,0011,0 =+=+= kgmsPPP A 1. 11,014,003,0 =+=+= kgmsPPP A

(2 .)

Jm

Pm

PE

Jm

Pm

PE

B

B

A

A

B

B

A

A

02675,010.2410.25,28,0

14,04,0

)03,0(2

)(2

)(

03025,004,0

11,02

)(2

)(

332222

..

222

..

=+=+=+=

=+=+=

% :

%57,11100.03025,0

03025,002675,0100.%

.===

EE

. . (4 .)

() () .

(2 .) ()

NtPP

tPF

NtPP

tPF

BBBB

AAAA

7,02,0

14,035,065,0014,0

7,02,014,0

35,065,011,003,0

===

==

===

==

(2 .)

(2 .)

.P = P .

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

0 0,2 0,4 0,6 0,8 1t (s)

F (N

)

AF

BF

23 ( )

5

4 (15 ) . () ,

. .

=== ===

n

1i

2ii

n

1i

2ii

n

1ii rmrmLL IL = (1 .)

() () ( ) , .

= 0M LL = = (1 .)

() : , . , . , , . (L==). (1 .)

.

.

ll

ll

l

ll

l

23

331

23

31

23

0

22

..

g

m

gm

M

gm

ImLL

===

==

h. 1 2.

4623

31

21

21

2

22221

llll ===== hghg

MghMMghIEE MM

:

6021

2

42

2

2 ==

=

= lll

l

l h

A

== ll00

23 xx

23

0l=x

(12 .)

2

3 lg=

x0

l

h1

2

23 ( )

6

5 (15 ) . y

KyF = , . ,

KyFFy == . ... KD = (5 .)

mKmKD === 2 . =

2T KmT 2=

: KyFyF == ..

(2 .) . , S

mg. S S ( ). ,

)( gamSmamgSF

SF

y

x

==+==

(1) (2) xgamgamgamFx l)()()( ===

.

... l)( gam

, DxFx = gagam >> 0)( l (6 .)

llgamgamD === 2)( .

gT ==

l22

(2 .) 6 (20 ) . () (...)

( ) ( ) . (2 .)

() ...

, .

(2 .)

+x

+y

mgS

S

F= -Dy

y-y

+

....

23 ( )

7

. () dx 10101 == 1.

srad

MK 5

4,010

1 === sm /5,01,0.501 == (3 .)

() . sm /5,001 += . :

+=++=+=+=

9,02,3.5,05,0.4,0

)()( 0101....

mMmMVVmMmMPP

smV /2=

.. (3 .)

() . =+= 9,010

2 mMK

srad

310

2 = x02 ===

3/102

202022

VxxV mx 6,002 = (3 .)

() t1 M

. 44

3 211

TTt += 1 2 .

sMT 4,010

4,0221 ===

smMT 6,010

9,0222 ==+=

+=+=46,0

44,0.3

443 21

1TTt st 45,01 = (2 .)

() t0=0s

. 1 T2

(5 .)

d=0,1m

.

=10N/mm=0,5kg

+

M=0,4kg =3,2m/s

-1

-0,5

0

0,5

1

1,5

2

2,5

t (xs)

(m

/s)

0,1 0,2 0,3 0,4 0,5