Сборник задач ТСПП

						# . 9.6		9.8,
)% .
=	=		o		= 6	& ;F4 6=0& ;F =-=F			+;F
F	.min eα −			1		30 = - 130			=60 – (-100;) = 1
	F		Ff	k
F=F-– F =– 100 –& ;F-							=4	–1F;1 FF=4 –F- F		&
F2	=F1 +		16= 0 – 13;0F3 =F2 3=0 3;0Fmax=1						=F160;P 2F=2 2= ·	30.= 60
			F			& ,	&		&	&

		# . 9.6		9.8,
,
3&0,				32&0.$
"			22&0.
9.10* .
,			F-=	10&0,
F = –& ,50		" F = &2,0
F.. =&5?

81

9)%.10. .
	= 150+12-F=5 + 50;= 55
F34-=F-+F1|2-| 10= 0 + &50;F1 = F		&
F3	=5 ;Fmax=4 =F3 F+F4 =3-5 + 1++5;0 = 155
, F2 =	&	&
	F
$ :P 2F=2 =2 +3F 5=F+		5& =. 10

# . 9.8	9.10,
)% .
= 20	+F34- =100 + 50; = 150
F1 = F & ;F- = F=F34-+F12-;F =12- F= F		&
F3, F2 =1 F+12-F=20 + 15&0;F4= =173 F+034- F= 70 –&50; = 120
Fmax=3 F= &17;0
$ :P 2F=2 2= ·	17&0 .= 340

	# . 9.9		9.10,
$ P 1&0 34&0,				33&0.
9.11.
" ,
F.. =& ,F		& F-				&
	5	2=0 ,			= 70,
			F34- = &10.%0

82

: , –

.

9).%11. .				)% .
F12-= F-–F34- = 70			– &10;0 F=12-–=103&0;
F1	=	+12-F=5 + 30;= 35F1 =5 ;
		F	&	&
F3	F2	. = 5;		F3 F2 =maxF= 10;5
,		=. &		,	&
		F
F4	=3 F+34-F= 5 + 10&0; = 10F4 5=7&5;
P 2F=2 2= · 5& .= 10				=	7;0
				F- = F	&
				P 2F= 2= · 10&5 .= 210
( ,
,				– .

# . 9.10 9.11,

# . 9.10 9.11,

9.12%. ,

, , :F = &25;

83

α = 2,56F ;

5 . =

10 (

F

= -10;0

. =

&

ef

.

&

;F..

&

).

9.13%.

,

1, 2, 3

,

:

20

=

α

= 2,56F ,

.

-2,0

. = 3 . = 5.

F1.

=& ,F

&

ef

.

&

,F..

&

. F2.

=& ,F

&

α = 2,56F ,

&

ef

.

& ,F..

25

=

0,

. = 3

. =

1.5

9.14. , ,

( ) , . & " .

9.15#.

( &-max &+max)

( )&. , ..

," .

9.16#.

( )

( 0 90˚)% ".

.

9.17. , "

" "

.

9.18.

( " ).

9.19%.

, ,

.-

	= − 100& ,		= −		10& ,
	F		F
F	= 15& .(
F.min= 20&		,
		.min=			= 5& .
		F		F

84

10.

. :

				1,QQ2,Q3…,
(	)
		1,LL2,L3…,(	, -
	),			–
	!					.i
				i
" , ,
, ! # ! ,
,
.
$ !

! .% # #

!

.

:)

,)

, ." !

! ,

! ,

! ." !

! :		,QL , – -
		! ,
.&	, ,

- , ,

( )$. !

. .					( )
Q	>	n
		1
					QL+ Q+ ...L+
				=							.
					1 1	2 2		n
				LP	1+	2+	+	n		,
					Q Q...Q
	' , , :
				= 0, 015-0,01,
i= 0, 003-					" !
				0, 0 , i

# : !		–
, ,
	–

! .

: ,

( )

, ,

, ."

.

85

10.1. ,

: 14,

3,3 (

m = 1,27

=

),

z = 2.0,

5,94

=

/8 .! " ,

2 , 4 ?

#10.1. $ $

−

F =

F"

m (g− w=)i

m+(

=

(âï

m

âï

pc

nï

,

ipî w m

(mâï

mnï

+ .

% $ m=

0

=)m+14 20(1,27+ =

.

m+ (z+ m

% $

=

+

0zm= +

=

,

m

m

14 20 1,

:p

−

39,4)

i= 8(158,2=

39,4)

(158,2

4

+

‰.

, z= 1 ,ip= 4 ‰, z=

–ip= 3 ‰;" ,

.

p " & & .

10.2. $

m =

10,0

= /4,

= 5‰,

= /7,

,

= 3

( = 15. $ ' .

10.2.1

$ ' & ($ . ( ,

& $ ,& $ ) &

: =

+ + ,

($ ,

& ,

F

F F

–

F–

–

$ $ .

mg(+ +)w .

) :ma=

:100a= 100107(+

)5+ ,15

a= ,027/2.

* :t=

ν

=

4

8,14≈ 15.

a

,027

ν

$ :l= ν cpt=

t=

415= 30,

& – (3

)

′l l

t

3

.

2

= +ν =

30+ 4=

+ ' " $ ( $ $ ):

2

[l mg(+ +w)]

mv=

,

2

mv2

1002 4

=

=

.

l2mg( w

)i

B2 100

10(0,007 0,005) 15

[

+

+

[

+

+ ]

3

]

* :t=

l=

30= 15.

ν

ν

cp

2

# :a=

=

4

,027/2.

86

10.3. ,

" & & , , ( '

ψ

= 0,12,

=

1/0.! ( ,

ψ " , w"–

?

10.3. & & :

max

i,

ç÷

,

F

=

F+ F

1000gPψ = 1000gP+

ma

, & , , ,

–

Fmax,F,Fi –

,.

P=

' :

i=ψ −

=w0,12− = 0,1=

‰.

,

max

"

,

ψ

" & & ,"

.

10.4. &

$ 2,5&

& , 10,

z = 2.0,

m=1,1,4

m=

2,, ( '5

ψ = 0,12, w = /8.

10.4.

=

+

i,"

& & :

max

F

F

F

1000gPψ =

1000gP+

, maxi=

Pψ −

ñö

n,

Pn–

ç÷

n

ma

P

$ ,.

n

=

+

+

=

+

+

=

;

P

P (z0

m) m10 20(1,1

−

−

i=

10,012

8,2,0

08= 2,1 ,066= ,0065= 5,6‰.

max

828,

828,

10.5.

10

2,5

& z = 20.,

m

=

1,14

= 2,,, ( '5

ψ

=

0,12,

= /8 ,

! = 0,0/2.5

10.5.

:

=

+

i+

a,

"

max

F F

F F

1000gPψ =

1000gP+

+w( i .

ç÷

n

max

10'.4 :

Pψ − P(+ w11010a)

0,12−

82,8(0,008+

0,0055)

=

ç÷

n

=

≈

≈ ‰.

maxi

P

82,8

0,0

n

- , ψ

0,0/25 "

1‰",

.

87

10.6. 2,5 (

m = 1,14 m = 2,),5 $

, ( ' ψ

=0,020, 10,

=0,12,

	= /8,		0,0= /52.
	10.6.
	"
	F= 1000gP+ (+w i=0,11a ) 1000+					10+	10(0,0=			,
å		å
:
	F= 1000gP+ (+w i=0,11a ) 1000+					10+ 3,64(0,008≈ 12 .
âàã		âàã
% " :
		=	ψ =			=			.
		Fmax. 1000gP		1000 10 1					=F −	=
		'			F=	F	−
		z				max.			12000 33

= F= 8650= .

z F 1220

0,020

,

10.7.	$ , '
0,00= &4	& . $ ' . 10 15.

2,5 ( m = 1,1), 4

= 1/1.! & ' (

ψ 0,= 1 (

" & & ?

10.8. $ ,

: –,, ( ' ψ–,

–w, –, –v,	–L,$ '
.
10.9. "

( ) , :

–, ;	–; –;
, ( '	–ψ ./ &
, ( ' ψ .

10.10. , :

Σ– ,, ( '

" –.!f ?

10.11. $ & 90

, : –L 4=0; –

.= 2,		= 5‰,	= 1,5
t		(
w	= /8. $ ' .

88

10.12. " 14

, 2,5 (

m = 1,14			),	z= 2.0,
			m = 2,75
		/ , = 0,003,
		= 9
! = 0,0/2.4
10.13. $ , –, ;
–G, ; (–,; –v,/;
– , ‰;	–w / ;			–t, ; $
' .
10.14.			($ $ $

, : )–,

, ( ' " & ϕ–, –

0 ,, ( ' ψ–.. & " .

10.15.

& & , :

–, –,, ( ' ψ–,

–w, –.

10.16.

& & $ , :

	–	, –0,		–
,	–,, ( ' ψ–,
–.w
10.17.		$ & – +G(),
, &' . ,			; (
), ( ',		ψ–; –w;		–
, ‰;$ ' .
10.18. $ '$ $
, : –R, ;			–, ;

, *–, ;, ( '

( –f.

10.19. $ ,

: ( –, ; –1 2, ;

*–1 * 2, ,, ( '

ψ–, –R.

89

10.20. (–,

'$ ( , : , ;

, ( '	ψ–; –R,;				*–.
10.21.	$ ,				–, ;
–G, ;				–v, /;
–, ‰;		–w, /; –B.
10.22.	, ' "		–
, : *– , ;			–R,;
$		–;	– , ;, ( '
	ψ–.

10.23. , , ( ' ,

' , " & ?! , ( '

– + " + " "

?

	10.24. $
,						4					:Q1=			38/0,
	Q2= 30/0,Q3= 40/0,Q4=					25/0,L1= 3,L2= 1,,5L3= 2,
	L3= 4.
	,
& & "
, :
	%			%				%				%
	L1 = 3			L2= 1,5				L3= 2				L4= 4
	/		#	/	#			/	#			/	#
			i,‰		i,‰					i,‰				i,‰
	l,			l,				l,				l,
	400			10	100			2				500		10
	500			2	300			10				200		9
	100			3	200			50				300		8
	800			5	400			3				400		2		1
	900			8	300			7				200		3		9
	300			6	200			5				400		5		5

90