Сборник задач ТСПП

:

–

,% , , ,

, , .,

–

(

) , ,

( ),

.

%

,%

–

,% .

( (

)

F−

c .

* + :

N

=

F−

v

!,

)

1000

η

N

F−

η

v k

=

,!

)

(

100

k

+

0,8-1,2.

–

=

F

1t

F

...t

"

2

+

2

+

+

2

1

t+

2

1

n

;

Fe

+t...+ +

tθ

c,

1

2

n

1

N Fe

=

,! ,

4)

10

*

–

,;1,F2,F…n–F ,

"

F

,;1

= 0,2+5 –

,0,3% 5

(

1=1).

6.1.

, : ;

–v, /;. ,

–1 =0,25

÷ 0,35; 1,t2,3t,t

( . . 6.1).

. 6!.1.

( 6.1)

6.1.

N F

–" : =

, ;

10

2

+

2

+ +

2

.

1

1

2

1...

– :F

F t F t

c!

t t... t

=

+

+

+

+

θ n

,

1

2

n

1

λ =

F .

1,25

F

' -

–

(

);

1,25 –,

;Fmax–

% ;F

–

.

( , % $ - ,

)) $$

- .*

F.

( )

1

Fmax $

v=

2,/5, % % )

F1 = 4!4

1t=

50,0F2 = 2!0 2t= 20,0

F3= -!100t3= 10,0

, = 15,0 $ .

6.2.

N F

–" : =

, ;

10

–

:Få

2

+

2

+ +

2

;

1

1

2

1...

=

F t

F tï

!

t+ +t...+ +

tθ c,

1

2

n

1

F=

2

+

2

+

2

= ! 150100

44500500200201002000,35100

+

+

+

4

;

=

49000

= 2,5 .

N

100

12

. 6.2. (),

() ()

( 6.3)

6.4.

2

+

2 +

+

2

–

:

;

1

...

,

=

F

1t

2F1

t

!

F

t t... tn

c

+

+

+ +

θ

,

1

2

n

1

Få

402 300+ 2 20+ − 5002 ( 10) 400

2

=

=

! ;

300 500 400 0,35 250

+

+

+

– :N=

F

=v23500= 1,63 .

1000

1

6.5.

,

: –Q, / ;

–L, ; %

–β , .%;

$ –q0, /;

$

–v, /; ) –w0,

)

–w--;*

η–.

6.5.

. 6.3

6.5

–. , :q=

Q

, /;

6,3

v

– ) % ) :

g(w0 cos– ),sin;

F2-1= L β

β

!

q

F4-3=

g(w0 cos+ sin(w cos+ ),sin;

L β

β

β

β !

q

) +L g q

–

( ):

=2-1F+4-,3F;

F =- F

!

– : =

F−

.

N

100

η ,

+

N0

, $ :n=

Np,

N

N0 –

(

).

0

& % %

$ $

N= n N.

1

0

6.6.

(% ) 5.2, 5.53.,,5 5.

v= 5/, )

= 0,95, 5.25.3

%

,--* /

=

0,85);

% θ ′

= 70% θ ′′

= 7./0 θ ′′

,

f= 0,1;

0,15; 0,2;

0,3.

7.1

tg= f( –

),

,

(

)

(

)

f.> f

.! , ,

,

f, 1 =

arctg1;f2 =

arctg2;f

3= arctg3;f4= arctg4.f

" , f1:

arctg=

0,1º ..= 6

7.2.

,

,

=15º?

7.2.

wmax=

tgº=150,26# .

"

,

w

,

15=º.

7.3.

,

,

w,

l,

.

7.3.

arctg= w.

! ,

$

.%

w1

<w –

.

,

l.

&

v

v

' ( ( :

2

2

(

)

(

)

2

2

mv−

mv= l

−T =W l

sinmβ −g1

βc w

) v=

2+v2lg(sinβ − 1 wβ .

7.4. 25º ,

f 0,3=*.

(

)

1/.+

(

, .),

1 /,

= /3?

7.5.

,

l = 6

= 10º, (

l

=30; 40,; 60

v= ,0. (

7.5.

= mgH= mglsiβ ( l –

-

)

)

.

l(

l(

) :

β =

β +

,

mglsin

mgw( c

l

β

0,17

0,

=

sin

=

6

=

w lcos l

6 0,98 30

.

β

+

+

.

=

40w=

,026,

=

50w=

,0021.

l

l

/ ,

w>

0,01,

. , :

β −

β

−

=

sin

co= s6 0,17

0,01= 6960,98.

l l

wwl

0,01

v

= /3,

w = 0,1,

= 15º.

27.7. ,

“

“

3/

cos

=

2010 0,26

–2001,010,97 .= 326

:F =mgsinβ –f mgβ F;

,

/ ( 10(

)

aν

3= 0,3/ ,

=

=

t 10

(

=

=

=

F

ma200 0,3

, 10

1 =

+

=

+

=

F

F

F326 60

8.1.

,

F.. =

300, 0

F = 10,0

F = – 14,0

!

( kn= 1,1÷1,15)" .

'!

F

=Fn.·pk.–( 1)F ;3·(1,1=

5 – ;1) = 0,45

F

;maxF=1 =F140 +3 ;= 143

=1 =maxF F=n.p+.F F

F2 =Fn.p3=. ;F3=2·(Fk– 1F)2;+3=F3 ·

(1,15-1;) + 3 = 3,45

F4

=

=F3 +F;F4 F3,4= 5 + 100 = 103,45;

! ! F =F – F

–

103,4=

5 – 143; = - 39,55

– ! $

=F2 +3 3=F+ 3,45.= 6,45

"2. ! ! .

( . 8.1, 8.1

,

,

F1

2F .

'! !

. F !

1,

! :#

F =.)

|+n.,pF = (

= 3.

+ F+ =F F

F+)Fk·– (1)F4 ;=.

F

F

xF

+

−

−

F

Fn k+

1=

=

.

= 140 30 100= 24,31,155;

k

1,15

n

F2 =

+F1

10= 0 + 24,35,

= 124,3=124,355 · ;0,15 = 18,

F

24,35 + 100 +; 18,65 = 143

F3 =maxF=1+nFF+=F

F = –F.

=4 –1 =F3 – 24,5. = 21,5

F

(

$

=F2 + 3F124,3=

5 + 143, = 267,35

, ! . 1.

8.2. ! ,

, : ! !

q

= 4/0,

q0 = 1/5,

L =

15,0

! !#!

w0 = !0,2,w

=!0,4# !, β = 1 .

*8.2. ! ! # ,

.

=

β +

β +

β +

β , ;

F

0q L(g0

cosw

sin

)q

L g( w

=

+

+

+

=

.

F

15 150 9,81 (0,2 cos10

sin10) sin40 10)50 9,8 (0,4

, : #

F

=50 ,F

=100 ;

F. = 3, v 1,=/2,η

=

0,9,

! !

k

= ) !1,2.

! ! ! # ,

k

=

1

k = 1,2, ! .

8.3.= 1.(8)..2,

"

k

"1.

! .

F

= F+ F;

5=0 + 100;= 150

F

N

F v N

=

=

150

= 200

1000

1000 0,9

η

( $

=F222= ·

53 ;=Fmax1015=6 3 .

"2.

! # .

F

= 15;N0 = 20;$0 =F222= ·

103 ;= 206