239-274 Ορμή2007
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Transcript of 239-274 Ορμή2007
-
239
O
1. .
m uG
.
.
, .
:
1: m1, m2 m1 > m2, u
G.
1 2F ,FG G
1 2F F . , , ,
.
2: m1 = m2 = m, 1 2u ,u
G G 1 2 .
1 2F ,FG G
1 2F F . , ,
.
,
,
,
.
,
.
= =
JG JGJG JG JG JGp p m
p m SI 1 Kg
secm
.
H :
: . : . : . : , .
-
240
2. .
n n21 p,...,p,p .
,
.
1 2 np p p ..... p= + + +G G G G
( ).
1 ( )
: p1 = 10 Kgm/s, p2 = 20 3
Kgm/s, p3 = 40 3 Kgm/s, p4 = 60Kgm/s, .
:
.
.
03x 3 3x
3 mp p 30 40 3 p 60Kg
2 sec= = =
03y 3 3y
1 mp p 30 40 3 p 20 3Kg
2 sec= = =
04x 4 4x 4x
1 mp p 60 p 60 p 30Kg
2 sec= = =
04y 4 4y 4y
3 mp p 60 p 60 p 30 3Kg
2 sec= = =
,x 1 3x 4x ,x 1 3x 4x ,xp p p p p p p p p 10 60 30 = + + = + = + G G G G
3p
x3p 1p x
y3p
y
x4p
4p y4p
2p
600
300
O
-
241
,x 1
,x
,x
p pm
p 40Kg msec p 40Kgsec
= =
G G
G
,y 2 3y 4y ,y 2 3y 4yp p p p p p p p 20 3 20 3 30 3 = + + = + = + G G G G
,y 2
,y
,y
p pm
p 30 3Kg msec p 30 3Kgsec
= =
G G
G
2 2
,x o ,y
,y,x,y
,x
mp p p p 10 43Kg
secp p p p 3 3
4p
= + == + = =
G G G GG G G G
G
3. .
m ( ),
uG
.
, .
. :
p p m
p m
= =
G GG G G G
.
x,op
p y,p
-
242
4. .
m, t1=t pG
t pG
,
.
p t :
p p p p p ( p )= = + G G G G G G
o :
2 2
p p p 2 p p (180 )= + + G G G G G
:
0
0
p (180 )
p p (180 )
= +
GG G
:
" " " ".
. :
2 2
p p p 2 p p (180 )= + + G G G G G
.
:
ppp =G
p p
p p
1800 -
-
243
2 m, ... .
. ) t= T4
, ) t= T2
.
. t= T4
,
p pG G
p p p p p ( p )= = + G G G G G G
2 22 2
p p p (m ) (m ) p m 2= + = + =G G G G
p p p m m p 0= = =G G G G
. t= T2
, ,
: p pG G
)p(ppppp +== 2mp) m( mp =+=
=
2mp
pp
0pppp ==
t=t1
t=t2=t1+ 4
t=t3=t1+
2
450
p p
p p
p p p
-
244
5. .
m,
F pG t :
F m
m mF m F m F t t tt
= = = = =
G G G G G G GG G GGG
F pp p pF F |p|t t |F|
t
= = =
G GG G GG G GG
.
.
=JGG p
Ft
...,
. F m = G JG .
, .
6. .
FG
t.
FG
t
:
FF
F
J FJ Ft
|J | |F|t
= =G
GG
G GG GG G
S.I. 1sec.
-
245
,
- .
F|J | |F|t=GG G , . ( - - ).
1. ( )
( ).
2. Fp J= GG G : .
: JG
sec = 2m m
Kg s Kgss
=
3 1 = 10 m/s.
,
2 = 10 m/s.
m = 1 Kg
t = 0,1 s :
. .
. .
(+)
2
F
KF
B
1
-
246
. +=== )(mpmmpppp 2112
=
=sm
20Kgp
pp
sm
20Kgp
. ... :
==
==
200NFt
pF
pF
tp
Ftp
F
4 m = 0,2Kg h = 45 m
t1 = 0. ,
t2 = 6,1 s.
. g = 10 m/s2.
. :
1 1y h
2 2
gt 30m/s gt1 1 2h
y gt h gt t t 3s2 2 g
== == = = = =
0 = (t=0) (A)
h
() 1
(+)
KF
B KF
()2
0 = ()(t=6,1sec)
-
247
. :
=
==
==
== =
==
=
22
22
0
tth,y22
2
20
0
gt21
th
g
tgt0
gt21
ty
gt
gt21
ty
gt
20
30m/s2gh2g
hg
g21
g
h 2222
2
222
2 ====
s 3tg
t 2
==
To :
s 0,1ttttt 2 ==
:
N 122Ft
)m(mgF
tmm
FBtp
F K21K12K =++===
KK F,F :
===
N 122F|F||F|
FFFFF
KK
K
K
-
248
7. (...).
, , .
, .
, .
. : 0FGG = .
() .
.
F 0 =GG
( )
:
p pF F F
t t : F 0
= + = =
G GG G G
G
pF
p 0 p .t : F 0
= = = =
GG G G GG
-
249
, .
F 0 0 . = = = G GG G G
1.
.
.
1 2 v0 0 = + + + =G GG G G G ( )1 v0, , 0 G G
2. ,
.
( , ..),
.
1.
, . ,
.
.
" " .
, ,
m, G . ,
...
( ),
.
:
mp p 0 p p p p V m V
M= = + = = =G GG G G G G G G G
G
mM
VG
-
250
,
, '
. , ,
, .
, :
= mV M
, -.
, ,
..
2.
.
.
.
,
. ...
,
,
.
=
+==
pp
pp
pp0ppGG
GGGGGG
3.
,
.
, .
,
,
- ' ' .
0p =K
.pK
.pK
-
251
, . ,
.
1 2 m1
m2 ,
'
1G
2G
.
'
t.
1G 2G .
.
2 1 1 1F m =G G
1 2, 1 2 2 2F m =G G
2 1. , 3
:
1 2 1 1 2 21 2 2 1 1 1 2 2 1 2 1 2
F F m m m m m m
t t t t = = = =
G G G G G GG G G G
( ) ( )1 1 1 2 2 2 1 1 1 1 2 2 2 2m m m m m m = = G G G G G G G G
1 1 2 2 1 1 2 2 1 2 1 2 m m m m p p p p p p + = + + = + =G G G G G GG G G G
.
;
, .
, 2 1F G
1 2F G
.
1FG 2F
G ,
1G
2G
1 2 , . ,
,
1 2 0BF 11 =+GG
0BF 22 =+GG
,
.
2G
1G
1 2
12F G
1 2 21F
G
2G 1G
1 2
2G
1G
2FG
1FG
12F G
1 2
21FG
-
252
, ,
-
-
.
.
: .
.
.
.
.
.
2G
1G
2G 1G :
P
GG =
MHX E
KG
2G
1G
m1 m2 : = PP
GG
( ) K212211 mmmm GGG +=+
MHX E
2G
1G
2G 1G
: P P= G G
1 1 2 2 1 1 2 2m m m m + = +G G G G
MHX E =
-
253
5 =1000g
=4m/s. m=20Kg,
1=304m/s 1G
. 2G
;
,
.
:
s/m26080100040806080100041020
3042010004)201000(m)m(
m)m(ppppp
222
212
12.
.
.
=+=+=+=++=+
+=++==G
GGGGGGGG
6 .
.
1 = 6 m/s 2=12m/s.
. .
1
G 2
G
oA m2 m1
2BG
1BG
2FG
1FG
AA o
m2 m1
1KFG
2KFG
G
2G
1
G
-
254
. :
=+
==++== 0pp
0mpppp0pp
21
21
KK
====
=2
mmmmpp
pppp
2
1221121
21
21
1
2
2
1
mm
7 m1 = 2 Kg m2 = 1 Kg
1 = 6 m/s, 2 = 5 m/s, .
m1 1= 4
m/s, .
. .
. .
. t = 0,1 s
.
. :
1 2 1 2 1 2 1 2p p p p p p p p p p= + = + = +
G G G G G G
1 1 2 2 1 1
1 1 2 2 1 1 2 2 2 22
m m m mm m m m 15
m s + = + = =
m1 1 m2 2
1F 2F
1
2
(+)
0
-
255
. :
ppp =
.
sm
Kg 20pmmpppppp 111111
111
11 ====
sm
Kg 20pmm)p(ppppp 222222
222
22 =+===
. m1 1F m2. To
2F . 1F , 2F
( 21 FF = ).
...
=
tp
F :
200NFs 0,1sm
Kg 20F
t
pF 11
11 ===
:
200NFF 21 ==
8 m1=2Kg =20m/s
m2=8Kg.
m2 2=8m/s.
. m1
.
. m1
m2.
-
256
. . :
2121
pppppp +=+= GGGGGG (1)
21 p,pGG
(p2=0) 21 p,p GG .
m, .
(1) :
1 1 2 1 1 1 2 2 1 1 1 2 2p 0 p p m m m m m m + = + = + = + G G G G G G
1 1 1 1
40 642 20 2 8 8 40 2 64 12m / s
2 = + = + = =
1G
oG
, . m,
.
. :
%100
%1
2 = (2) 1: m1 2K : m2
2 21 1 1 1
1 1K m K 2 20 K 400J
2 2= = =
2 22 2 2 2 2
1 1K m K 8 8 K 256J
2 2 = = =
(2) %64%%100400256
% ==
2,1FG
m1
m2
G
(+)
1,2FG
1G
2G
-
257
9 =9Kg
. m=1Kg,
=100m/s, .
.
;
. ;
. ;
. =0,5,
.
g=10m/s2.
. :
+===+= V)m(mppppppp ...GGGGGGGGG
s/m10V10100
VV)19(1001V)m(m ==+=+= . :
=== mmVpmVmpppp GGGGGG
smg
90p1001101p ==
G
m M
(+)
VG
NG
TG
BG
x
G
=0
0
-
258
.
.
.
H :
E = (1)
.
J5000100121m
21K
2
2
===+=
=+=+== 100510)19(21V)m(
21V
21 TE
2TE
2TE
2
J500 = (1) J4500EJ)5005000(E ==
. BG
,
G
G
.
.
:
t V t = = (2) 21x V t t
2 = (3)
yy :
( )yF 0 N B 0 N B 0 N B N M m g N 100N = + = = = = + =K K K
T N T 0,5 100N= = T 50N= xx :
xF m T m 50 (9 1) = = = + K K 25m / s =
=0 (2) :
(2) o0 v t 0 10 5 t t 2 s = = =
(3) :
21x 10 2 5 2 x 20 10 x 10m2
= = =
0
-
259
10 m
0 = 20 m/s. t = 3 s
m1 = m2 = 2m
. A m1, ,
1 = 20 m/s .
m .
0
20
gt (1)1
y t gt (2)2
= =
t1 = 3 s (1) 0
20 10.3 10m/sec 10 m/s
= = =
G GG
.
2x 2p p=
2y 2p p=
(t=0)
0
(t=3sec)
2
1
(t=3sec)
p
y2p
2p
x2p 1p
y
y
x x
(+)
-
260
t0 , . :
xx:
pppp0pp0pp0pp 21212x12x1y
.
x
. ===+==
2m
2m
21 = (3) yy:
2m mpppppp 22
2y
y
.
y
. ==== (4)
(3), (4):
0
1
2
2
1
4512020
2
2m
2m
2m m
(3)(4) =====
sm
220
22102
2
21 22
22 ====
-
261
9 2 .
1. :
. .
. .
. .
. .
. .
x .
2. :
. kg/m.
. kgm.
. kgm/s.
. kgs/m.
3.
;
) .
) .
) .
4.
xx. .
;
P
t0
A
B
-
262
5. 1 2 , m1 m2 (m1>m2) ,
.
.
;
) 1 .
) 2 .
) .
) .
9 ... -
1. :
. .
.
.
. ,
.
. .
. .
.
.
() () .
2. , , .
.
:
. .
. .
. .
-
263
. .
x .
3.
;
4. , ;
5. m1, m2 (m1 m2) . m1 .
:
. 21 ppGG =
. 21 ppGG =
. 21 ppGG =
. 21 p2pGG =
;
6.
.
.
-
264
,
;
7. .
:
. .
.
.
.
.
. .
8. .
;
. .
. .
.
.
. .
9. m1, m2 m1=2m2
. ,
.
. .
.
, .
. m1 .
. , ,
.
m1 m2
2G
1G
m1 m2
-
265
. m11 = m22.
;
10. , m1=2kg,
m2=3kg
1=5m/s.
G , : . =2 m/s
. 121
1 mm
m
GG+=
. 121
2 mm
m
GG+=
. = 0
;
11.
,
:
. 0p =G . 1 m2p
GG = . 21 mmp
GGG += . 21 mmp
GGG =
12. K
.
vK:
) ) vKK = )
2
vKK = ) 2v KK =
1G
m1 m2
2G
1G
m1 m2
-
266
13. :
) .
) .
) .
)
.
14. :
)
.
) .
) .
) .
15. m1 K
. m1
m2=3m1.
) 4K
) 4K3
) 3K2
) 2K
-
267
9
1. m1=1kg m2=2kg
1=6m/s 2=4m/s .
.
(. 14Kgm/s, -2 Kgm/s, 10 Kgm/s, 52 Kgm/s ) 2. 200, ,
750,
50. ,
, ( )
10m/s.
(. 190 m/s)
3. M=60kg =9m/s,
m=30kg.
. g=10m/s2
=0,1.
(. 18 m)
2G
1G
m1 m2
2G
1G
m1 m2
m1 2
G
1G
m2 2
G
1G
m1
m2
=120o
i) ii)
iii) iv)
-
268
4.
.
=60 , m=0,1kg,
=500m/s.
=100kg,
.
(. 0,25 m/s)
5. m=0,5kg
1=30m/s.
2=10m/s,
t=0,25s.
) t.
) ,
.
g=10m/s2.
(. 20 kgm/s, 80 N)
6. m=1000kg 72km/h.
.
0,2s,
) .
) .
(. 20.000 kgm/s, 100.000 N)
7. 1=2105 kgm/s. t=5min 2=14105 kgm/s, . .
(. 4000 N)
-
269
8. =5kg =4m/s
, . m1=1kg
1=8m/s oK
.
;
(. 3 m/s)
9
1. m=0,05 kg ,
=2 kg,
.
=/2 V=5 m/s,
.
(. 400m/s)
2. 1, 2
2 1. m1=0,5 kg
m2=1,5 kg 1=32 2 V=6 m/s,
. 0,15 s
, :
. .
. .
.
.
(. 12m/s, 4m/s, -3Kgm/s, 3Kgm/s, 20N)
3. m1=1 kg
xx =5m/s m2=4 kg
-
270
.
2=2m/s .
) m1 .
) m2
.
(., -3 m/s, 8 kgm/s)
4. m1=0,2 kg
m2=0,8 kg.
,
1=15 m/s 2=5 m/s, .
.
.
5. m1=3 kg m2=2 kg
1=15 m/s 2=30 m/s , .
.
) ;
) ;
(., -3 m/s, -54 kgm/s, 54 kgm/ s, 0)
6. m=0,05 kg =100 m/s.
=0,95 kg ,
.
) .
) .
) .
=0,5 g=10m/s2.
(. 5m/s, 5m, 237,5J)
VG
2G
1G
m2
m1
-
271
7. m1=1Kg 1=12m/s
m2=3Kg,
2=6m/s. ,
1=15m/s
. t=0,1s ,
:
) 2K m2 . )
.
(. 3 m/s, -270 N, 270 N)
8. m1=6Kg
1=10m/s.
m2=4Kg, 2=5m/s,
1K
. m1
1K =6m/s 1K . :
) m2 .
) .
)
, 0,05s.
(. 11m/s, -1, -480N, 480N)
-
272
1. M=60 kg A =10 m,
d=4m. m=80kg
. ' ;
2. , =1600Kg m=40Kg =300m/s.
) ;
) ,
x=1m;
(. 7,5m/s, 45.000N)
3. m=0,5Kg d=0,2m. =30m/s
0,1s.
, :
) .
) .
(. 27,5m/s, 12,5N)
4. =3 kg , =9 m/s. , m1
m2, m1=2m2. m1
1=3 3 m/s, . 2
. .
5. =50 m/s. t=2 s .
h=30 m,
. .
g=10 m/s2.
A d
-
273
6. =10 m/s. , 3/4
, m1=m2=m. m1
1=10 m/s.
, .
g=10 m/s2.
7. =5Kg . m=50g 1=400m/s,
2=100m/s. ,
S=4,5m.
) .
) .
(. 3m/s, 0,1)
8. =2Kg =30. t=1s , m=1Kg
, , .
, :
) .
) .
) .
g=10m/s2 .
(. 5m/s, 25m/s, 300J)
9. , h=0,8m,
=0,98g.
m=0,02Kg,
=400m/s. :
) .
)
.
(. 7,64 Kgm/s, 3,2 m)
h
M m
K
-
274
10. =30 m1=m.
m2=3m =6m/s.
.
m2 4m/s.
) ;
) m1 ;
) m1 ; ,
.
g=10m/s2. .
(. 0,6s, 6m/s, 3,6m)
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![Critical attractors and q-statistics - Europhysics News · PDF file[11] A. N. Starostin, V. I. Savchenko, and N. J. Fisch, Phys. Lett. A 274 (2000) 64. ... Instituto de Fisica, Universidad](https://static.fdocument.org/doc/165x107/5a781bc47f8b9a4b538e7682/critical-attractors-and-q-statistics-europhysics-news-a-11-a-n-starostin.jpg)
