Сборник задач ТСПП

=

;

– % :

,1490+ ,1560+ ,025= ,055

&

0,55 100–%%

, 0

,0149100%= 27%

,027160= 43/ , 0

– /43 0

– /74.

,055

" :

–%

30 ,

–%

92/ (

25

),

–% 5 .

' .

3.7,

Q

()

m () .

(

“ ”).

#

, ! ! , $

“ ”%.

, ,

–

& & ().

# - ,

–

, (

,

) ,

& (

! ).

’

+ -

, :

f=

,

f $–

($ );

FN –

(

) .

% !

$

= m·am, – , ;

–

(

),/2.+

:

." ,

- =

0,0-5 –÷$ 0,1!, ,

. -

= 0,0/5 $÷ 1,1-

.

, ,

,

.

% , ,

! , , ,

! .

( -

F =

,

W±T+P

m, $

f0,

sico0 ns

! , /2 $ ,

- .

F= W± + ,

F – , !

;W= mgω cosβ

– ,

! , ;* = mgsinβ

– –

( ),

" ;

, – ;Pi=

– " (“+”)

,

( )

( “–”) ,

.

# ν = const(,a= )0 :

F′

m g w

β sin=

) 100

9,81° +

°(0,1=

=

( cosβ +

$ :

F′′

m g w

β sin=

) 100

9,81° −

(0,1° = −

=

( cosβ −

% !

F "" , ,! ! !

,! , 7&1, .

# :

m

a

100 9,81° − °(0,1+ cos1=

F′′

m g w

=

( cosβ − β sin+

= )

( 7&9 ! :

a

F′′

79

2

m 10

0,8

=

=

=

4.)3. m =

10,0 !

0 ( = °)10

, , , F = &10.0

, /2,

w = tg6˚

t1= 5 ,

t2= 8, t1.

4.3.

m

(g coswβ −

β sin+ ,)

* :F=

−

β − β

−

−

= 1,73(0,120,985 0,17

a=

F m (g cosw

sin=

)

100 100 9,81

1

m

100

+

5 :

v= +v

=a0+ t1,737=

5 8,685

5

0

1

) 8 :a2=

v5=

8,685= 1,085/2

t

8

2

2

2

) :l1=

0v=1

ta1 1=t1,73=721,7125

2

2

2

2

) :2l=

a2

2=t1,08=534,78

2

2

$ ,

( ( ,& )

P+ * − W=

B;

B= m+a msinβg−

mβgcos= w

=

100 1,085 100 9,81 0,174 10

2 +

−

=

4.4.

0 ,

,

w

= 0,2?

tgβ =

4.4.,

w

′

=8°

.

w,

- β = arctg= °

.! !

F=

m gcoswβ +

mβ g,

sinβ =

−

β

−

=

°

′

′′ .

F m gcosw

100 100

9,81 0,1 1

m g

=

=

0,0

β =

100 9,81

2

2

arcsin,0019316

20

/ , :

=

=

100=3450)

E

m2v

2

*

( " " ):

=

+

,

E

(W

l=

E =

450

=

450= 3,84

T

T

W

100 9,81 0,1 1 100 9,81 0,0193 98,1 18,9

+

+

+

.

$ : =

+

=

+

0= 1,5 .

3

v

v2 v

2

0 :=

lT= 3,=852, .

v

t

1,5

#

!

"

. =

* ;a* =

vt=

2,57=

/

;

:

P m

3

1,17

Pi= 100 1,17= & ;117=

= 117

3,85= ) 450

E iPT

4.6.

m = 10,0 !

"

( ),

12°., , !

2 ,

w

30%?

4.6.

: * − W= 0, !

*

m gsinβ −

m g βwco=

,

w= tgβ =

tg12° =

.

, ,w

m, ! ""

.# w

30%!, w = w0,7·0,1= 5

m = 200 .

* " " :

4.7.

,

0( =°)10 " " ,

v= /2,

w =

0,14.

14.7. tg10° ≥

, ! .

4.8. (

) m =

3000

" 1 n = /c4,

5

1

= /c1. !

,

f= 0 ,

w = 0,01?

4.8.

" "

( ), :

ν

2

ν

2

m n

−

m

= (

W+ W) ,

2

2

B

T

m

1 n = /4c1

= /1c – ;WB=

WT= + f –

;+

–

;l= 5–

.

2

2

" "

2 = 3000−

4

2

3000= 225001) &(

2

" " :

À= W

= l

m =g3000w l 9,81= 0,0

Â

B

WÒ = l −ê Å= Â22500À − =1500

" " :ÀÃ=

WÒ=

ÀÃ=

21000= 420

l

5

$ " :+ = 4200= 21000&

0,1 2

P

=

1 2

,

– " , :

= i

Pi

m

a

E 22500

2

ê=

1,5

=

=

m l3000

ν

−ν

3= 2

0 :tã=

n

ê=

à

1,5

4.9.

( ),!

,

, t = 10

""

, 1 n = /c3m, =

20,0

w = 0,1, 0

=°.15

:* − W− F= 0,

*4.9.

F= * − W;

T=

m singβ = 200

9,81= &0,26; 510

m gcoswβ =

200

9,81= 0, ; " :

:W=

P= m= 200

=0,

,

a=

ν ï=

3= 0,3 – .

i

t

10

ã

(Pi=

0):=F − T= W− 510=

1 ;

&

:F=

+Ti− P= 320W+

=60 ,

"

,!

6&0.

4.10.

F=

F−

F

*

&

+

,

l= 100 q= 30

/ = 20 ,

F+ = 100 ,

w = 0,4.

4.10.

FÒ= q l= g30w100 9,81= 0

F* = F& − F+ ,

$

=

+ =

+

=

F&

* F+ F11772 1000

$

20:F* = 1177220=

23

10

& : X=

F−

′ =F

−

=

F &

T 12772 2354

4.11.

, ,

q1 = 10q2 0= 5/0,

2, w1 = 0,1,

w2 = 0,15, 0

=°.10

$4.11. :

lβcos− g+ w(

)βq; q l g

F= q

l gcosβw+

q

1

1

1

2

2

50−

1

2

F=

100

2 9,81+0,1

0,98

2

9,81 0,15+0,98,21− 150= −0,329,81& 63,801

1

- , F ,

.

$ :

( ;

F= (+q q)

lβsin+g

β lcosg+

2

1

2

1

1

2

F= 503,3+ 144,21+ = 1

2

4.12.

! !(

),

! ! w = 0,3!, 3

= 180˚, 2F2–= 150& .0

, 1 , ! ! !

! 5%

F2?

4.12.

ωα

ωα

=e1500 2,56=

F1= e , F1=

2F

F

2

:F′T=

1−F 2=F3840− 1500=

$

& ! ! ! :F1= 1,052F=

1,05= 15 :

F′′ =

7 ,!

2340− = 75 , 2

T

1575=

3840−

.

åwα ;F Fwα

π

F2

å 0,22å

=

=

= 850

=

1

F

2

1

1

=F1 = &85,0 (

=F2 = 115& ,13 – F1 F2.

* '

, ( ! !–

)

F3-=4 100& ,0F5 = &60?0

4.14.

- :

F =F2-1 F+3-2 +F4-3 +F5-4= 200 +

900 – &100,0

! F =F5 –F1

= 1450 –& .600 = 850

# :F5 = &60,0F1

= 285& , 0 F =

225& , 0

'

(.

4.4)

250&0, 180& , 0-&300,0&100,4000& , 0

F1 =

100& . 0

4.15.

" ′

= &30.0

" "

( 0

= 30˚)

a= 0,0/2.4

" ! 10%&.

( )

)

! )

F' =W' = &30(0. 4).;W54 ,=m ·, g w=· 300w

= 0

3000

;

! )

F''–W''–P*– = 0,. (4! ).5,

F′′

m gcosw

m1,1 à m sing

3000 (10 0,01 0,87 1,1 0,

= β +

+

β =

+

+ = 93

4.17.

l ,

*4.17.

F=

+Ò =W

q(sinlβ +g

β ,w

l=

20000

=

20000= 57

353

100 9,81 (0,26 0,1 0,97)

+

4.18& .

% !

! ! ( !

3

=

°180,f =

0,F-3 =

2000& ),0 :

)! ! ! W

= &20;! )0! ! ! ?$

( . . 4.1).

4.18.

(

):′c

20000+ =

200

;

)

!

! ! !

F− =

! ) !

! !( ! ):

′′

=

α

=

.

f =

Fc−

−F

20000 2,56