# ΜΕΘΟΔΟΛΟΓΙΑ ΑΣΚΗΣΕΩΝ 1ου ΚΕΦΑΛΑΙΟΥ

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vmarousis.blogspot.com 1

1o

1. ( . ) . 2. ,

. 1 : 0,2 sec ; :

/2 ( ) , .

2: . 40 , ; : 2 , 20

.

3: ( ) 3 ( U ), 80 . ; . ; : H = 3U ( = 2U = U ) 4

,

3. ,

. : t1 x1=+0,1m t2 x2 = 0,2m x = 0,3m S= 0,5m.

4. , , . : x = t , , = max t, , = max t , F = Fmaxt, .

-x +x

0 +0,1 +0,2 -0,1 -0,2

-x

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: : x = +2 + >0, x = 1

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(1) (2)

=0 (1)

=0 (2)

=1 (1)

=1 (2)

=2 (1)

:

sec = max (10t+ ) = max(10 + ) = max( ) >0

sec = max (10t+ ) = max(10 + ) = max( )

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9. . :

10. :

) . = - 8(2t + /2). = -max(t+0) : = 2 rad/s , max= 8

2 = 8 = 2m. ) ( 10cm) =10 cm. ) d = 20cm d = 2A = 10cm. ) .. ( ) :

: E) x , (...)

11. .... (...) D= m2 :

x, , , , . (1) :

. ( , .

12. . 1. .., = 3U ;

2. .. ( ) , =3U;

:

x = At x

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13.

.

, :

14. , +x

x , , ,

( ).

.

(1) (2) : 1 = 2 , U1 = U2 ,

F1 = F2 , 1 = 2 , 1 = 2 .

-x= - d/2 +x = + d/2 ..

1

F1 1 F2 2

2

1 2

- +

d

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15.

. . . ( k ) , 1/m.

Hooke : F= k ( ) . F . F = 0 w = F : F = w F F= D x, x . . ( ) .. .

: =

: =

, .... =

( ).

(. 3 )

(. 4)

w

x= k

F = F

w

F F

x

(. 1)

(. 2)

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16. .. D

.

1 : .. F = 0 .

2 : x , (F) , . 3 : F, : F = Dx D .

4 : D

.

: ) (. 2) : F = F = k x ( 1). .. F = D x ( 2) . ( 1) ( 2) D = k B) : (. 3) F = 0 w = F w = k (3) ( . 4) :

F = w F F = w k( F = w k F = k x (4) .. F = D x (2) . (4) (2) D = k

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17.

18. :

4, . , . , . , . ( ), ( ), ( ). = U, , U 0, . ( ) ( ) .

< 0

> 0

-A +A 0

+ -

= -

= 0

= +max

F = +Fmax K = 0

U = Umax

= +

= 0

= -max

F = -Fmax K = 0

U = Umax

= 0

= max = 0

F = 0 K = Kmax U = 0

> 0, F>0 < 0, F< 0

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19. .

a. . b. . c. ,

i) , F = 0. ii) , =0.

iii) , x

0.

d. : e. , x

. f. x = (t+0) , = (t+0), =

2(t+0)

20. ...;

, : F = m, F = m2x

:

m = 3 kg = 0,4m

k = 150 N/m.

.

:

F=w kx0 = mg, x0= mg/k = 0,2m

x,

w

F. Newton

:

F + w = m F+w = m2x F = m

2x w

D = k = m2,

:

F = kx , : F = 150x 30 (S.I.).

x.

x0

x

W

W

F0

F

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21.

.. = 1= 2. D1 = m1

2 D2 = m2 2,

D = (m1+ m2) 2. D = D1+D2

22.

. : A1= 2A2 T1 = 2T2

2 = 21

:

=

:

:

:

23. ( ) ( ..).

m1

m2

A1

A2

t

x

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.. .

: .. :

.. :

2

1

m2

m1

(+)

m1 m2 m1 m2

1 2 1 2 (+)

m1 m2

1 2 (+)

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.. . . H .. :

.. .

m1

.

( ) ( ) ( ) ( V )

.. . .

. . . ( . ) : F= 0 g = k . : F = 0 (+m)g = k(+x) .

2 1

.. & .

(+)

m

x

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24. ( )

m1 ...

m2 ,

, :

) , .

) m1.

) ... : F = -D1x F = - m12 x (1)

, , (1) : F = m1

2 x m1g = m12 x

x = (2) : max = m1(g +

2) . x = + (2) : min = m1(g

2) (3) . () ,

: min 0

(3), m1(g 2) 0 g 2

, , f .

25.

) :

.

) : F

. ) :

) :

N = m1(g 2x) (2)

N

m1

m2

m1g

g x

+

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1. . , .

2. ( ) . .

3. . )

t= 0 (1) . Vmax= E , Q . (2) q= Q i = 0 . q = Q(t) I = I(t) . = Q )

L C

E,r L

(1) (2)

Q

--------

++++++

(2)

----- C

++++ Q

E,r L

(1)

i

i

E,r E,r

L L C C

i i

i i

_ _ _

+ + +

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.

. . . . () : t = 0 ,I = +I, q = 0

I = -I (t+) I = -I = -1 = = rad

:

) t=0 , :

: t=0 . t = 0 . , . LC , ..

.

4. q,i,Q,I, ...

.

(1)

:

5. q UE UB. UE= 3UB (1) Q . .. :

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(2)

(2) q= Q (t) (2) :

: ,

: ,

: : , , .

6.

.

7.

) :

) :

) :

UE + UB = .

(1)

) :

VL = VC

8. : (i) . : i

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, .

, , , . :

(1)

.

(1) t = T t = (N+1)T = 0, 1, 2, :

:

() .

1. F = - b, . +1 +1. :

, .

(-)

(+)

C L i

(-)

(+)

i L C

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.

: 20%. 4 10cm 5 ; : 20% 80% 5= 0,8 4 = 0,8 10 = 8cm.

2. F= -b k . : 0= 40cm = 2sec

-1. = 10cm;

: t=

t =

3. F = -b

1 t1 2 t2 . : t = 0 = 25cm. t1= 20sec 1= 16cm, 2 t2= 30sec ;

:

= = = 25

:

4.

:

5.

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( : F) . :

1. H

.

,

2.

, . . . .

3. . x = (t + ) , = max (t+0) , = - max(t+0) , F= - b = - b (t+) : = =2f , f .

:

: = = 2f , f .

A o1

A o

f o f 1 f 2

A o2

f

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. :

4.

, F= F F= b. . :

F= F , x = 0.

5. =.

> max>Umax .

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1. ..

x1= A1(t) x2= A2(t+) : x = A(t+)

.

2. , , :

1 2 x1 x2 x = x1+x2 1 2 = 1+2 1

2 = 1+2

1 2 1 2

1 2

01 02

3. D D = m2 .

,

A A2

A1

x2

x

x1

t

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,

, .

. . 1 2 . , :

(1)

(2) (3)

(1) (2) (3):

, . = /2 = 90

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4. ..

1 : x1= 1t 2 : x2 = 2t : x = x1+x2 = 1t + 2t = . . . . .

.. , .

1 2 (1)

.

:

:

:

H :

5. O :

6. ,

.

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