deberes.docx

15.4 El rotor rotor de una turbina de gas está está girando a una velocidad velocidad de 6900 rpm cuando la turbina se desactiva. Se observa que se necesitan 4min para que que el rotor lleg llegu ue al repos poso. Si se supo upone que el movimie imient nto o es uniformemente acelerado, determine a la aceleraci!n angular, b el n"mero de revoluciones que e#ecuta el rotor antes de llegar al reposo Datos:

rev

$% 6900

1 min

&

min

60 s

2 π rad

&

1 rev

 % '((.56

rad seg

 t% 4 min % (40 s )f% 0 *%+ %+

 a.- )% )i *t

*% -

/omo )f% 0  rad s 240 s

rad

7225.56

ωi t   % -

%- .011

2

s

b.- 1

 % )i.t 

2

2

α t 

240 s

% '((.56

rad s . (40s 

¿ ¿

1 2

(−3.011 rad ) ¿ s

2

1 rev

% 2669'.6rad &

2 π rad

 % 1'92.5 rev

15.9 El movimiento de la varilla 3 es guiado por los pasadores en 3  , los cuales cuales se desli deslian an en las ranuras ranuras mostra mostradas das.. En el instan instante te que se indica, % 407  el pasador en  se mueve 8acia arriba  a la iquierda con una velocidad constante de 6

¿  . s

 etermine a la velocidad angular de la

varilla  b la velocidad del pasador en el e:tremo 3

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Datos:

% 407 ; % 6

¿  . s

  cte

)3 %+ ;3%+  A

;3 %

;



;

B

%



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6

¿

s

sin50

 %

V 

VA sin55

=

A B

sin sin 75

¿

;3% 6.4159 s

↑

 A

¿

B

s

;

% '.56'

V 

)3%

 

∈¿  ¿ 7.567 20

A B

407

 %

s

rBA

¿ rad

)3% 0'2

s

rad

15.50 El brao 3 gira con una velocidad angular de (0

s

  en sentido

contrario al de las manecillas del relo#. Si se sabe que el engrane e:terior / es estacion estacionario ario,, determine determine a la velocida velocidad d angular angular del engrane engrane , b la velocidad del diente del engrane localiado en el punto .

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)%+ ;%+

;% )3.r3 rad

% (0

 0.1(m

s m

%(.4

<

s

0.05 m sin sin 45

CIB

 %

sin sin 45

CID

 %

/=% 0.05 m

/=% 0.0'0'1 m 2.4

V B

)%

CIB

sin sin 90

 %

 m s

0.05 m

rad

% 42

s

;% )&/= % 0.0'0'1 m 42 m

%.94

s

45

rad s 

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Datos:

@% 07 ;E% (mAs 8acia aba#o  a la derec8a )E%+ )3%+

0.05 m

CID

%

sin sin 90

sin60

/=% 0.4 m

CIE

2

 %

0.433

2

 

0.2

2

/=E% 0.614 m CIB

2

 %

0.433

/=% 0.(5 m

2

 

0.5

2

 B (0.40.(

  cos150

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2

V E

)E %

 %

CIE

m s

0.6143 m

rad

% .(6

s

;% )E /= rad

% .(6

  0.(5 m

s m

% 0.215

←

s

0.815

V B

)3%

CIB

 %

m s

0.12 m

rad

% 6.'9

s

15.96 os varillas varillas 3  E se conectan a tres tres collarines como como se muestra. rad Si se sabe que la velocidad angular de 3 es 5 s  en el sentido de las mane maneci cilla llas s del del relo# elo#,, dete deterrmine mine en el inst instan ante te que se muestr muestra a a la velocidad angular de E, b la velocidad del collar?n E.

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Datos:

rad )3%5 s

tan

ω DE =?

;E%+

0.2 0.4

 % (6.567 CID

0.2828 sin26.56

 %

sin135

/=% 0.44'm

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CIE sin108.44

0.2828

 %

sin26.56

/=E% 0.600m

;E% )E./=E rad

% 4.99

% (.994

s

  0.600m

m

m

s

 %

s

↓

15.11 Si en el instante mostrado la barra 3 tiene una velocidad angular rad constante de 4 s  en el sentido de las manecillas del relo#, determine la aceleraci!n angular a de la barra    b de la barra E

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•

;elocidades

;% )3 44.' in % 1'2.29

¿ s

(5.56

Barra BD

CID sin63.43

CIB

 %

sin51.34

40

 %

/=% 4.4 in /=% 9.4 in 34.4 ∈¿

∈

¿ sin 65.23 65.23

¿

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¿

%(04.29

 2.65

s

32.02∈ ¿  ¿ 204.89

V D

)E%

 %

¿

s

¿

rad

% 6.4

s

3celeraciones Barra AB

Barra DE

a3% a3n  a3t a3% a3n%

2

ω

a3t% *3. r3 %0 .r%

4

2

¿ ( 44.7 )

¿ % '15.(

s

2

 

6.4

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%



 D

a

B

ω BD

 n%

2

¿

r % 5.( 40 % % 1021.6  1021.6

 D

a

B

 t% *  r % 40. * 

s

↑↓

 D

a

% a

a

B

←

2

 D

 n

a

B

¿ 111.54

¿

s

2

t ¿

51.4

(.0( .*E

2.65

%'15.(

s

2

6.4  1021.6

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CD -111.5

  cos 51.34 51.34

  (.0( .*E

51.34   (.0( .*E  D  D 111.5   sin 51.34

-111.5

  cos 51.34 51.34

  (.0( . αED

57.59

*E %

( 32.02 )( cos 38.65 38.65 )  % (.

cos38.65

 % '15.(

  cos 63.43 63.43

 - 1021.6

  sin sin 38.65 38.65

 % '15.(

  sin 63.43 63.43

  40. * 

cos38.65

 % '15.(

  cos 63.43 63.43

 - 1021.6

rad 2

s

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Datos:

Gadio % r ;/%;F % cte. )3%+ *3%+

↑

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dω AB

*3%

dθ

.

dt 

d(

 %

sin θ

dω AB

 %

dθ

2

r cos θ

 . V  ₒ )

2

% V  ₒ ₒ

%

*3 %

r

r

cos θ

.

3

+ sin θ

2

( 1 + cos θ ) sin θ 2

2

r

V  ₒ ₒ

 .

3

3

cos θ

2

.

 

1

2

+ cos θ ¿ .

H

dt 

 % )3

  . ;F

¿

2 cos cos θ sin θ

dt 

dθ

2

r cos θ

dθ

V  ₒ ₒ

 .

dθ

sin θ

 .

dθ

tan θ

3

sin θ

 .

2

r cos θ

. ;F