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Σημειώσεις του Νίκου Αναστασάκη,καθηγητή Φυσικής στο ΓΕΛ Βάμου Χανίων
Citation preview
2008-2010
:
1-4
, ,
:
5-20
.
5 11
:
21-43
&
22 23 25 33 37
43-47
44 45
48-56
,
57-67
2
57 61
:
61-89
( )
69 70 73 75 78 80 81
1
1. ;
.
.. xA = +3m, x = -2m -
.
2. ;
,
.
x & x .
.. , - :
x = x - x = (3 (-2))m = 5m. , : xA = xA - xA = (-2 3)m = -5m. ( ).
3. ;
() .
:
: m/s
-3 -2 -1 0 1 2 3 (m)
2
km/h.
, t = 2s, :
:
:
, , , ,
(.., , , , ).
. ,
. , -
,
4. ;
s, -
. .
100m 50 . s = 150m.
5. .
, , , ...
;
-
(s) (t) , :
3
s1 = 200m t1 = 100s. t2 = 50s 400m t3 = 150s. :
S = (200+400)m = 600m
t = (100+50+150)s = 300s.
:
:
: :
.
. -
.
4
1. ,
-
x1 =
4m, x2 = 2m,
t1 = 4s. x3 = 6m.
t2 = 5s. , t3 = 10s x4 = -2m.
. .
. ;
. .
. ;
2. 10km 15min.
. ;
. t =10min
;
. ,
. ;
-5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 (m)
5
1. .
( ). ,
.
x t .
(1)
x = x x, :
(2)
x () t
.
:
(3)
( ),
.
. = -10m/s. x = 50m ( , . ). t =
40s:
x = t = -400m s = 400m.
x = x + t = -350m.
x x - .
:
(1) (2) .
.
,
.
6
2.
- (x t) -
( x)
( t).
t, x,
.
( t = 0)
:
-
, .
-
, x.
(0) , -
, .
( t = 0)
, ,
:
,
.
, -
.
-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5
-0.5
0.5
1
1.5
2
2.5
3
3.5
t (s)
v (m/s)
1 2 3 4 5 6 7 8 9
2
4
6
8
10
12
14
16
18
20
22
24
26
28
t (s)
x (m)
x
x
t
t
7
5m/s,
. t = 0,
x = -10m, .,
:
x = -10 + 5t
, t1 = 2s,
t2 = 4s .
- .
x t ( ,
):
t = (3-1)s = 2s, :
= x = 10m
,
S = 10m.
2s 4s
0 10m
-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
-14
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
14
16
18
t (s)
x (m)
-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5-0.5
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
t (s)
v (m/s)
8
1: . /.
9
1. x = 50m,
= 15m/s.
. t = 30s,
.
. ;
. =
-5m/s;
2. (x = 0)
to = 0 = 2m/s.
. t = 5s;
. 20m ,
;
. , , ;
3. 20
. t1 = 10s
1 = -2m/s. t2 = 5s 2 = 6m/s.
. 10s ;
. ;
. , (. .);
. ;
4. . 4m/s
x = -10m.
. t1 = 2s, t2 = 2,5s t3 = 5s.
. .
. .
10
. , .
5. , :
(t = 0) x = 0.
t1 = 5s x1 = 10m.
t2 = 7s. x3 =
4m, t3 = 10s
. (x-t) .
. tA(0 5s), t(5s 7s),
t(7s 10s);
. .
. ;
6.
-
.
.
,
.
i)
; (
).
ii)
t = 0;
iii) ;
, :
. ( t )
.
. t = 4s.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
2
4
6
8
10
12
14
16
18
20
22
24
26
28
t (s)
x (m)
11
1. ( ;)
, .
. ,
( ) .
.. , - = 2m/s -
= -
1m/s2.
-
. -
,
= -
4m/s =
-4m/s2 . -
( )
m/s2 ( S.I.)
2. - .
,
. (
), -
.
, -
, . -
.
(+)
12
, :
(4)
,
t.
(4).
, , (4) :
, -
, (-)
, .
, , -
:
(5)
:
(6)
, (5 & 6) x, -
.
,
,
, :
(7)
13
(-) .
.
, -
, :
; !
, , :
;
(7) ,
!
, :
.
1. 30m/s.
4m/s2. t = 2s, :
= | | ||t = (30-42)m/s =
22m/s
:
s =||t ||t2 =
= (302- 44)m = 52m.
:
:
14
2. x =
2m, = 15m/s = -3m/s2.
-
,
:
= + t
= [15 +(-3)2]m/s
= 9m/s
:
x = x + t + t2 = [2+152 + (-3)4]m = 26m.
:
x = t + t2 = [152 + (-3)4]m = 24m.
, , -
:
s = | | t - ||t2 = [152 - 34]m = 24m
3. , x = 0
to = 0 = - 4m/s = 1m/s2.
t1 =
2s, -
:
1 = + t
1 = (-4 + 12)m/s
1 = -2m/s.
() 2m/s.
t2 = 4s, :
2 = (-4+14)m/s = 0, .
t3 = 6s:
3 = (-4+16)m/s = 2m/s. ,
2m/s. ( ).
-8 -6 0
15
:
x = x + t + t2.
:
x1 = (-42 + 14)m = -6m
x2 = (-44+ 116)m = -8m
x3 = (-46+ 136)m = -6m.
:
x = x3 x = (- 6 0)m = -6 m.
, :
x = t + t2
= (-46 + 162)m = -6m.
3. .
. ,
, .
, . , -
.
.. = 2m/s2 = 0, - -
. ( 2s
4m/s).
, - ,
( )
( -
). ( 2).
2: . /
(m/s)
t(s) (m/s) t(s)
0 0 0 0 4 2 4 0 = 4 2-0 = 2 8 4 8 4 = 4 4-2 = 2 12 6 12 8 = 4 6-4 = 2 16 8 16 12 = 4 8-6 = 2 20 10 20 16 = 4 10-8 = 2 24 12 24 20 = 4 12-10 = 2
16
-
,
.
, -
.
:
-
,
. , , .
1 2 3 4 5
-4
-3
-2
-1
1
2
3
4
t (s)
(m/s^2)>0
17
1 2 3 4 5 6 7
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
t (s)
x (m)
: .
;
, .
().
, , -
(
)
18
1. = 2m/s2.
t = 0 x = 4m = 3m/s:
. ; ( ).
. t = 2s;
. ;
. ;
2. = -2m/s2.
t = 0 x = 0, = 4m/s:
. ; ( ).
. t = 1s;
. t;
. ;
3. = 2m/s2.
t = 0 = -5m/s:
. ; ( ).
. t = 1s;
. ;
. ;
4. , 1 = 4m/s.
2m/s2, t = 2s.
,
.
.
, .
19
. ;
. 2s;
5. , , 1 = 1m/s2,
t = 1s. t2 = 2s 2
= 0,5m/s2.
. ;
. (t2);
. ;
6. , .
t = 0 x = 20m,
= 8m/s = 6m/s2 . T
x = 60m = -4m/s = -2m/s2.
. ;
. , .
. t = 1s
;
. t = 2s;
7. 6m/s
3m/s2, .
. ;
. ;
. .
. ;
8. x = 0,
= 1m/s2.
20
. ,
.
. ,
, .
. ( )
t1 = 2s t2 = 4s.
. , .
9.
. = +40m/s
4m/s2.
. , .
.
.
. ,
.
. , .
10.
,
.
x = 0.
. ; .
. .
.
4 ;
. ,
.
. .
. .
1 2 3 4 5 6 7 8 9
2
4
6
8
10
12
14
16
18
20
22
24
26
28
t (s)
v (m/s)
21
1.
.
.
. .
. , -
.
2. , ,
Force .
: 1N (1N = 1kgm/s2)
. -
, .
, -
.
3. ;
, -
: , -
(...), ...
. , (-) -
.
, - , -
, ...
22
( ) (..
).
4. ;
( ).
, (.., ).
F1 =2N F2 = 3N - F = F1+F2 = 5N.
, - F = F1 F2 = -1N.
5.
o
.
(...) :
().
.., m = 60kg. ... w= mg ., - 600 .
160kg. 1600. - 400, .... ! -
.
m -
(kg). , -
.
g ,
.
g=10m/s2.
23
o
( ) ,
x ( ).
k
( ).
( -).
w =5N , F 5.
. - , F
, -
.
x -
.
,
.
24
.
1. . ; .
2. m1=5kg m2=10kg. -:
. 5kg 10kg . 5 10 . 50 100.
;
3. 50kg; g = 10 m/s2.
4. k =200N/m x1 = 5cm.
. .
. x2 = 5cm, ;
5.
-
.
.
x =
2cm;
. -
.
6. k = 100N/m. x.
1 2 3 4 5 6 7
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
x (cm)
F (N)
25
1. :
: . ,
-, -
(... 3 ).
trailer - (). trailer
().
.
( .., ).
w = 0,5N . ,
w = 0,5N . ,
!!!
:
( , ).
, , .
2. ( 1 ):
()
. ,
m, -
:
, . , -
.
, , .
!
: ( ,
), ,
.
w
w
26
, , ( -
).
- ( )
.
. ,
(.. ).
:
, ,
.
3. ; ( )
, . ,
( ),
. .
.
,
. -
.
:
()
, m .
m1 = 2kg, = 2m/s2, F = 4N.
(2F=8) -
, 2 = 4m/s2.
(F =4N) , 2m = 4kg,
, /2 = 1m/s2.
m
2m
2m2m
27
:
.
4.
;
, :
= . & x = t
, -
:
= || ||t & x =||t ||t2
, -
, . -
,
, .
-
, (
).
, -
(., ).
:
1. m = 3kg
, F1 = 8
F2 = 7N .
o :
F = F1+F2 = 15N
o :
o t = 2sec :
= t = 5m/s22s =10m/s
o :
m
28
2. -
= 2m/s,
-
F =2N
. m =0,5kg.
o :
o
, .
o (=0) :
o :
.
o (F-t)
(-t) :
3. -
.
o
t = 6s, -
.
o -
1 -
. , = 5
m
1 2 3 4 5 6
-2
-1
1
t (s)
F (N)
0.1 0.2 0.3 0.4 0.5 0.6
1
2
t (s)
v (m/s)
2 4 6 8
2
4
6
8
10
12
14
16
18
t (s)
x (m)
29
-
, :
F = 0 F-T = 0 F = T = 5N
o t = 6s, .
. ,
, .
30
-
1.
. m =
100kg,
. ;
.
.
; ( ).
. .
g = 10m/s2.
2. .
F = 20N:
.
:
i. .
ii. .
iii. .
. ;
.
3. .
. , .
. ,
.
. ,
.
31
. ,
.
4. ,
=20m/s.
(, ) F = 400:
. (
);
. 5min;
. .
5. ,
, 10.
5, 15 .
= 4m/s,
. .
. t = 0,2min;
. ;
6.
.
m = 6kg, :
.
.
.
.
t =
5s.
. t = 2,4s.
1 2 3 4
2
4
6
8
10
12
14
16
t (s)
v (m/s)
32
7.
F = 20N. , m = 10kg,
. ; .
. .
. = 6m/s;
.
.
8. m = 500kg
, .
F1 = 400N F2 = 650N.
t = 0 = 10m/s
. t = 0 xo = 0.
. ( )
.
. ,
t = 4s;
. .
9.
.
m1 = 4kg m2 = 8kg
12 . t = 0
, d = 2,25m. :
. ;
. ;
. ;
. ;
m1 m2
d
&
33
1. .
- , -
-
.
,
2. , -
:
-
F -
:
(1)
:
(2)
:
= 90 ( ):
(3)
(4)
= 0 ( ):
F = F1 + F2 (5)
= 180 ( ):
F = F1 - F2 (6)
&
34
F1 = 30N F2 = 40N, :
= 90 :
, 36,9.
= 0o : F = 30 +40 = 70
= 180o : F = 30 - 40 = -10 , . .
( )
(3) (6) (1) & (2)
. .., 90 = 0, 90 = 1.
(3)
, .
&
35
-
1.
F1 = F2 = 5
= 120o.
. .
. ;
. ,
.
2. F1 = 43 N F2 = 4
m = 2kg .
. ,
90o;
. ( )
;
. ;
. 30, ,
;
m
&
36
1. .
, , -
. , ( )
:
,
.
, .
()
( )
.
-.
, -
.
2. ( ).
o :
-
,
() -
.
.
y
x x
x x
37
o :
,
( )
( ) :
Fx = F
Fy = F
F = 50N = 30o (30=1/2 30 = 3/2).
.
3. : !
,
.
,
, -
( -
)
.
, -
-
.
-
.
,
.
(.,
)
.
38
( )
:
= FA (8)
:
= o FA (9)
, (8 & 9) (
), -
.
:
, . -
(, ) -
.
. -
. ,
, .
-
.
. -
.
.
1. w =10N -
,
.
= 0,3.
o :
Fy = 0 FA = w = 10N.
( , -
!)
o :
39
= FA = 3N.
o .
.
2. -
F = 15N
. m = 5kg
= 0,25.
=4m/s.
o
yy ( -
).
Fy = 0 FA = mg = 50N
o :
= FA = 12,5 N
o :
Fx = F T = 2,5 N
o xx, :
o 6 sec, :
= + t = 7m/s
3. , = 45 -
. F = 202 N, m = 6kg
( )
= 0,3. -
.
o -
:
Fx = F 45 = 20
Fy = F 45 = 20
o
. -
.
40
Fy = 0 Fy +FA - mg = 0 FA = mg - Fy = 40N
:
T = T = FA = 12N
, Fx > T, .
o :
2 + 2 = 1
0 0 rad 0 1 0
30o /6 rad 1/2 3/2 3/3
45o /4 rad 2/2 2/2 1
60o /3 rad 3/2 1/2 3
90o /2 rad 1 0 -
120o 2/3 rad 3/2 -1/2 -3
180 rad 0 -1 0
41
, g = 10m/s2
1. F = 30N
.
=60o .
m = 5kg:
. .
. ;
. .
. , -
;
2.
1m/s.
m =250g.
= 0,2:
.
.
. ;
. ; , ;
. .
;
. .
3. m1 =2kg m2 = 4kg ,
.
= 0,4.
. ;
. ;
42
. .
. .,
.
4. , ,
. t =0
F = 16N. m1 = 4kg m2
= 2kg
= 0,3.
. ;
. .
. t = 3s;
. , .
5. F
= 102 N = 45
.
= 0,25
m = 3kg.
. ;
. .
. ; .
6.
. H
2003
m = 30kg.
30. = 1m/s2.
. ;
. ;
43
. .
. ;
7. = 30,
m.
.
.
.
.
;
. ,
.
. ,
.
44
1.
, , . -
, . .
:
2. ( ):
t, :
= gt
y :
3. :
:
. ,
, , -
.
1 2
5
10
15
20
25
t (s)
v (m/s)
1 2 3
5
10
15
20
25
30
35
40
45
t (s)
y (m)
45
4. ;
.
( ).
(. ), -
. , , ( ),
. .
5. :
:
:
, y
( ). ,
,
.
6. ;
, -
:
-
( )
y
y
46
,
7. :
, ,
.
, ,
( ).
y = gt
y :
8. ...
(= ) :
x
y
47
1. -
= 20m/s.
t = 1s, :
= gt = 10m/s
:
y = t gt2 = 15m
2. , t = 2s, :
= gt = 0
:
y = t gt2 = 20m
, -
. , 20m, .
3. , .., t = 4s:
= gt = -20m/s
y = t gt2 = 0.
-
, . , -
!
, -
48
1.
-
-
2.
-
. ,
s
().
.., - 2m/s,
2m.
. -
.
, -
, , .
,
, f .
t , :
:
, = 1,
, t = T
sec, Hz (Herz = 1/sec)
s
R
49
t = 4sec, - = 28 . . -
3. .
. :
-
.
,
.
. -
:
-
.
:
= R
R .
-
,
-
. , -
, ( -
) -
.
= /2 rad, t = 3s . : 1 = 2 = = /t = /6 r/s.
, R1 = 3m R2 = 2m, :
R
s
s1
s2
50
1 = R1 = /2 m/s & 2 = R2 = /3 m/s
:
s = R
, = R.
(rad). -
180 (.., 2 rad 360o, /2 rad 90o ...)
, = 3,14.
.., R=2m :
s = 2R = 23,142=12,56m.
4. . ;
, -
.
H ,
-
, .
:
5. ;
( )
.
.
, F ( = Fr)
:
F = Fr = m
R
51
m =2kg, R = 4m - = 2m/s. -
:
= 2/R = 4/4 m/s2 = 1m/s2.
() : F = m = 2.
: FN w = m . ...
:
-
, , -
6. , .
:
o , s = 2R,
t = . :
o =2 (360) t = T. :
o :
:
, . -
, , -
, .
52
.
1. , = 10m/s.
R = 50m m = 1200kg.
(. ) :
= 2R/T T = 2R/ = 6,2850/10 s = 31,4s
:
f =1/T = 1/31,4 z.
:
= 2/ = 23,14/31,4 r/s = 0,2 r/s.
( = R = /R = 10/50 r/s = 0,2 r/s )
:
= 2/R = 2m/s2
:
F = m = 2400
2. -
-
. -
R = 2m, m
=100g (= 0,1kg) N = 4
t = 2s.
H :
f = N/t = 2Hz.
:
= 1/f = 0,5s
R
53
:
= 2f = 4 r/s
H :
= R = 8 m/s
:
= 2R = 162 m/s2
:
F = m = 1,62 ewton.
:
F = Fr = FN mg FN = mg + F = 1+1,62 17 ewtons
= 30 , -
wr :
F = Fr = FN wr = FN mg30
3. -
R = 3m.
= 0,2 r/s , = 0,6
r/s.
:
A = R = 0,6 m/s
B :
B = B R = 1,8 m/s
:
To A = t.
To B B = Bt.
(
2 rad ), .
:
B
A
54
A
sA = A t = 3 m.
:
55
1.
. ;
. .
.
.
. .
2.
(1) (2)
.
;
. .
. .
3. :
.
. (0)
.
. .
4. 6 sec 3
. R = 0,4m.
. ;
. .
. ;
. t = 1,5s.
(2)
(1)
56
5. 28
().
385000 km , :
.
. .
. m = 7,51022kg.
;
( =3,14. )
6. , -
. A = 5m/s
B = 6m/s 40m, .
. .
. .
. .
; ;
7. (
)
.
,
= 2m/s. m = 200g
R = 20cm.
.
.
. ;
. .
. ,
;
g = 10m/s2 .
R
A
57
1. ( ) ;
, .
.
-
2. , ,
;
. ,
m :
,
.
: kgm/s.
. m1 =2kg m2 =4kg .
1 = 2 =20m/s.
p1 = m11 = 40kgm/s p2 = m22
= 80kgm/s. ,
3. ;
, m
, .
, .
.
m
58
4. ;
, , .
, . :
(2 -
).
.
1. F = 20N t = 5s. -
100 kg.m/s:
2. =20m/s,
m=250kg ( ).
F = - 400N ( ),
t :
m2 = 1500kg,
:
3. m = 76kg, -
,
= 9m/s.
t
= 2s,
:
, -
t2 =0,5s ( -
!)
:
!
59
5. 2 & :
-
, :
, ,
.
1. m = 2kg,
1 = 5m/s 2 = 10m/s. t
= 5s.
2 .., :
...:
.
2. , F = 30.
2 ,
:
.
(
30kg.m/s)
60
6.
.
,
.
.
,
.
m1 = 0,2kg, m2=0,4kg
1 = 10m/s 2 = 5m/s -
. :
, :
7. ;
(
), .
:
bowling () ,
. 1 = 2m/s 2 =1m/s -
m1 = m2 = 5kg. :
(+)
61
p=p1 +p2 =m1 + m2 = 15kg.m/s.
( -
),
.
:
p = p2 = 5kg.m/s.
8.
( ), -
;
.
m1 m2
1 2 -
.
, F12 F21 (-
). , 2 :
, :
F12 = - F21
:
F12 F21 :
: , -
(.. -
)
62
:
,
. (.,
).
:
1. m = 0,5kg 1 = 1m/s
, .
.
2 = 1m/s, ( ):
m1 = m2 :
1 = 2 = 1m/s
:
p1 =p1 p1 = 0 m11 = -0,5kgm/s
p2 =p2 p2 = m22 - 0 = 0,5kgm/s
t = 0,5s,
:
2. 1 =200m/s
. m1 = 0,1kg -
m2 = 1,9kg. :
p() = p1 +p2 = m11 + 0 = 20kg.m/s
,
(-
), m = m1+m2 =2kg
= 10m/s.
,
,
:
p() = m = 20kg.m/s.
63
3. , . mo = 5kg
m = 0,05kg.
=400m/s.
, :
=
( ).
:
9. :
(
), .
,
.
:
.
(.. ) ( -
!)
64
-
, g = 10m/s2
1. m,
.
.
:
. p = 0 . p =2m
. p =-2m . p =m
2.
. ,
;
.
.
. .
.
3. , m1 = 225kg
= 1m/s.
t = 1,5s.
. ;
. () ;
. o
, t2 = 0,5s
. (t = 1,5s)
m2 = 300kg;
65
4. ,
F1 = 50N F2 =30N
. m = 4kg.
.
;
. t=2s;
. t = 2s;
. ;
5. ,
m1 = 2kg m2 = 3kg
1 = 6m/s 2 = 4m/s
. :
. 24kgm/s . 0
. 24 N . 2m/s
6. . ;
. m1 m2 m2 m1.
. m2 m1 m1 m2.
. .
. .
7. m1 = 200g 1 =
3m/s m2 = 100g
, 2 = 2m/s. , m2
2 = 4m/s.
. ;
. ;
. m1 .
m
m1 m2
66
. ;
8.
= 0,5m/s ,
.
m = 50g
m = 950g.
. ;
. ;
. ;
. 0,4s, ;
9. m = 900m/s,
(m1 = m2 = m/2). m1
1 =1200m/s,
.
. m2;
. m =2000kg,
.
. t = 0,3s.
;
. , m1
, m2;
10. m = 1,5kg, h=0,8m.
( ).
, :
.
.
. .
67
. t = 0,5s ,
.
. .
11. ,
.
m = 201kg.
= 2m/s.
m = 1kg :
. ,
.
. .
. ;
. h = 50m,
, ;
12. 1 =200m/s.
m2 = 1950g
,
. 50g
= 0,25.
. ;
. ;
. .
. ;
m
68
-
1. :
O -
. ,
. -
, -
.
. , .
.
.
, -
,
.
2. :
O , .
. ,
.
. -
,
.
-
. ,
.
, -
: . , ,
:
,
...
69
Joule (S.I.).
3. :
. m,
, :
:
-
, . ,
bowling , -
, .
:
1. m = 2kg = 2m/s .
:
= m2 = 4J
( =4m/s)
:
= m(2)2 = 16J
:
= (2m)2 = 8J.
,
2.
. m = 600g =
3m/s. :
= 1 + 2 = m2 + m2 = 5,4J.
. ,
. !
70
4. :
.
,
, ...
1. .
( ).
.
, ,
! ,
, .
2. ,
(
).
!
3. ,
. .
5. ;
. -
,
. ,
-
,
.
; -
.
,
( !),
(, -
).
,
71
.
:
,
. , (,
). ,
(.. -
), .
, ,
. -
, , -
. , -
!
.
,
,
( );
6. :
m , -
:
U = mgh
U :
h: , (-
. ).
, h1 = 80cm .
100g, :
U = mgh1 = 0,1100,8 J = 0,8J.
A , h2 =3m -
. , :
U = mg(h1+h2) = 0,1103,8 = 3,8J.
72
.
(
)! , . -
7. :
-
, l.
( -
-
). , -
.
l ,
-
-
:
( k ).
k = 40N/m. l = 5cm,
:
U = k l2 = 400,0025 J = 0,05J.
, l =10cm,
, !
U = k l2 = 400,12 J = 0,2J
l
l
73
8. ;
.
.
, .
.
, -
.
, : , , -
, . -
, , .
9.
. -
,
, , W (work):
W = Fx x
Fx
.
-
, . .., ,
-
.
, , -
.
S.I., Joule.
, ,
. , , -
.
.., (),
, ().
74
-
.
,
-
-
.
,
, .
1.
F=0,5N. x = 0,6m.
:
W = Fx = 0,50,6 J = 0,3J.
2. F = 100
60o, .
s = 10m. :
W = Fx s = F60s = 100 10 J = 500J.
, :
W = F s = Fs = 10010 J = 1000J
3.
, -
.
k = 20N/m x1 =
0,1m. :
|F| = k|x| . .
,
F x:
WF = = kx1x1 = kx12 = 0,1J
F
F2
F1 W
x1 x2 x
|F|
F
W
x1 x
x
75
10. H .
m F (). -
x.
;.
, :
(1)
:
(2)
, (3)
T , F, x (2) & (3):
:
(t)
( (1)) ,
!
. , -
.
,
:
76
.
:
, ,
.
, ,
. , , -
, -
( ).
, -
.
.
3. , .
F = 10N, T = 2N.
s =2m, -
:
WF = Fs = 20J ( F )
WT = -Ts = -4J ( )
, . :
K = WF = (20 4)J = 16J.
-
( ,
).
4. ,
, =45. -
F = 102 N
m = 1kg. O
. -
s = 0,8m:
.... (1) (2) .
m
(1) x (2)
77
(2) (1) = WF(1->2)
m2 - 0 = Fs45
:
,
, ,
.
5. 5N, m = 1,5
kg, 1 = 2m/s.
x = 4m,
-
.
, -
( ).
.
( ).
.
2 -
:
... ( (1) (2)):
2:
x
78
11. T
.
w = 5N, h1 = 80cm .
, h2 = 20cm.
y = h1 h2:
W = wy = 3J.
U1 = wh1 = 4J
U2 = wh2 = 1J.
, ( ,
, -
)
:
, -
( )
W = - U
W = U - U
, : -
!
79
.
1. m = 100g (=0,1kg) h1 = 8m.
.
:
U(1) = mgh1 = 0,1108 J = 8J.
h2 = 3m:
U(2) = mgh2 = 0,1103 J = 3J.
:
W = U(1) - U(2) = 5J
, , W =w s.
2. ,
(2):
... ( (1) (2)):
2 1 = W (12)
2 = 5J = U(1) U(2).
. ,
.
12.
.
. -
.
,
.
, .
s h1
h2
80
,
.
WF = - U
WF = U -U
., ,
. , .
:
,
.
.
k = 40N/m l1 = 4cm. -
(l2=0), .
:
WF = - U
WF = k l12 - k l22
WF = k l12 = 0,032J
:
= WF = 0,032J
13. .
, ,
..., .
, -
:
+ U = E
81
, (.. ),
.
.
, -
,
, (, -
, ) -
, ,
-
, -
.
.
14. ; -
...
-
.
100km/h. 10s, 12s, 15s
... .
( ) (P)
:
:
82
W = Fxx
, , :
Watt
(=Joule/s).
83
, g =10m/s2.
1. -
m,
.
;
.
.
. .
. .
. .
2. :
.
. .
. . ,
. , .
3. l. -
, :
. . . . .
4. - ;
. , -
.
. , .
. -
.
m m
84
. , -
.
5. m = 2kg, = 5m/s.
. ;
. ;
. .
;
. ;
6. m = 200g 10 m -
. . h = 5m
, = 10m/s.
. ;
. , 5m
.
. .
. ( );
;
.
7. 180m. m = 80kg,
:
. .
. , 20m.
. ,
.
. () , ()
;
, t = 0,5s.
85
8.
, m = 100g.
k = 25N/m.
l .
. ,
.
. ;
. -
;
. , -
;
*. ;
9. -
F = 20N.
m = 4kg -
= 0,2.
.
.
. s = 3m, -
.
. F 60 ,
;
10.
= 3m/s. m = 200g
= 0,3.
. ;
. ;
.
. i) ;
ii) ;
m
l
k
s
86
11.
m
= 0,6kg
.
h = 40cm.
. ;
. ;
. k = 120N/m
. ,
;
. ;
12. h = 20m. N
.
.
. .
. , -
;
13.
,
, .
,
;
.
m
h
k
87
14. -
, -
.
,
-
.
. B A.
. .
. ,
A.
15. -
, 30o.
-
m = 1,2kg.
h1 =
40cm.
. ;
.
(
80cm).
.
;
. ;
, , , i) ii)
. .
16. m1 = 600g m2 = 1200g,
k = 60N/m.
l = 6cm.
.
A B
h
m
h
m1 k m2
88
. ;
. ;
. .
, ;
. .
;
.
17.
, F = 200
.
. O
= 0,5
m = 20kg,
= 30.
s = 4m.
.
. ,
(2 ). , ,
.
. ;
. ,
;
. ,
; ( .... )
31,725
18. m = 1200g 1 =
4m/s. ,
, = 0,3
. d
.
89
.
;
. ...,
.
. ,
; ;
. .
.
;
;
19. ,
h.
.
d
, . ,
d :
. . .
.
20. m = 3,3kg ,
. F = 5+2x (S.I.),
x .
. x1 = 2m
x2 = 6m;
. F
x.
. ,
, 6m.
.
, 6m.
d
h