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