Задача Д1 (рис. Д1.8, условие 5)

1. ( . 1.8, 5)

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D

m = 4.5 , V0 = 22 ,

, .

: , – ( .

. 1.8).

Q (Q = 9H ,

! )

' ( )

" = mg,

R,

N1

Q. ( Az

))$

$ * :

m

dVz

= ΣF

m

dVz

= P + R

z

+ N

+ Q .

(1)

dt

kz

dt

z

1z

z

#

P = Psin 30 = mg sin 30 ,

R

= -R = -μ ×V ,

N

= 0;

Q

= -Q;

z

z

1z

z

, # .

+",

Vz = V ,

dV

dV

μ

0.5mg

- Q

m

= mg sin 30

- μ ×V - Q

= -

× V -

μ

.

(2)

dt

dt

m

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! "

n =

0.5mg - Q

=

0.5 × 4.5 × 9.81 - 9

» 26.145

.

(3)

μ

0.5

dV

= -

μ

dt

nV - n

- nC = -

μ

t

n

V - n

= -

μ

t.

(4)

V - n

m

1

m

C1

m

( ,

t = 0 V = V0

= 22 , !

n

V0 - n

=

0

= V

- n = 22 - 26.145 = -4.145 .

C1

1

0

!"! :

k =

μ

=

0.5

» 0.1111c-1;

(5)

4.5

m

(4) (5) # D

)$

n

V - n

= -kt,

V = n + C e-kt

(6)

C1

1

*

t = t1 = 3c,

D : V

= n + C e-kt1

, .

B

1

V = 26.145 - 4.145

× e-0.1111×3 » 23.175 .

(6)

B

2. & ;

VB

*

(V0

= VB ).

' (

) "

= mg,

N 2 F.

( !

m

dVx

=

F

4.5 ×

dVx

= 3t

dVx

= 0.6667t

(7)

dt

x

dt

dt

' (7)

Vx = 0.3333t2 + C2.

(8)

, , D # ,

* t = 0.

t = 0 V = V0

= VB ,

VB ! (6),

(8) #

C

2

= V

= 23.175 . (8) : V = 0.3333t2

+ 23.175

B

x

dx

= 0.3333t2 + 23.175

dx = (0.3333t2 + 23.175)dt.

(9)

dt

x = 0.1111t3 + 23.175t,

(10)

x − #,

t − #.