...3 A # - D: # A . L % R F < . - R D ' A 8 C # ? : A * / * I - D / * I L 0 D * ; 9 I L 8 R F < & #...
Transcript of ...3 A # - D: # A . L % R F < . - R D ' A 8 C # ? : A * / * I - D / * I L 0 D * ; 9 I L 8 R F < & #...
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I: ( ) 1: ................................................................ 1 2: .......................................................... 6 3: ............................................... 13 4: ................................. 26 5: ......................... 35 II: ( ) 6: ........................................................................ 44 7: .................................................................. 54 8: .............................. 61 9: .............................. 67 III: 10: .......................................................... 74 11: ............................. 86 IV: 12: ...................................................... 94 13: ............................... 101 14: ............................ 108
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V: 15: ....................................... 117 16: ...................................... 124 17: ....................................... 130 18: .............................................. 135 19:
......................................... 142 20: ....................................................... 150 VI: 21: .................... 157 22: ........... 167 23: ................................................................ 173 VII: 24: .............................................. 182 25: ............................ 186 26: ........................................................... 190 27: ..................................... 194 28: ................ 202
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I: ( ) 1:
1. (Mechanics motion) 1.1
, . .
. 1.2
. .
2. ,
. . :
, , .
24.000 . ,
.
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O . .
: . 1) :
'x x . - .
O 'x x 'ox x . - ,
. - . m .
'o x x OM OM .
1.2 'o x x x OM 2m
OM .
2) : -
. :
'x x 'y y O
.
0 1 2 3123
O M x'x m
1.2
M
O 1 2 3123x'x m
45 4 5
1
2
3
1
2
3
y
'y
m
4
5
4
5
x
y
Mx
M y
1.3
.
.:
“ ””.
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- , .
- OM
1.3. M 'o x x OMx 3m
'oy y yOM 4m ; 'o x x O 4mx
'o y y O y 3m .
5.
s mn h . : 1h 60mn 3600s
. ,
(00:00 12:00 24:00 ).
t t .
: 8h , 1 7 ht ;
7 h 30 mn , 2 7 h 30 mnt . , :
2 1 30 mnt t t . , .
.
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1. ? 2. ,
. : . . . .
3. , , . , ? ?
4.
. 5. M ABC
R = 1m 1.4. M A, B, C, D, E ,x y .
y
x
C
D
E
60
30O
M
1.4
:
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2:
.
1. 1.1
ox . 0t 0M t M ,
0t t t S . 0M M 2.1
S .
x ox S
x ox S .
0S x x (2.1)
0x 0M x M . ,
. 1.2
:
x'x
0xx
so M0M
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.
0
S Svt t t
(2.2)
S (m) , v (m/s) , 0t ,
t , 0t t t .
2.2 0 0t t t : Sv S vtt
(2.3)
(SI) v (m/s) , S (m) t
(s) .
1.3
S t . Svt (2.4)
- 2.2 -
.
- St.
2.2
v
v
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:
8
2. 2.1
, ox , (
) 2.3.
0t 0M 0x . t M . 0t t t
M x . 0M M S .
(2.4) 0M MS v t . , OM :
0 00OM OM M M OM S . ox :
0x x S 0 0xx x v t t (2.5) (2.5) :
. 0 0t :
0 xx x v t (2.6) xv (2.5) (2.6) v .
v ox . , xv v . - v ox ; xv : xv v .
2.3
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- v ox ; xv : xv v . (2.6) 0 0x .
, : x v t (2.7)
2.2 A B
60 km . A 40 km/h B
20 km/h . A ?
:
:
ox AB, O A. A B
0( 0)t 2.4. 0 xx x v t :
- A: 0 0x , A 40km/hxv v Ax t :
A 40x t (1) - B : 0 60 km,x B 20km/hxv v ( Bv ox ).
Bx t : 60 20Bx t (2)
A
B
60km40km/h20km/h
Svv
??
tx
Av Bv
60kmS
2.4 ສ.ວ
.ສ
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A B 40 60 20 1hx x t t t
: 1ht t (1) (2)
A : A 40 40 1 40kmx t
2.3 (2.6)
x
t t ,
. ,
A
: 40Ax t
B A
: 60 20Bx t . 2.5.
3. ,
. , , . .
; .
t 0 0.5 1 1,5 2 3
0 20 40 60 80 120
60 50 40 30 20 0
40Ax t
60 20Bx t
2.5
40A tx60 20B tx
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.
, .
4. A B
O : AOv ( A
O) BOv ( B O), A B
ABv 2.6. :
AO AB BOv v v (2.8)
- A B :
v v v - A B
:
v v v - A B
:
2 2 2 cosv v v v v
Ov v .
x O
AOvBOv
A B
2.6 ABv
x O
AOvBOv
A B
x O
BOv AOvB A
O
BOv
AOv
ABv
x
2.7
ABv
ABvສ.ວ.ສ
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:
.
,
12
1. . 2. . 3. ? 4.
. 5. . 5 s 4 m,
25s 44 m.
. 6. A B
20km A B. A 60km/h, B 40km/h.
. A , AB .
. . 7. , 40km/h
60km/h. :
.
. . 8. A B 3
, B A 6
. A B . ?
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3: :
. .
1. 1.1 (Average Speed)
S t
. Svt (3.1)
(3.1) S t.
. ; . , .
1.2 (Instantaneous Speed) ,
. , t . S
. St
. ( ) ( ). v .
Svt (3.2)
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.
.
14
2. (Acceleration) 2.1
0v 0t v t , 0v v v
0t t t . . , v t , v a t .
a .
0
0
v vvat t t
(3.3)
. ,
. 2(m/s ) .
2.2 0t 0v , t tv 0t t t ,
0tv v v . , :
0
0
tv vvat t t
(3.4)
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2.3 1)
0v v , v
0v v 3.1. a
0v v . 2)
0v v , v
0v v 3.2. a
0v v . 3)
0
0
v vvat t t
0 0t , t t :
0v v at (3.5) (3.5)
.
3. 3.1
, a
0a . (3.5), v t . ,
3.3.
3.1
3.2
0v vva
0v
3.3
0v0v
v
v
a
O t(s)
v(m/s)
2 4 6 8 10
2
4
6
10
0v
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3.2 ,
a ( 0)a .
(3.5), v t . ,
3.4.
4 . 4.1
1) ,
. ,
3.5.
S vt . : S vt .
3.5 v t OA v OB t .
. 2)
, .
0v , . ,
3.4
v
t 3.5
0v
tv
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0v , v t 3.6.
, 0v . ,
0v , v t 3.7.
4.2 1)
OMNP 3.6 : 0
OMNPOM + NP= ×OP =
2 2v v t
A
(3.5) 0v v at : 20 0
OMNP 0( ) 1
2 2v v atS A t v t at
20
12
S v t at (3.6)
(3.6) .
2) OMNP 3.7 :
0OMNP
OM + NP= ×OP = 2 2
v v tA
(3.5) 0v v at 0a :
0v
v
t
0
2v v
S tv
t
0
2v v
S t
0v
3.6 3.7
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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20 0OMNP 0
( ) 12 2
v v atS A t v t at
20
12
S v t at (3.7)
(3.7) . 3)
(3.6) . ox
3.8 0 0 0OM = OM + M M = + x S OM ox :
0x x S 20
12
S v t at
20 0
12
x x v t at (3.8)
: (3.8) 0 , 0x x ox; 0 , 0x x ox. 0 , v a ,
0 , v a x ; 0 , v a , x .
: 21m/s . 8 A 3m/s
B A 150m. 21m/s B A
M t
va
0va
x'x
xso 0 0M 0t
0x
3.8
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2m/s . A ?
:
ox AB,
A, A B 8 h 00.
20 0
12
x x v t at
A 01 3m/sv ox . , 2
01 10, 1m/sx a : 2
1 32tx t (1)
B 02 = 2m/sv ox. 02 = 150mx 2
2 = 1m/sa :
2
2 150 22tx t (2)
1 2x x :
2 2
23 150 2 5 150 02 2t tt t t t
: 1 10t s 2 15st . 2 15st
, . , 10t s .
3.9
1v1a
2v
2a
: 21
012
2
02
1m/s3m/s
1 m/s2m/s
AB 150m
avav
: ??
tx
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20
(1) (2) A.
(1) 2
1103 10 80m
2x
4.3 ,
00
v vv v at ta
t 0v va
(3.6) :
2 20 2v v aS (3.9)
00
v vv v at at
a 0v vt
(3.6) :
0
2v v
S t (3.10)
5. (Free Fall) 5.1
.
. , “ ”(Aristotle)
. :
- . . .
- , . .
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- , .
. ?
?
: - . - . - .
.
. , ;
.
5.2
( ), (Newton)
. -
( ) .
3.10
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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22
- ( )
. :
- . - - .
.
, .
. ,… .
5.3 1) . 2)
. 3) .
: v gt (3.11)
g . t . 4) :
212
h gt (3.12)
5) g
( 3.11). .
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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23
212
h gt
2
2hgt
.
g 29,8m/s .
g . g
. g
2 29,8m/s 10m/sg .
5.4
.
. g .
3.11
ສ.ວ.ສ
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24
1. , ? 2. ? 3. , ,
? 4. :
- 2 m/s 22 m/s 10 s. - 2 m/s 32 m/s 30 s.
5. - ? 6. ? 7.
(+), (-) ? 8. 3m/s ; 20s
7m/s. . 9. 36km/h .
20s . .
10. 20,1m/sa .
36 km/h? ?
11. , 20s 36km/h.
54km/h ( )?
ສ.ວ.ສ
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25
12. 3.12
. : .
? . ,
. 13. 270 m.
3 .
14. , 4s . 330 m/s
29,8m/sg . ? 15. 0v
t . () ?
16. 5 m/s .
. 2s ?
. . 210 m/sg .
3.12
ສ.ວ.ສ
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:
( )
26
4:
1. (Projectile Motion) 1.1
. :
, , , .
. 1.2
. 1t 1M 1r ;
2t 2M 2r .
2 1t t t : 1 2 2 1M M r r r . mv t
2 1
2 1m
r rrvt t t
(4.1)
1 1t r t (4.1)
t r 2 1 .
:
1v
1M
2v2M
2r
1r
r
o
4.1
ສ.ວ.ສ
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27
0lim
t
rvt (4.2)
(4.2), 0t 2 1 , 0r .
: - : 2 1 . ,
1 2 1 . , 1 .
- : .
- ( ): 2 1 1 2 ( r )
S . ,
0lim
t
Sv vt (4.3)
1.3
. 1t
1 1v .
2 2 1t t t
2 2v . 4.2.
2 1t t t
2 1v v v . v , 2v 2 1 ; '
1 2
4.2
1v2v
1
'2
2
4.2
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28
1v 2v . '1 2 2 1v v .
'1 1 2 , '
1 1 2 ; , 1 v t . , ma
1 2
v t :
mvat (4.4)
ma v . a 1 1t
v t , t :
0lim
t
vat (4.5)
: a (4.5) lim v v
(4.4).
: 1) ta 2)
ca 4.3. v a t
tv cv . : - t tv a t
v tv v , v .
:
0
limt t
vat (4.6)
4.3
tv
ta
ca
a
ສ.ວ.ສ
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(4. 5) (4. 6) v (4.5) , v
(4.6) . ta v
, ; ta v , , .
- c cv a t v cv
v . :
2
cvar (4.7)
r . ca r
. , . t ca a a . a :
2 2
t ca a a (4.8)
2. (Circular Motion) .
: .
2.1 1) : ( ) .
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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30
2) M0 0 0t , t M S
0 0M M ( = M M)S 4.4. :
Svt (4.9)
v (4.9) ,
. 4.4,
R
0M OM . “ ”. SR
(4.10)
(rad). 2 rad 360 .
, N , : 2 N (4.11)
t ( “ ”).
t (4.12)
rad/s (4.11) (4.12) :
2 Nt
(4.13)
Nft (4.13) 2 f . f .
(Hz) / .
4.4
y
xO
M
M0
v
v
SR
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3) .
T. : 1 2Tf
2T
(4.14)
4)
Svt, S
R
t :
v v RR
(4.15)
, 0S S vt ., :
0 t (4.16)
0 0 0t . 5)
, . ,
a ca .
cva at (4.17)
M1 1v , M2 2v , 1v 2v
. 2v
1v (4.5) '1 2N N v . '
1 1 2M N N 1 2OM M ,
1 1 1(M N OM ; 2 2 2M N OM ; 1 1 2 2M N //M N ) .
1v2v
2N
2N1N
1M
2M
2vv
4.5
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32
; '
1 2 1 2
1 1 1
N N M M=M N OM
1 2M Mvv R
0t ; 2M 1M . 1 2M M 1 2M M S v t .
(4.17) : v v t
v R
2v vt R
: 2
cvaR
(4.18)
2.2 1)
.
2) , ,
ta .
t .
0lim
t t (4.19)
v t . v
: .v R (4.20)
(4.20) t v Rt t
.
0t : ta R (4.21)
. 2rad/s
ສ.ວ.ສ
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3)
20
1 2
S v t a t ,S R
v R ta R :
20
1 2
t t (4.22)
: 0 t t (4.23)
2 20 2 t (4.24)
0
2t (4.25)
, 0t ; : .
0t ; .
1. 10cm
, 0,2s. .
2. 30cm 10 . . .
3. ( ) 3cm ( ) 4cm.
. 4. 6400 km
24 . : . . . . .
ສ.ວ.ສ
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5. 1800 km/h .
. 2100m/s . 6.
1 5cmR 1 180rad/s 2 30cmR . :
. .
. ( ) 7. , 51 , 17 .
. 1 . ?
. 1 30 . ? 650 mm.
8. , 6 200 / , 5
. 3100 .
. 9.
1m. 1 10st 50m ( ). 2 5st ?
10. . 6s 36 rad/s. : . . . .
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35
5:
1. (Linear Motion) 1.1 1
A B 8 ; A O 20 km;
B O 40 km . , A 40 km/h
B 20 km/h 5.1. ? O ?
:
:
0 0t . 0 xx x v t
: - A: A 0 (120 )4x t - B: B 40 2 )0 (2x t
: A B 20 40 40 20 3hx x t t t
11 .
0A
0B
A
B
20km
40km
40km/h
20km/h
xxvv
?
?
tx
5.1
1v2v
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:
. . .
36
t (1) O : 20 40 100kmx t
5.2.
1.2 2 ,
. 10 m/s 6 m/s.
? ? :
- :
6 3cos 53
10 5w
b
vv
t 0 1 2 3 4
A 20 40x t -20 20 60 100 140
B 40 20x t 40 60 80 100 120
5.2
S(km)
t (h)O 1 2 3 4
20406080
- 20
20 40Ax t
40 20Bx t
100120140
10 m/s
6m/sb
w
vv
?
?bv
5.3
bv bwv
wv
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37
53 .
- : bw b wv v v 2 2 2 cos ,bw b w b w b wv v v v v v v
3cos , cos cos
5b wv v
2 2 310 6 2 10 6 8m/s
5bwv
8 m/s.
2. 2.1 1
O A B 100 m 10s . B
15 m/s . : . A. . . . O A. :
AB 100 mx AB 10 st B 15 m/sv . A ?v . ?a . OA ?x 5.4
5.4
v
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38
. A.
: B AAB AB2
v vx t
AB
A BAB
2 2 10015
10
xv vt
5 m/s
. .
: B A ABv v at B
AB
15 5
10Av va
t21 m/s
. O A.
: 2 2A 0 OA2v v a x
2 2 2A 0
OA
5 014,5 m
2 2 1
v vxa
2.2 2 0 = 6 m/s.v
? ? 2= 10 m/s .g : 0 6 m/sv
2g = 10 m/s ?t
max ?y + :
20
1
2y v t gt
g . , :
2 6 5y t t 0y . :
20 6 5 1, 2 st t t
g
0v
0v
maxy
5.5
oy (+),
0 0t O. ,
0 0y 5.5.
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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39
1,2 s . + :
2 20 2tv v g y 0tv .
, 2 2
2 00
60 2 1,8 m
2 2( 10)
vv g y yg
max 1,8 my
3. 3.1 1
20cm 25cm/s .
, ?
: 20cm R 2= 5 cm/sta
2c ta a 0 0v
?t
3.2 2 1 3m/sv
=10cm 2 =v 2m/s . ?
2 .............(1)c ta a
: 2
...............(2)cvaR
0 .............(3)tv v a t (3) (2) (1) :
2
2tt
a ta
R
2
2 2 0, 22,82s
5 10t
Rta
ສ.ວ.ສ
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40
:
v R . , 1 2 .
1
2
.....................(1)
- .............(2)
v Rv R
1
2
1
2
v Rv R
3
2 0,1
RR
0,3mR
R (1) 1 310rad/s
0,3
vR
102
2 2f f /s 300 /mn
96 /mn
3.3 3 30 /s
. 60 . : . . . . :
30f /s, 60N , 0
. ? . ?t
5.6
2v1v
?f
1
2
3m/s
2m/s
10cm 0,1m
vv
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41
. 2 2
0 2 00, 2 f 2 N
2 22 220
0 2 307,5 rad/s
2 2 2 2 60
fN
. 0 t
0 0 2 2 3,14 30
25s7.5
ft
1. , 40 km/h 60 km/h.
. 2. . 1mn
54km/h. .
3. 40 m , 20s;
50m . , :
. . . . . .
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42
4. A B 15 m/s 4m/s2, B
30m/s A. 2s 52 m. A B.
5. A 24m/s . 10s
30s. 28m/s B. A B.
6. 5s, 5m. 3
? 7. , 20 m/s.
, .
8. , 3/4
. . 9.
1,25 m/s2. 40 m . .
10. 8km/h , 6km/h . .
? 11. 8m/s 2km
1,2 m/s; 30 .
?
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43
12. 30 cm 33 / 16 : . rad/s2? . ?
13. , 1 10st
1 16mS , 2 5st 2 3mS . 1 2;v v .
14. 10 m 0.7cm . g = 9 8 m/s2,
: . . . .
15. 1s.
n . . ສ.ວ
.ສ
ສະຫງວນລຂິະສດິ
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:
.
44
II: 6:
1. (Concept of Force) .2,
.
. (N). ( ) ( ).
:
6.1: 1) 3
6.1. 2) .
. 3) 2) 2).
.
6.1
FF
F
ສ.ວ.ສ
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45
: - , . - ,
. - ,
. - ,
2) .
, 4 : , , .
4 : , , . , .
I .
, :
.
2.
: -
. -
. - . - .
6.2
ສ.ວ.ສ
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:
:
:
.
:.
46
: 500 N,
30 1cm = 100N.
3. F
ox oy xoy : -
F . - F ox oy ;
xF yF F .
4. 4.1
, C A B ( C A B )
. , . ,
. : .
1) 1F 2F
. 6.5 2F
1FF
6.3
500N
100N30
y
xxF
yFF
O 6.4
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47
: 1F ,
2F ; 2F , 1F . . F
, . F 1F
2F 6.5.
2) : 1F 2F .
: 1F
2F . F 2F , 1F . F
1F 2F 6.6.
3) ,
; .
.
: 1F , 2F , 3F 4F .
6.6
2F
1F F2F 1F
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:
48
: 1F 2F
12F ; 12F 3F 123F ; 123F 4F
1234F 1F , 2F , 3F 4F .
1234 1 2 3 4F F F F F
: 1F 2F 12F ; 3F 4F 34F ; 12F 34F
1234F 1F , 2F , 3F 4F .
1234 1 2 3 4F F F F F
,
:
1 2 3 4 ... nF F F F F F n
ii
F
6. 8
1F
2F
3F4F
4F
1F
2F
3F
34F
12F12F
34F
1234F
1F
2F
3F
4F
2F
1F
3F
4F
12F12F
123F
3F4F
123F
1234F
4F 6.7
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49
4.2
F 1F 2F
.
: - 1F
2F ;
xoy
( 1F x ).
1F 2F F 6.10. - 1F 2F
ox oy 1 1 2; ; x y xF F F 2 yF 6.11 :
1 1xF F , 1 0yF
2 2 cosxF F , 2 2 sinyF F ox : 1 2 cosxF F F oy : 2 2 siny yF F F
: 2 2 2x yF F F
2 2 21 2 2( cos ) ( sin )F F F F
2 2 2 2 2 2
1 1 2 2 22 cos cos sinF F F F F F
2 2 2 2 21 1 2 22 cos (cos sin )F F F F F
2 2
1 2 1 22 cosF F F F F
1F 6. 9
2F
6. 10
x
y
1F
2FF
2F F
1FxF2xF x
6. 11
yF2 yF
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, .
: .
.
:
50
ox :
y
x
FtanF 1 y
x
FtanF
2 2 21 2 1 22 cosF F F F F
: + 0 : 1F 2F
6.12 6.12 .
F 1F 2F .
1F 2F .
+ 0 : 1F 2F 6.13.
+ 90 : 1F 2F 6.14.
2 2
1 2F F F
4.3 :
1) ;
. .
F
2F 1F
6. 13 1 2F F F
6. 12 1 2F F F
2F1F1F
2FF F
1 2F F F
6.14
F
2F
1F
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51
2) .
. ? , ? .
:
- 1 . - 2 .
0;
, . , 0 .
1 2F F 1 2 0F F F
: , :
- , , ,
0. 1 2 0F F
- ( ),
0.
1
0n
ii
F
6.15
1F 2F
O
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52
1. ? 2. ,
. ? .
3. . 4. ? 5. ? 6. :
. 500N 1cm = 50N
. 1200N 1cm = 100N
. 75N 1 cm = 25N
7. .
8. 9N
12 N. ?
. 1 N; . 5 N ; . 15 N ; . 25 N
3F2F
1F
2F
1F
3F
4F
5F
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53
9. 10 N , 10N.
? . 90 ; . 120 ; . 60 ; . 0 10. F 1F 2F
a b
1F 2F F ? . 1 2F F F
. 1 21
2F F F
. 1 2 1,73F F F
. 1 2
3
FF F
11. P = 20N ( ).
OA
OB . OA OB.
30 30 a
b
A
B
O
120ສ.ວ.ສ
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; ,
, .
.
.
54
7:
1. I (Newton’s First Law) 1.1 :
? ,
; , .
.
(Galileo). :
1) 1
2 7.1 . 2)
h 1, 1
2 2 h
1. 3) 2 2),
2 2), .
4) 2 3) 2 3).
7.1
1 2
h
h
h 2
1
1
1
2
2
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55
2 1
. , , 2
.
.
1.2 , (Isaac Newton)
; I :
; ,
, .
2.
, .
. ,
. I
.
3.
vat
.
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:
. :
56
. :
- . - .
4. II (Newton’s second Law) 4.1
1) . .
2) 1) . , ?
?
: .
, . 4.2.
.
, II . :
, .
Fam F ma (7.1)
a , F 2 . , (7.1) :
Fam F ma (7.2)
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57
4.3. ,
. F a .
: 1 2 3, , ,..., nF F F F - : 1 2 3, , ,..., na a a a :
1
1
1
Fam
, 2
2
2
Fam
, 3
3
3
Fam
, nn
n
Fam
- : 1 2 3 ... n
n ii
a a a a a a
- : 1 2 3...
n
n ii
F F F F F F
, II :
Fam F ma
n n
i ii i
F m a (7.3)
(7.1) (7. 3) F a (7. 3) .
xoy . (7.3)
:
1 2 3
y 1y 2 y 3y
+ + + .....+
+ + + .....+ (7. 4)x x x x nx
ny
ma F F F F
ma F F F F 4.4
(7.1)
. : .
: - .
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58
- ( , ).
5. III (Newton’s Third Law) 5.1
1) . .
2) . . - ? - ? - ?
:
, ; , .
, ; , .
.
5.2 ,
. : ,
.
AB BAF F AB BAF F (7.4)
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59
5.3
: -
. -
, . -
.
1. I, II III . 2. ? 3. ? 4.
( , ,...)? 5. ? 6. . 7. . 8. :
. 9. 10 4 . :
? , ?
10. II ? . F ma . F ma . F ma . F ma
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( )
.
60
11. , 5m/s .
? . . . . . . . 5 m/s.
12. 8 kg 22m/s . ?
. 1,6 N; . 16 N; .160 N; . 4N 13. .
25m 5m/s. . 5 kg.
14. 50 ; , 6m/s2.
.
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ສະຫງວນລຂິະສດິ
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61
8:
1. (Gravity Force) 1.1
(Nicolaus copernicus) , (Tycho
Brahe) (Johannes Kepler) .
.
: -
. -
.
- .
1.2
1m 2m
( 1 2m m )
8.1
8.2
1F 2F1m 2m
r
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ສະຫງວນລຂິະສດິ
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(
.
62
( 2r ).
1 2
2
m mF Gr
(8.1)
G 11 2 26,67 10 Nm / kgG
(8.1) : - . - , r
, F 8.2.
1.3 (Weight) ,
, . (8.1) :
2( )
mMP GR h
(8.2)
M , m . R , h .
P mg (8.2) :
2( )
GMgR h
(8.3)
(8.3)
g .
(h << R) :
2
GMgR
(8.4)
g
h(km) g(m/s2)
0 9,806 1 9,803 4 9,794 8 9,782
16 9,757
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63
2. (Elastic Force) 2.1
, ; ,
.
.
2.2 (Hooke’s Law) 300 ,
, (Robert Hooke)
: 1)
( 0 ). 1 (
1F mg ). . 1 1 0 1F .
. 2) 1), 2 ; 3 ...
; 2 ; 3 ... 2 2F mg ; 3 3F mg ….
2; 3;... 2; 3;.. .
0
8. 4
1
8.3 ( : Google search)
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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64
2.3 .
, ; . .
.
( ). :
, .
F kx F kx ( 8.5 ) k ,
(N/m). , .
x , (m); (-)
( x ). 2.4
- .
- , ;
. - . - ( ),
.
8.5
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ສະຫງວນລຂິະສດິ
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65
2.5 - ,
. - : , , , …
1. ?
. 2.
? 3. ?
, ? 4. .
. 5. . ?
? 6. 1 kg 10N.
, ?
8.6
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ສະຫງວນລຂິະສດິ
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66
7. . : 38,4 107m,
m = 7,37 1022kg M = 6,0 1024 kg. 8. , 50 000 , 40 000 .
1 km.
20g. 9. k =100N/m 10cm
? 10. , 15cm;
9N, 18cm. ?
11. , 20N, 50mm; 80mm. :
. . . . 12. , 10cm; 5N
8 cm, 10N, ?
13. 2 . 50s
400m. k = 2 104N/m ,
?
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ສະຫງວນລຂິະສດິ
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67
9:
1. (Friction Force) 1.1 1) ( )
.
9.1.
. 2) 1)
9.2.
3) 2) 9. 3.
4) 1) 9. 4.
5) 1) 3) . -
? ? -
? 1) ? ? - 4) 5) 1)
? ?
9.1
9.3
9.4
9.2
vf F
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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.
68
: -
.
( Sf ); ( kf ).
: ( Sf ) ( rf ). - ( S kf f ). - ( S rf f ). - ( f )
. - .
: , .
f N f N fN
(9.1 )
f (N) . . N (N=mg).
- k .
maxk Sf f . , k S . - k S k S .
0,01 1,5 .
- (9.1) ; ( S k r ).
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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69
2. (Centrifugal Force) 2.1
I ; II
, . .
II :
2
2C
vF m m RR
( 9.2 )
. - ,
. , ( t ca a a ). ,
:
2
C t tvF F F m maR
( 9.3)
tF .
CF . - ,
( 0ta ). , ( Ca ). , :
2
CvF F mR ( 9.4 )
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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.
:
70
: : 1)
9.5.
2) ( 9.6).
. , .
3) ,
( 9.7). ,
; (F )
.
9. 5 9. 6
StF
P P 9. 7
N
F F
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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71
2.2
9. 6; ( ) ,
( CF ) .
9.8 .
. :
. : ,
, 9.8 .
: - .
, A 9.9.
- A, B C.
- ,
D .
- : + ,
.
9. 8
Max2<s mF r
MaxsF
9. 9
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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72
1 24
1 24
C gF F 2
2( )
GmM mv
R h R h (9.5)
(m M )
(9.5) GMvR h
(9.6)
+ ( h<<R )
GMv gR
R ( 2
GMgR
) (9.7)
g = 9,8 m/s2 R = 8,4 106 m 7,9km/sv .
1.
: - .
85kg, 4 10 1957,
1 96 . - :
1 1 . ,
.
72
:
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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73
1. ,
? 2.
. 3. ,
? . . . . . . . .
4. .
5. ? . 6. 1500 kg
. 0,02. .
7. 0,5 kg .
1m/s; ? 0,10 g = 9,8m/s2.
8. 20g . ,
? 1m 0,08. 9. 1200 kg
36km/h. ? 50 m , g = 10m/s2.
10. .
. 6400km; 6,14 1024 kg.
:
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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:
:
74
III: 10:
.
. .
? . .
1. (Momentum)
: 1:
50g, 100g 150g, .
. . - ? - ? - ?
:
. 2v gh
g h . , .
150g 100g 50g
1m
10.1
100
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ສະຫງວນລຂິະສດິ
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75
P mg . ,
. 2:
100g 1= 0,5mh
( ). .
100g 2 1 mh 3 1,5 mh .
- ?
- ? - ?
: P
. .
2v gh 1h , 2h 3h .
,
; , . ,
.
. P .
10.1 10.2
1h
2h
3h
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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:
.
76
.
P mv (10.1)
P kgm/s
:
, .
2. m
0v , F
t tv . II
F ma vat :
vF mt
F t m v (10.2)
0tv v v
, 0tF t mv mv (10.3)
0 0( )t tmv mv m v v m v
0 0t tmv mv P P P P m v (10.4)
(10.4) (10.2) :
F t P (10.5)
(F t ) (Impulse). I ,
m m F F0v tv
10.3
t
ສ.ວ.ສ
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77
(N.s ) (kg.m/s ) .
I F t (10.6) : ,
, , ,... .
1: 0,4 kg
35 m/s . 25 m/s .
. :
0,4 kgm , 0 35 m/sv 25 m/stv ?F t
- (+) (-)
- 0tF t mv mv
F t 0,4 kg ( 25 m/s) 0, 4 kg 35 m/s
24 kg.m/s ( ) 3.
3.1
. : ,
: .
III : .
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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78
, (
, , ) : .
3.2 - ,
( );
. 1 2 2 1
3 . . -
, . .
- . sinP .
.
.
4. 4.1 1
,
. ( ).
,
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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79
. ,
10.4. - ABF A
B
BAF B
A
t A
B
- III : AB BAF F
B B A Am a m a B B A A
B A
( ) ( )v v v vm mt t
B B B B A A A Am v m v m v m v A A B B A A B Bm v m v m v m v (10.7)
A Bm m : A B A Bv v v v
B 0v A 0v : A Bv v
(10.7) ,
.
2: 4000 kg 40 km/h 2000 kg
10.5. . .
x xO 10.5
B
ABFBAF
10.4
A
P mv
P mv0P
0P
ສ.ວ.ສ
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80
: 1 4000 kgm 1 40 km/hxv 2 2000 kgm
2 ?xv
- xox , O .
- : A A B B A A B Bm v m v m v m v : 1 1 2 2 0x xm v m v
1 12
2
4000 4080 km/h
2000x
xm vvm
4.2 2
. :
- A B
10.4. . -
10.4. .
- ( 10.4 ).
- B A
( 10.5. ). - A 1A 10.5. . - B 1B 10.5. .
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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81
- B
B . 2B ( 10.5. ).
- A B .
- B A B
2BB . - B A B
1BB A 1AA ( 10.5. ).
A
1B
2BB
1A
1
2 B
A
1A
1B
2B
10.5
A
2
1
1v
1v
2v
B
( )
( )
10. 4
ABA
B
ສ.ວ.ສ
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82
: (
) t
. , B A
B 21
BBvt. B A
A B 12
AAvt
11
BBvt
. :
2 1 1BB BB AA
t t t 1 1 2v v v (10.8)
A B m . , m (10.8) :
1 1 2mv mv mv (10.9)
.
3: 3200kg x 10m/s 1200 kg y
20 m/s . O 10.6.
( ):
1 3200 kgm 1 10 m/sv
2 1200 kgm 2 20 m/sv
1 2 ?v v v ?
y
xo
10.6
vyv
xv
2v
1v
ສ.ວ.ສ
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83
- : =
1 1 2 2 1 2+ = ( )m v m v v m m ox : 3200 10 0 (3200 1200)xv
3200 107,27m/s
3200 1200xv
oy : 0 1200 20 (3200 1200)yv1200 20
5,45 m/s3200 1200yv
v : 2 2 2
2 22 2 7, 27 5,45 9 m/s
x y
x y
v v v
v v v
- x 5,45
tan 0,75 377,27
y
x
vv
1. ? . 2. ? . 3. ? 4. . 5. 15 000 kg 50 km/h
? 6. 0,5 kg 20 km/h
60 kg . 10.7.
.
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84
7. 3000kg 10 m/s
1000 kg
15 m/s. ?
8. 0,2 kg 10 m/s
10 m/s 10.9. :
. .
. .
10.7
10. 8
10. 9
10 m /s
10 m/s
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85
10.10
9. 150 g 25 m/s ,
40 m/s 0,002s 10.10.
. 10. 0,6 kg
20 m , 5 m .
3,05 s 10.11. ( 210 m/sg ).
11. 15 t 10 m/s
20 t . .
. 12. 100g
5 m , 1,8 m .
2s 10.12 : . . . . . .
A
B C
1h
2h
10.11
m
10.12
m
1,8m
5m
1v2v
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86
11:
1. (Action-Reaction Motion) :
, , , , ,…
1.1
M (
). m v .
V ; . , .
.
P = P 0 MV mv
MV mv (11.1)
(11.1) .
, .
.
11.1
Mm
vV
M
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87
, ,… , .
: 10g 400 m/s 4 kg . .
: 10g = 0,01 kgm 400 m/sv
4 kgM ?V
1.2 (Explosions)
11.2. .
. :
1) 2 ( 1 2m m m ), .
11.2
1 2
11.3
1 2
A B
- - P = P
0 MV mv MV mv :
4( ) (0,01 400) V
1 m/sV
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88
2) 2 11.3.
3) 1 2 .
. 4) 1 2
B . 5) 2 1
A .
6) .
7) , ,
.
: . , .
. : P = P
1 1 2 20 m v m v
1 1 2 2m v m v (11.2)
11.4
1 2 .
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89
2. (Machine on gas)
. : , , , ,... 11.5.
-
11.5
11.4
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.
.
90
2 : :
2.1
. 11.5 .
: SR-71
3 X-15
6,7 . 2
: . .
: , ,
11.5. . .
.
11.5. . 2.2 ( )
. 2 :
SR-71 X-15
11.6
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91
11.7
CFM56
.
( ).
11.7 . . :
.
.
11.7 .
. .
.
.
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92
. , . : .
.
M V m v .
M m V . :
( )MV M m V mv MV mvV
M m (11.4)
V , v V .
.
.
1. . 2. .
. 3.
? 4. ? ? 5. 2 kg 2000 kg
600 m/s . .
ສ.ວ.ສ
ສະຫງວນລຂິະສດິ
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93
6. 5 kg
15 m/s
11.8. , 15000 kg .
: . ( ) . ,
?7. 1,27 kg.
56,2 g , 6,1 cm 0,0218 s. , . :
. . . .
8. 3,5 kg . 52,7g ; 1,27 m/s
75 m/s . .
9. 415 10 kg
220 m/s . 48 10 kg 600 m/s .
?.
11.8
ສ.ວ.ສ
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:
94
IV: 12:
1. 1)
““ ” :
.
. F m
AB = S 12.1. F . , :
. W .
W FS (12.1)
F (N) S (m)
W (N.m) (Joule)
J .
F
SA B
m m
12.1
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95
2) F
S 12.2. 12.2 .
S .
F 1F 2F 1 2F F F . 1F cosF 2F sinF
. 2F . , 1F .
: ( cos )W F S cosW FS (12.2)
: - 0 cos0 1 .
cos0W FS FS - 0 90 cos 0 . cosW FS - 90 cos 0 . 0W - 90 cos 0 . cosW FS - 180 cos 1 . W FS
12.2
S BA
2F1F
F
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.
.
. .
96
1: 50 N 30 12.3. 10 m,
?
: : 50NF = 30 10mS : ?W
: cosW FS
: 50 10 cos30W 3500 250 3 J
2
3)
m A B
S 12.4. .
12.4 : 1 2F F f P NW W W W W W (12.3)
1 1 1// 1// 1+ = = cosF F F FW W W W F S
1 1= cos90 = 0FW F S
2 2FW F S fW fS
cos90 0PW mgS cos90 0NW NS
(12.3) : 1 2F F fW W W W 1 2cos ( ) ( )F S F S fS
1 2( cos )F F f S (12.4)
12.3
30
sin30F
cos30F
S BA
F
12.4
1F
f
2F
N
P
1//F
1F
A BS
ສ.ວ.ສ
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97
1 2( cos )F F f ( F ) . (12.4)
.
4) - F ,
F S;
F S 12.5. W = FS (12.5)
- F .
1F 2F 1S 12.6.
1F , 2F 1S .
1 212F
F FW S (12.6)
1 2
2
F F F :
WF = 1FS (12.7) (12.7), F , .
2. (Power) ,
. . ,
. P .
O 12.6 (m)S
(N)F
O S 12.5 (m)S
1S
2F
1F
(N)F
F
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98
WPt (12.8)
W FS Svt
,P
F v :
FSP Fvt
(12.9)
: - (J/s) (W ). - . - , ( kW ); (MW )
(hp ). 1 (1 kW) = 1000 W 1 (1 MW ) = 1 000 000 W 1 (1hp) = 746 W
3.
.
100%WW
(12.10)
W W
(12.8)
WPt
W Pt W P t :
100%PP
(12.11)
P P .
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99
1. , . 2. ? . 3. 2 kg 600 m.
? ( 0,02 g = 9,8 m/s2).
4. 50 kg 1,6 m ; 30 .
:
. .
. 60 N.
5. 60 kg 8 12.7.
30 cm 10s. .
6. 20 1 . 1 3 6m 1 , 1
60 kg. ? 7. 42 kg
- 12.8. 0,25 m 2s
?
F
h
P 12.7
12.8
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.
100
8. 80 kg F 37 2m/s. 0, 2.
: . F 5 m. . F. 9. 1000 kg
30
15 m/s 12.9.
. 10. F
S 12.10. F 6 m
12 m . 11. 25N
10kg 2s 12.11.
. .
. 0,1 210 m/sg .
12. 0,4kg 10 m/s 0,1s .
.
12.9
F
12.10
F(N)
8N
2N
6m 12 m
S(m)O
12.11
25NF
37
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101
13:
1. (Energy) 1.1
: ,
, ,…
. , .
.
E .
. : , , , , , ,
.
. : .
1.2
.
E W (13.1)
. J kJ .
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102
2. (Kinetic Energy) 2.1
: .
. , . .
. kE .
2.2 : -
. . -
60cm;
. 60cm.
- 13.1 .
- ; .
- .
, .
- 1 60cm .
13.1
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103
W
2vO
2W kv
13.2
. 50cm .
- 2, 3 4 .
/
m (kg ) m (kg )
F (N)
S (m)
2v (m/s )
W ( J )
1 2 3 4
: ;mmF g
m m
W FS 0,5mS , v at
ma gm m
( 2= 10 m/sg ), t
. W 2v
. 2v W
.
2W kv (13.2)
k , k . F m
a . ( 0 0v ) :
2 2v aS (13.3)
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104
II Fam
a (13.3) :
2 2Fv Sm
21
2FS mv
21
2W mv (13.4)
(13.4) (13.2) : 2 21 1
2 2kv mv k m (13.5)
(13.4) v :
21
2kE mv (13.7)
kE ( J ). 0 0v
v .
2 20 2v v aS Fa
m :
2 202
F S v vm
2 20
1 1
2 2FS mv mv (13.8)
0 = = k k kW E E E (13.9)
(13.9) ,
.
: 1200 kg 72 km/h. . 12m .
.
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105
: : 1200 kgm , 0 72 km/h = 20 m/sv , 12 mS 0v .
: ?W , ?F-
2 20
1 1
2 2W mv mv :
2 41 0 1200 (20) 24 10 J
2W ( )
-
4
424 102 10 N
12
WFS
( )
F m
S f 13.3.
F f , ( )W F f S .
= kW E :
( ) kF f S E kFS E fS (13.10)
,
. .
F
f
S
13.3
m
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106
1. . 2. ? . 3. 6 m/s ;
70 kg . ?
4. 50g 600 m/s
200 mm 200 m/s . ?
5. 30N 3 m . ? :
. .
. 10 N .
6. 0,6 kg A 2 m/s, B 7,50J. :
. A. . B. . A B. 7. 5×104kg 1,15×104 m/s
4×105N 2,5×106m . :
. . . .
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107
8. 200g 2g 1cm .
10m/s
13.4. ?
9. F 20N
1kg 0,5m 13.5.
0,2 . :
. . . .10. 13.6 6kg
F . 2m .
50
80(N)F
(m)S0 1 2
13.6
30
F
13.5
13.4
ສ.ວ.ສ
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.
108
14:
1. (Potential energy) .
, . :
. .
14.1. .
. .
, , .
. PE .
14.1
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109
1.1 1)
m h
F mg 14.2.
:
W Fh mgh (14.1)
(14.1)
mg
. , : pE mgh (14.2)
, h mg .
J kJ . 2)
1h 2h 14.3
:
1h 1 1PE mgh .
2h 2 2PE mgh .
: W Fd
2 1 2 1( )W mg h h mgh mgh
PW E (14.3)
m
mg
F
h
14.2
m
mg
F
1h
14.3
2h
d
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110
(14.3) .
1.2 (Elastic energy) 1)
F
x . x
14.4.
. .
.
.
.
2) :
- .
14.5.
- .
0x
x
x
F
F
( )
14.4
F
14.5
0x
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111
- 1 cm .
.
(cm)x 1 2 3 4 5
(N)F
F x
. ?
F x ? F
x . F x F kx (14.4)
k N/m. F x , k
. F . x
x :
0 1( )
2 2
FW x Fx
21
2W kx (14. 5)
x .
(14. 5) :
21
2PE kx (14. 6)
(N)F
(cm)xo 1 2 3 4 5 6
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, .
112
: 0,20 m 50 N ; 3 kg .
? ( 210 m/sg ). :
: 50 NF , 0,20 mx , 3 kgm : ?PE
- k 0,20 mx 50 N
50250 N/m
0,20
FF kx kx
- x 3 kg
.
F kx 3 100,12 m
250
mgmg kx xk
-
2 21 1(250)(0,12) 1,8 J
2 2P PE kx E
2.
. :
2.1 m
1h ( 1) 1v , 2h
( 2) 2v S 14.6.
, :
S
1h
2h
1v
2v
1
2
14.6
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113
2 22 1 2v v gS
2 22 1 1 22 ( )v v g h h (14.7)
1
2m (14.7) :
2 22 1 1 2
1 1( )
2 2mv mv mg h h 2 1( )mgh mgh (14.8)
k PE E (14.9) (14.9)
. (14.8) :
2 22 2 1 1
1 1
2 2mv mgh mv mgh (14.10)
(14.10) 1 2 . ,
, .
2.2 : 1
1x 1v ; 2 0x
0v ; 3 2x 2v 14.7.
.
2 2 2 2 2 22 2 0 0 1 1
1 1 1 1 1 1
2 2 2 2 2 2kx mv kx mv kx mv (14.11)
(14.11) 1 0v , 2 0,v 0 maxv v 0 0x . , : 2 2 22 max 1
1 1 1
2 2 2kx mv kx (14.12)
(14.12) .
14.7
1x0x2x
F
F
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114
3. :
. 3.1
. 1m
1v 2m 2v
, 1 2v v . 1v , 2v 14.8.
: P = P
1 1 2 2 1 1 2 2m v m v m v m v
1 1 1 2 2 2( ) ( )m v v m v v (14.13)
: Ek = Ek
2 2 2 21 1 2 2 1 1 2 2
1 1 1 1
2 2 2 2m v m v m v m v
2 2 2 21 1 1 2 2 2( ) ( )m v v m v v (14.14)
(14.13) (14.14) : 1 1 2 2v v v v (14.15)
3.2.
1 2v v v
: , .
1m 1m1v2v 2v1v
2m
14.8
2m
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115
. '
1 1 2 2 1 2( )m v m v m m v (14.16)
. Ek = Ek - Ek (14.17)
2 2 21 1 2 2 1 2
1 1 1( ) ( )2 2 2kE m v m v m m v (14.18)
1. ? 2.
. 3.
. 4. ? 5.
. 6. ? 7. ? 8. 0,4 kg
50 cm 80 cm
14.9. .
9.
50 kg A B, C , D E 14.10.
.
mg
F
1h
2h
30 m
60 m100 m
A
B
C
D
E
14.10
14.9
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: :
.
. :
116
10. A, B, C, D, E F 14.11. 50 J .
11. 5g v 2kg .
3cm 14.12.
.
12. 0,1kg 100N/m 20cm .
14.13. F . :
. A, B, C, D E .
. EF .
14.11
hA
B
14.12
E F
D
A
B
C0,5m
1m0,2
k=100
O
0 0v
F 0v
10m
14.13
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117
V: 15:
1. :
1) .
2) .
3) . .
4) II
. . 5) , . 6) .
2. 1: 2
800N, 0,02.
20m/s ? ? ( 210 m/sg ).
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ສະຫງວນລຂິະສດິ
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118
: 1) : 2t 2000kgm
210m/s
m/s20
02,0
N800
gv
F
t
: ?t ?S
2) oxy , O
, ox oy .
3) :
- F .
- , .
- P .
- N .
4) II F ma F f P N ma (16.1)
(16.1) :
N
P
F
y
o
f
x
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119
x: F f ma (1)
f N mg (2)
y : 0N P N P mg (3) 5) - a :
(1)F fF f ma a
m
f mg :
F mgam
2800 (0,02 2000 10)0,2m/s
2000
- t :
: atvvt 0 0 20 0100 s
0,2tv vt
a
- S :
: 20 0
1
2S S v t at 0 0S 00v
2 21 1 20000,2 (100) 1000m 1km
2 2 2S at
6) : 2 2
0 2tv v aS 2
02 2 0, 2 1000 0 20 m/stv aS v
2 20 2tv v aS 0( ) (20 0) 100
1000 m2 2
tv v tS
2: 2,5 A 54 km/h B 36km/h 50s.
0,04, : . ?
. ? ( 2m/s8,9g ).
ສ.ວ.ສ
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:
120
: 1)
: 2,5t 2500 kgm
0 54 km/h 15 m/s
0,04
50 s
36 km/h 10 m/st
v
tv
: . . ?F
2) oxy , O .
x y . 3)
: ( 1 3) 4)
II F ma F f P N ma (16.1)
(16.1) :
x : F f ma (1) f N mg (2) y : 0N P N P mg (3)
5) -
: 200
10 150,1 m/s
50t
tv vv v at a
t
.
F
f
N
P
o
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121
- : F f ma ( )F ma f m g a 2500(0,04 9,8 0,1) 730 N 6) F maF mg ma
mg
730 2500( 0,1)0,04
2500 9,8
3: 1000kg 3000N 45 ,
. ? ( 0,2 2= 10m/sg ).
: 1)
: 1000kgm
2
3000N
45
= 0,2
= 10m/s
F
g
: ?a 2)
oxy , O , x y .
3) - F :
1F ; 2F .
- f .
F
1F
2F
f
P
N
45 x
y
o
ສ.ວ.ສ
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122
- P .
- N .
4) II F ma F f P N ma (16.1)
(16.1) :
x: cos 45F f ma (1)
f N (2)
y : sin 45 0 sin 45N F P N mg F (3)
( sin 45 )f mg F (4) 5) 1). a :
(1): cos 45F f ma cos 45F fam
(4) : cos 45 ( sin 45 )F mg Fam
2
3000 0,7 - 0, 2(1000 10 3000 0,7)
1000
0,54 m/s
6) (1) cos 45F f ma cos 45 sin 45F mg F ma
( )
sin 45 cos 45
m a gF
1000(0,54 0,2 10)3000 N
0,2 0,7 0,7F
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123
1. . 2. 10kg 8 m.
5s? ( 0,01 210m/sg ).
3. . . 400 N , 2040kg.
. . 36km/h 45m . .
5s. 200N 2m/s10g .
4. A B 2kg 0,5kg 20N .
A A B 0,2 .
: . A B ? . A B ?
5. 40N 5kg 30 . (
0,2 210m/sg ) : . . . .
30
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:
124
16:
1.
. .
: :
1) .
. 2) . 3) . 4) .
- ? -
?
(1) (2) (3) (4)
16.1
P P P P
F F
F
F
y
y
O
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125
: 1) .
II : F P ma 0a
oy :
0F P F P mg F .
2) II :
F P ma oy
: F P ma
( )F m g a , F P (16.2) (16.2) P (
F ) P ( ). P F ( )P F m g a P . .
. 3) II :
F P ma oy
: F P ma
F ( )m g a (16.3)
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:
:
126
(16.3) 'P ( F ) P ( ).
P F ( )P F m g a P . .
.
2. 1:
5 m/s . ?. (
210 m/sg ). :
: 0 =5 m/sv : ?h
?t 210 m/sg
2 20 2tv v ah (1)
a : F ma F P : F ma P ma mg ma a g
( 0tv ) a g (1) :
2 20 (15)
11, 25m2 2 10
vhg
t:
.
: 00
tt
v vv v at ta
0 ,tv v a g
02 2 153 s
10
vtg
16.2
0v
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127
2: 20kg 16.3. 4 ,
4 . :
. 1 2 2s 2m/s.
. 2 3 2m/s.
. 3 4 4.. .
: : 20kgm
1 2 3 4mh h h : ?F
oy . . 1 2
II : F P ma
oy
: ( ) (1)F P ma F ma mg m a g
a : : 0tv v at
20 2 01 m/s
2tv va
t
(1) : 20(1 10) 220NF
220N . .
16.3
y
o
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128
. 2 3 II :
F P ma oy
: 0 20 10 200NF P F mg
. . 3 4 4
II : F P ma
oy
: ( ) (2)F P ma F ma mg m a g
a :
: 2 20 2tv v aS
2 20
2tv va
S 0v 3 2m/s .
220 2 4
0,5 m/s2 4 8
a
20,5 m/sa (2) 20(10 ( 0,5)) 190NF
190N . . .
10 m/ 2s . II :
F P ma oy
: ( ) 20(10 -10) 0F P ma F m g a
0N (0 ) .
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129
1. ? 2. 20 .
. 210 m/sg .
3. 0,25 2m/s
100 kg 1 . ? 210 m/sg .
4. 450 kg . 400 kg
? 210 m/sg .
5. 3kg
, 56cm.
? 2100 N/m.
16. 4
56 cm ສ.ວ.ສ
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:
130
17: 1.
m (17.1).
: 1)
ox oy . O
17.2. 2)
- P . . ,
ox oy : ox: sinxP P oy: cosyP P
- N , . - f
( ox ) . 3)
II : P f N ma (17.1)
(17.1) : ox: sin sinP f ma P N ma (17.2)
17.1
N
P
Px F yP
+y
x
O
17.2
f
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131
oy: cos 0 cosN P N P (17.3) 4)
- a : N (17.3) (17.2) :
sin ( cos )P P ma sin ( cos )mg mg ma (sin cos )a g (17.4)
( 0 ) : sina g .
- F : : F ma
(sin cos )F mg ( 0 )
: sinF mg .
2. 10kg
45 4m . ( 0,2 210 m/sg ).
: . . . . . . . . :
: 10 kgm ; 4 mh ; 45 ; 0,2; 210 m/sg . : . ?f ; . ?a ; . ? ; . ?tv
4mh45
?
17.3
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132
1) xoy. ox
, oy .
2) : - P . - N . - f .
3) P N f ma (1)
4) . f :
: f N (2) yN P
cos 45 cos 45N P mg (2) :
cos 45
0, 2 10 10 0,7 14N
f mg
. a: ox
:
x
x
P f maP fa
m
sin 45P fam
sin 45mg fm
210 10 0,7 145,6m/s
10
x
O
17.5
fN
P
yP
Px
y
N f
P
Px yP
+y
x
O
17.4
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133
. : :
4sin 45 5,7m
sin 45 0,7
h h
. tv : : 2 2
0 2tv v aS 2 2
0 2tv v a 0 0v 2 2 5,6 5,7 7,9m/stv a
1. . 2. , .
? 3. 30 ,
0,3. ? ( 210m/sg ).
4. 37 20m/s , 0,5. :
. 2s .
. . 5. 5
20,03m/s . 15km, 1,5km 200N ( 210m/sg ).
: . . . . . .
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:
134
6. P F .
? 7. m
. : . . . . . .
8. 2kg
30 17.6,
2m/s3 . .
9. 500g
17.7 3cm .
0,12. ? 2000 N/m.
10. 0,5kg 4m , 10m/s.
?
30
F
17.6
30
h S
17.7
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135
18:
1. 1: 1m 2m
, 1m
2m 1 2 , g . F 1m .
. :
1) : 1 2 1 2, , , ,m m F g : ?a ?T
2) xoy .
- ox . - oy , .
3) + 1: F 1, 1f ,
1T , 1P , 1N . + 2: 2T , 2f ,
2P , 2N . . ,
1 2a a a 1 2T T T (
III ).
18.1
‹ ‹
1P
2P
F
y
1N2T 1T
1f
2Nx
2m1mo
2f
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:
4)
136
4) :
1 1 1 1 1
2 2 2 2 2
(1)
(2)
F T f P N m a
T f P N m a
ox oy (18.1)
:
ox: 1 1
2 2
(3)
(4)
F T f m aT f m a
(3) (4) : 1 2 1 2( ) (5)F f f m m a
oy: 1 1 1 1 1
2 2 2 2 2
0 (6)
0 (7)
N P N P m gN P N P m g
5) - a : (5): 1 2 1 2( )F f f m m a :
1 1 2 2 1 2( )F m g m g m m a
1 1 2 2
1 2
( )F g m mam m
- T : (4): 2 2T f m a . a 2f :
1 1 2 22 2 2
1 2
( )F g m mT m g mm m
1 1 2 22 2 2
1 2
( )F g m mT m g mm m
2 1 2 2 2 2 2 1 1 2 2 2 2
1 2
m m g m m g Fm m m g m m gm m
1 2 12
1 2
F m gT m
m m
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137
2. 2: A, B 1m , 2m 1 2m m
. g . .
: 1) : 1 2,m m g
: ?a ?T
2) oy .
3) 18.2 : + 1: 1T , 1P . + 2: 2T , 2P .
, 1 2
. III : 1 2T T T ,
1 2a a a . 4)
:
1 1 1
2 2 2
(1)
(2)
T P m a
T P m a
oy (18.2)
:
1P
2T1T
2P
1m2m
y
18.2
a
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:
138
1 1 1
2 2 2
(3)
(4)
T P m aT P m a
(3) (4) : 1 2 1 2( ) (5)P P m m a 5)
- a : (5): 1 2 1 2( )P P m m a
1 2 1 2
1 2 1 2
( )P P g m mam m m m
- T : (3): 1 1 1T P m a
1 1P m g : 1 1T m g m a
1( )T m g a
a 1 2
1 2
2m m gTm m
3. 3: 1 15kgm 2 10kgm
45 18.3.
0,01. ?
4545
1m2m
18.3 2P
1xP1yP2f
1f2N 1N2T
1T
1m2m
18.41P
2 yP2xP
•
a
•
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139
: 1)
: 1 15kgm ; 2 10kgm ; 45 ; 0,01 : ? ; ?a T
2) xoy
ox oy . 3)
+ 1: 1P , 1f , 1T , 1N .
+ 2: 2P , 2T , 2f , 2N .
, 1 2
. III : 1 2T T T ,
21a a a .
4) :
1 1 1 1 1
2 2 2 2 2
(1)
(2)
P T f N m a
T f P N m a
ox oy :
ox: 1 1 1
2 2 2
(3)
(4)x
x
P T f m aT P f m a
(3) (4) : 1 2 1 2 1 2( ) (5)x xP P f f m m a
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140
oy: 1 1 1 1 1
2 2 2 2 2
0 cos 45 (6)
0 cos 45 (7)
y y
y y
N P N P m g
N P N P m g
5) - a :
(5): 1 2 1 2 1 2( )x xP P f f m m a 1 2 1 2 1 2( )x xP P N N m m a
1 2 1 2 1 2sin 45 sin 45 cos 45 cos 45 ( )m g m g m g m g m m a
1 2 1 2 1 2sin 45 ( ) cos 45 ( ) ( )g m m g m m m m a
1 2 1 2
1 2
sin 45 ( ) cos 45 ( )g m m g m mam m
(8)
(8) : 10 0,7(15 10) 0,01 10 0,7(15 10)
15 10a 21,33 m/s
- T : (3): 1 1 1xP T f m a
1 1 1sin 45 cos 45m g T m g m a
1 1 1sin 45 cos 45T m g m g m a (9)
(9) : 15 10 0,7 0,01 15 10 0,7 15 1,33T 84NT
1. 2 18.5. 1m 1000kg, 2m 2000kg
3 =m 3000kg .
; 1 2 20N. ?
1m2m3m
18.5
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141
2. A B 400g
. C = 20gm
A 18.6 . A C .
3. 1= 6kgm 0,2.
.
2 3kgm 18.7. .
4. A, B C 6kg, 12kg 8kg , .
18.8.
. ( 210m/sg ) 5. A, B C 2kg, 5kg 10kg
18.9. B C 200N.
. 6. 1 10kgm 2 3kgm
. 1m
30 2m 18.10. ?
7. 18.11. , .
45
A
B
C
18.7
1m
2m
FA
B
C
18.9
30
1m
2m 18.10
10kg
18.11
3kg
18.6
ABC
18.8
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:
142
19:
1.
: -
h 1 2 19.1. - , 2
1 .
: 1 , 2
. 2
: 1
. . ,
: .
: h S .
t. g .
19.1
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143
: 1)
: y h , x S : 0 ?v ; ?tv
2) ox y
O . ox , oy .
3) - ox. .
, 0 1 2 0x x xv v v v , 0x v t (19.1) - oy.
P . , II F ma . mg ma a g
21 2
2
yy gt tg
(19.2)
t (19.1) :
0 0
2
2
y gx v v xg y
(19.3)
4) tv
: t x yv v v 2 2
t x yv v v 0xv v , yv gt .
2 20 ( )tv v gt (19.4)
oxvo
1xv
2xv1yv
2 yv
y x
19.2
h
x
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144
2. :
0v ; 19.3. , g . :
. .
. .
. . . . . . . . . :
1) : 0, , v g
: . ?y . max ?x . ?,t . OA ?t . max ?y . ?v . ?
2) xoy. ox , oy
, O 0 0t .
19.3
19.4
y
x
O
A
B
0v
oxv
oyv
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145
3) - ox. .
, : 0 xx x v t 0 0, cosx oxx o v v v
0( cos )x v t (19.5)
- oy, P . II F ma mg ma a g :
20
1
2yy v t gt
oy 0 0 sinyv v . , oy :
20
1 sin
2y v t gt (19.6)
oy : 0 sinyv v gt (19.7)
4) .
(19.5) : 0 cos
xtv
(19.6) :
2
00 0
1 sin
cos 2 cos
x xy v gv v
22 20
tan2 cos
gy x xv
(19.8)
(19.8) . , .
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146
. O B ox
B O . , 0y (19.8)
:
22 20
02 cos
gxtg xv
2 20 02 sin cos sin 2v vx
g g (19.9)
(19.9) .
sin cos 1 (19. 9) maxx sin 2 1,
45 .
20
max
vxg (19.10)
.
B 0y ; 0y (19.6)
:
20
10 sin
2v t gt 02 sinvt
g (19.11)
(19.11) O B.
. , ( 0yv ).
0yv (19.7) :
00 sin v gt 0 sinvtg
(19.12)
(19.12) . .
t (19.12) (19.6) :
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147
2
0 00
sin sin1 sin
2
v vy v gg g
2 20
max
sin
2
vyg
(19.13)
.
( ox oy). : x yv v v : 2 2
x yv v v (19.12) 0 cosxv v = 0 sin yv v g t 0yv . 0yv . 0yv .
. 19.5
tan y
x
vv
(19.13)
19.5
y
x
O
A
B
yv
xv
v
ສ.ວ.ສ
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148
1. .
2. 2m, 7m .
. 3.
15m/s ; 60 . ? 29,8m/sg .
4. 30 10m/s . : . (
) 1m ? . ?
( , 210m/sg ). 5. 50m/s
53 ; . , 210m/sg , sin 53 0,8;
cos53 0,6 . : . . . .
. . . 2s 6s. . .
6. .
ສ.ວ.ສ
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149
7. 200m
50 m/s 37
5m/s.
? 210m/sg .
8. 0,2kg 45 19.7.
0,1m ,
? 400 N/m. 9. A
, ( B) .
20m, 12m 40m 19.8.
10. 30 19.9
5m/s.
?
A
B
20 m
12 m
40 m
19.8
37o
200 m
1S 2S
19.6
30
19.9
S0,1m45
19.7
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:
150
20:
1. m ,
f / . : . . . .
: 1)
: , ,m R f : . ?Ca , . ?T
2) xoy . O ,
ox C ; oy . 3)
: - CF (T ),
. - v , .
4) II F ma
C CF ma . . Ca :
: 2
C
vaR
2v fR R : 2 2C 4a f
20.1
c
v
CF
y
xo
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151
. T : : C CF ma CF
. 2 24CT ma m f
2. m .
R 20.2. ?
: 1) : , , m R : ? 2) xoy , O , ox C ; oy . 3)
: - P .- T ,
. , ox oy :
ox : sinxT T oy : cosyT T
4) - II T P ma
R
20.2
o
TyT
xT P
x
y
C
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:
152
: ox :
sin cT F2vm
R(1)
oy :
cosT P mg (2) - (1) (2) :
2
sin
cos
vmT RT mg
2sin
cos
vRg
sin, tan
cosv R
2
tanR
gtan
rad/sg
R
3. A B C
r 1 20.3. A C ?
: - : r : ?H - H
2H h r (1) + h: A C : A C kA PA kC PCE E E E E E
210 2
2 Cmgh mv mgr 212
2 Ch v rg
(2)
A
B
C
h
H
r
20.3
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153
+ Cv :
1 . , C
( C = 0N ) II F ma C CN P ma
:
2
20 CC
Cvmg m v grr
v gr
Cv (2) :
2 2,52
rgh r rg
2,5h r (1) : 2,5 2 0,5H r r r
A C 0,5r
4. R,
. : . ? . ? :
1) : ,R : . ? . ?v
2) xoy
. O
. ox
, oy .
20.4
x
y
fO
N
P
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:
154
3) :
- P .
- f C .
- N . 4)
II F ma :
P N f ma
:
ox: 2
C (1)mvf ma f
R
oy: (2)0N P N P mg . :
: tan tanN Nf N
1
tan
. maxv : (1) (2) :
2max
2max
mvvf R
N mg Rg maxv Rg
5. m
20.5. .
ສ.ວ.ສ
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155
: 1)
: ,m : ?cF
2) xoy . ox
; oy ox . 3)
: - P . - N .
4) II F ma .
: P N ma
: ox: sin = (1)CN F
oy : cosN P mg cos
mgN
N (1) :
sincos cmg F tancF mg
1. 0,5m
0,5kg.
0,3m 20. 6. .
20.5 P
sinN
cosNN
x
y
oCF
R
20.6
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:
.
156
10m
1m
20.9
2. 1kg . 5 m/s
1m 10m/s 2m. ?
3. A h
B R 20.7
B ?
4. 900 kg 72 km/h
1 mn . 150m
600N.
? 5. 2 m A B
. A B ?
6. 0,3kg A 4R
R 20.8. B
? 7.
100m 20.9
? 210m/sg .
R
A
Bh
0 0v
20.7
R
4R
R
B
A
20.8
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157
VI: 21:
1. (Moment force) 1.1
( 21.1) 2F 1F . 1d
1F 2d 2F . ,
. 1 1 2 2F d F d (21.1)
Fd
. M. d . ,
:
. M Fd ( 21.2.)
(N.m)
AP
B
H
21.1 21.2
M
F1F1d
2d
2FO dສ.ວ
.ສ
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158
: - . -
. 1.2
21.1, 1 6NF , 1 2cmd , 2 6NF
2 6cmd . 1F 2F . 1F 2F :
1 1 1 6 0,02 1,12N.mM F d 2 2 2 6 0,06 1,12N.mM F d
( ), :
0M: 1 2 1,12 1,12 = 0M M
2. 2.1 1) . 2) .
. 3) 1 2,F F 3F
21.3 . .
4) .
1 2,F F 3F .
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159
. .
: 1 2 3F F F ( 3F 3F )
1 3 2F F F ( 2F 2F )
2 3 1F F F ( 1F 1F )
. 1 2,F F 3F .
( 21.4). , . ,
, 3 .
1 2 3 0F F F
21.3
1F
2F
3F
1F
2F
3F
21.4
3F
1F
2F
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160
2.2
:
- . -
. 2.3
( ) .
.
1 2 3 ... 0nF F F F 1
0n
ii
F
3. 3.1.
: - O .
( 21.5. ).
- 1F 2F O 1F 2F
. 1 1OO d 1F 2 2OO d
. , :
ສ.ວ.ສ
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161
1 1 2 2F d F d 1 2
2 1
F dF d
O 21.5. . 1 2F F F O
. 3F . ,
3F 1F 2F . 3.2.
: -
;
. -
.
O
21.5
O O 3F
3F
F
1F
2F
2O
1O
21.6
1d2d
1o
2oo
ສ.ວ.ສ
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162
1 2F F F ; 1 2
2 1
F dF d
: 1 2O O 1F
2F , 1 1OO d 2 2OO d 21.6. 1d 2d 1OO
2OO . : 50cm
1 40NF 2 60NF .
. :
: 1 40NF , 2 60NF , 50cm -
: 1 2F F F
: 40 60 100NF (1)
- F
1d F
: 1 2
2 1
F dF d
2 21
1
F ddF
(2)
2 1d d (3)
(3) (2) 21
1 2
FdF F
: 1
60 5030cm
40 60d .
2 50 30 20cmd
30 cm 20 cm
O
1 40NF2 60NF
100NF
1d 2d
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163
3.3.
;
. 21.7.
, .
4.
: 1 2,F F 3F 1 2O , O O
. 1F 2F
; O 21.8. 2 1F F F O 3F
3F . 2 1F F F
3F 1F
2F 1 2O O . 1F 1 1OO d 2F 2 2OO d .
F , 2F
1F .
G
21.7P
O
21.8
1d
2d1o 2o
1F
2F
3F
F
ສ.ວ.ສ
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164
, 1F 2F O :
1 1 2 2F d F d 1 2
2 1
F dF d
:
1)
. 2 1F F F
2)
.
1 2
2 1
F dF d
: C
A 4NF A B 12NF
B A 40cm 21.9 . :
. , .
. , C .
. . :
: 4NAF , 12NBF , AB = 40cm
: . ?F ? . ?CF ? . AC ?
21.9
CA B
40 cm
AF
BF
CF
F
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165
. , : 2 1F F F
: B A 12 - 4 8NF F F
F BF AF BF . . , C
CF F . , C 8NF F
.
: A
B
CB
AC
FF
A
B
CB
AB + CB
FF
A
B
AB 4 40CB 20cm
12 4A
FF F
AC = AB + CB = 40 + 20 = 60 cm
, : 60 cm
1. ? . 2.
. 3. F
A, B, C 21.10. :
. , ? . , ?
4. ( ) 21.11.
: - ? - ?
21.10
F
21.11 F
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.
166
- ? 5. ( 21.12)
. 6.
( 21.13). 100NF
20cm .
2 cm . .
7. ( 21.14). O . OA = 10 cm , OB = 200 cm
= 500 NBF B .
AF A ?
8. 21.15 . OA
20 cm 30 O ; C ( ) .
20 N A . : . . . . 8cm
.
21.14 21.15
BFB
A
AF
A
CAF
21.13
21.12
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167
22:
.
1. (Center of Gravity) :
. G. .
1.1
: : - A .
A 22.1. .
T P . A A. A
A AA
A. - A : B, C,…
BB , CC
22.1 22.1 . - .
, ( ). ,
.
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:
.
:
:
168
2.2.
1.1. : ,
, ,... 22.2.
22.2
2.3.
: :
1) G
22.3.
G
G
G G G G
G G
A
A
T T T
A
A
B
B
AB
B
A
C
C
22.1
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169
2)
G. .
3) G. .
: - ,
. - ,
. 2.
2.1. .
: : , ,...
, 1 2( )m m
22.4. :
.
1 2( )m m . ( 1 2F F mg ),
A AG
GF
FAA
22.3
1m 2m
22.4
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180
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181
1. ?
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182
VII: 24:
1. (Heat)
. . 1798
(Count Rumford)
, .
. . 1840-1849 (Jame Joule, 1818-1889) .
, 1 24.2. ,
;
. , 2 . 4,186 J ,
4,186 J 1 Cal. , : .
. , : .
24.1
24.2
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183
2.
. , ...
. , , , ...
.
, .
.
: , , ...
.
. 3. (Temperature)
. , .
. (
). . .
:
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184
3 (24. )
21kE kT
kE . k -231,38 10 J/K T ( ).
:
(Degree Celsius), (Degree Kelvin)
(Degree Fahrenheit) C , K F .
.
. :
C F 32 273
100 180 100
t t T
C+273T t 9
F C +325
t t
5C ( F 32)
9t t
T (K) Ct ( C ) Ft ( F )
: 20 C (K) C+273T t 20 273 293 KT
24.2
100 180 100
373K 212°F100°C
0°C
FC
273K 32°F
K
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185
1. ? 2. ?
3 . 3. ? . 4. C K: 27 C ; 155 C ; 115 C ; 0 C 78,5 C . 5. K C : 450K; 89K; 175K 4,2K. 6. C
F , K; F C , K K F , C .
/ ( C ) ( F ) (K)
1 0 2 212 3 0 4 78 5 12
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.
.
186
25.
1. (Interior Energy) m
v . ,
2
2kmvE .
() . ,
PE mgh .
( k PE E E ) . ,
. . ,
. . ,
(V) (T) . U , U
(V) (T) : ( , )U f T V
, (U) ( )U .
2. ,
, . ,
. .
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187
, . ,
.
. , : .
3.
.
.
(Quantity of Heat).
.
1 1
(Specific Heat Capacity). C , Q
m T . C, Q, m T :
2 1( )Q Cm T Cm T T
SI, C
( J/kgK ), Q (J),
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188
(kg), T (K), T
. . , T .
3( 10 J/kgK)
3( 10 J/kgK)
( )
14,21 4,18 2,50 2,34 2,20 2,13 2,08 0,89
,
,
0,8 0,79 0,72 0,45 0,385 0,23 0,14 0,13
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189
1. ? 2. ? . 3. ?
? 4. ? 5. ? 6. 0,79J/kgK
? 7. 100g
20�C 40�C. 8. 2kg 17,6 kJ,
10�C. ? 9. ) 0,2kg 20 C .
30 C . ) 0,2kg
10 C . ?. 10. 2kg 4kg
. 20 C 80 C .
11. , 0,530kg 50W.
100s 17,64 C 20,77 C . ?
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190
26.1
26: 1.
, …
. ,
; , 26.1.
, ,
. ,
, . :
.
: 1,2 kg 500�C 20kg 20�C.
. 0,45 kJ/kgK , 4,18 kJ/kgK
.
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191
: : : Q Cm T
m 1,2 kg m 20 kg Q m C T
C 0,45 kJ/kgK Q 20 x 4,18 x (t-20) C 4,18 kJ/kgK
1t 500 C Q m C T
1t 20 C Q 1,2 0,45 (500-t) : 1t 1t ?
. ,
. Q Q
20 4,18 (t - 20) = 1,2 x 0,45 (500 - t) 83,6t – 1672 = 270 - 0,54t 83,6t + 0,54t = 270 + 1672
84,14t = 1942
194223,08 C
84,14t
: 23,08 C . 2.
2.1
26.2. .
. .
26.2
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193
.
: , ,
, .
, .
1. ? 2. ? 3. ? 4. . 5. 0,105 kg,
142�C 20�C. ,
42�C. ( )
6. , 0,3 kg 500g , 180�C 20�C.
? 7. 100g 50g
. . 60�C
?
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194
27:
1. ,
; , .
. :
.
2. .
2.1. ( , , ),
, 27.1.
.
. . :
, ; , . ,
.
27.1
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195
2.2. 0 C 0 ( )m
Ct ( )t m . - Ct ( 0 C Ct ),
. ot (27.1)
- t ( ),
.
2 1
t o
t t
t (27.2)
- Ct ( ) .
0
0 2 1( )t
t t
0 t (27.3)
00
t t (27.4)
0 t
( ).
: 0
=t (27.5)
1 C . (27. 5) 1 Ct ; 0 1m :
1
1 C (27.6)
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196
( -11K
K).
(27.4) : 0 (1 ) t t (27. 7)
t
0 27.2.
.
5 110 K 6 110 K .
( : Fe
63,2% ; Ni 36,1%; Cu 0,09% Mn 0,30%)
624 10 618 10 617 10 612 10
69 10 69 10 69 10
75 10
3.
. .
0
(m)
( C)to 27.2
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197
0V o0 C
. , :
0 (1 )tV V t 0
VV t
(27. 8)
. 1 C
0
VV
(27.9)
1 C .
( -1K ) . .
4.
. , , 0 o0 C .
o0 C 30V (27.10)
Ct :
0 (1 )t (27.11) V :
3 3 3
0 (1 ) V t (27.12)
0 (1 )tV V t :
3 3
0 0(1 ) (1 )V t t (27.13) 0V 3
0 (27.13)
3 3 30 0(1 ) (1 )t t (27.14)
0V
O T
V
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( 1/ )
:
198
3(1 ) (1 )t t (27.15)
2 2 3 31 3 3 1t t t t
3 3 2 23 3t t t t
3 2 23 3t t (27.16)
, , 2 3 . , 0 . , (27.16) :
3 (27.17)
: 3 .
5. 5.1
. .
, 27.3
( Ct ) .
0 C , ( ).
0 C - Ct : 0 C 0V Ct tV . tV
0 (1 )tV V t (27.18) :
- (27.18) 0 C - 4 C . -
1 C .
27.3 ສ.ວ
.ສ
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199
( 1/ )
5.2.
: 4 C 4 C 4 C .
,
.
6. . : , ,
,
, .
: - ( ),
.
5 C- 8 C
, 20 C
51,66 1052 10
41,1 1042 10
31 10
51,8 10
2 0 2 4 6 8 10
1000
998,8
999,6
999,4
999,2
28.4
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200
- , .
( 28.5).
-
( 28.6). - 2 ( )
( 28.7). (
).
( ).
().
: , , ...
, . , . ,
, , .
7. ,
. ,
28.6
A
Cu
Cu
A
28.7
28.5
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201
( ).
. , ,
, ( ).
1. .
2. . 3. . 4.
L
? . ,
? ? 5. 10 m
. 50 C
? : 6 -112 10 K . 6. 1672 kJ
0,60m 0, 20m 0,05m . ? : 3 37,8 10 kg/m ; 6 112 10 K , 460 J/kgK .
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202
28:
1.
, :
(Melting), (Vaporization), (Condensation),
(Freezing) (Sublimation).
:
.
. : ; ,
28.1
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203
(0 C ); , ; (100 C ).
.
, ; ,
, (100 C ); , 0 C
, (0 C ). .
,
. :
- , . -
, .
0
100
80
60
40
20
0
-20
C
A
B C
D E
28.2
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204
2. (Heat of fusion) ,
( BC ) ( DE ); , .
. , : , , ,
. :
.
3. (Specific heat of fusion)
.
q m kg, . q, m :
q q mm
(28.1)
( ) (J/kg).
1: 2 kg 0 C 0 C . ( 334kJ/kg )
: : m = 2kg : q m
334kJ/kg 3334 10 2q 56,68 10 J
: ?q 56,68 10 J
: , ,
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205
: , ,
K C 310 J/kg K C 310 J/kg
(Hg) (S)
(Sn) (Pb)
(Pt) (W)
3,5 13,7 63,1 54,2 159 234 273 392 505 600,3 931 1233,81336 1356 1473 1803 2047 3643
-269,5 -259,3 -209,9 -218,8 -114 -39 0 119 232 327,3 658 960,8 1063 1083 1200 1530 1774 3370
5,23 58,6 25,5 13,8 104,2 11,8 334 38,1 58,6 24,5 386,8 88,3 64,5 134 276,3 113
4,1 20,1 77,2 90,1 351 630 373 717,6 2023 2466 2933 1460
-268,9-252,9-195,8-182,978 357 100 444,6 1750 2193 2660 1187
20,9 452 201 213 854 272 2256 326 871 2336 1578 5096
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206
2: 0,5 kg 0 C 100 C ?
: : 0,5 kgm 0 C 100 C
1 0 Ct 2 1( )Q Cm t t
2 100 Ct 100 C32256 10 J/kg q m
: ?Q 2 1( )Q Q q Cm t t m
3 34,18 10 0,5 100 2256 10 0,5Q 3 3209 10 1128 10
31337 10 JQ
: 31337 10 J
4.
,
:
- :
. , .
- : , , . ,
.
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207
, , . :
, ; ,
; , , ,
, . ,
, . ,
. , .
, ; .
, , .
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208
1. , . 2. ? 3. . 4. ,
, .
5. 1 kg 5 C 100 C .
6. 100 g 100 C
5 C . 7. 5 kg
10 C 100 C . 8. 100 kg 0 C
100 C . : 70% 9.000 kcal /kg,
(1 kcal = 4,18 kJ).
ສ.ວ.ສ
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