Esami svolti Meccanica applicata alle macchine

+(B-

X(B-A) - -

Was (B- A)

[Te = -

, ~

, Was1(B- A)

Tre =

ra ~

,

, Was Vezz

2 1

Ecoriois =

-1 Gr

Wis = Won(61

= B) Va Varj

= +

- Wo(Ge-B)

War(6- B) Tor

= Ga +

- = Wr 0

Wr Wr

+

+ =

We Moto diretto

mag[welsnd

We

mag1 0 =

+ =

=

(1 ya)(Wal

Wo -

-

=

Wr dr Wr

= magTWeLand

W yWr 0

+ -

- =

mcgT(and Coppia resistente riportata albero motore

maga

(

Gy = =

= y

Dove è max?

migTle

↓ Cr 90

0 =

= =

d y

↓

2

Wr Wu =L

Wo

+ + dt

1mcV 1Jewe 1JrWi

Ec + +

= 2 2 2

sind

We- [L We

8 ma

me We

da +

+

g

Wr In Wr

= Wir

(1-ye))CWe

Wo In We

-

-

=

Wu Tur(sind

mag

-

= Wel

Jewe- Tr +I

I We Wn-MagTWe Jewels

Land We

We

War ya +

ma

yo =

metWWat Jet Wr

yaJrWWr

Wrya-MagTLand

& We

+

=

mig sind

Cryc

Wr -

= mi 55

ys[m + +

1 B fe

=

+

der be de

Ce +

+ +

=

S dead

+broup fery

orad crong +

+

= drind t

orindtheiß friny

cang +

=

Velocità:

S odsind-bBsup -I sand-gysy

- = B i

=> ,

adeed

adrasd b fycasy

Bra

+ +

=

Accelerazione:

S -sind-brad-gising-girery

erind-arasd-bsup-bouß

- = B i

=> ,

adood-Isand

trad-asind braß-beauß figcay-giring

+ +

· =

Was Üs

Was B Y

=B; in

Wo

; ; =

= =

2 &

= war) ri)

usr(A

V a) wej

+ =

= -

-

-

= Bin(tbi suj)

Va Wan(t Al Vanj

ep-tprip Voxi

+

wej

Waj + +

+ =

=

+ - =

n

= Wi(A1- (tr A) w

2) Wi

=+ =

-

- pj)-ppj

p

Wan(6e A) wppjpruppo

We

Wilde-A) +

+

a n -

+ - =

= =

primp Dox enet

- +

=

= -w

ir

;

Wej

- = 2xyj)

yπ1(yi

Va Vo Es1(6 Vai Va

+

d Lyri

y

wij Wej yj +

+

+ = =

+

-

- - =

= -

wayj-gen

Non(6 World - d

-

Ta + =

- -

= o

-wijj-tan

= R

&

=

Want des

West = dt Va

Wan Gr F V V (rW mgVe

=Vex mgVa

. mj

+ +

+

mj

+

. =

. -

-

= .

Wa 1mV WismV

E 1W

1

1 Wo 1 Jo

+

+ +

+

= 2

2 2

=J toWels Jo

Ja Inww

mVaday

mVoex mV

Ve We wer

Wit

Was W

+ la t +

+

+

+ + ex

Vo 1/B-A)

= Vexi Vaj

(Bpj LBaue

Was Wrj

+ + +

= =

-

Jawals Jor Jo

Ja Juwi

mVayday

Vo WastmVsx

CrW Va

FVox-mgVor-mgVoy War

We ha Was

+ Was

+ m

+ day +

m +

enex

+ + ex

=

Ricavo Cm wir

Suar

-

Legami cinematici: Ve

T Va Retim

faNe ResWr

V

Ne We

; RetWr

We ;

Wr ;

; Re Wa

Ji ;

Meg Meg ; twe

;

Twir

;

Wi ga ; de a

da

= =

= =

=

= = =

= =

= Re

MagftwriMriMet

Wa MaggidheTWr W n

+ Meg

Twe

-

= Ri

I MegRW

Mayfu-Magand Moto diretto

+ e

ya)We In WnWn)

(1

(1

Wo ya))(Wm-

- - -

= =

- IMVWMV

ErrWMaVi +

*

IrWrWin

= J Wi

We

+

dt MagarbReT-T-Mag-fg--- I

-Srascent =

fMsgrid MegfMghn

ys(5 )we

*

5 +

Cro +

+

= Ja

2

Wr Wa We 0

+ + =

Wr dr Wr

=

We Va-Cus-TeVe-Newa

Magrind

=

Analisi flusso potenza:

Wz We Wa We

&

+ >

= -

= =

-(1-ya)

Wo Or Wr

= (Magrind---JeMeg-fgRTW-(-y

te + ( Mig-Magfughe

e se

Cre f

+

= VAR

Cost

b &

B

R

c + 2

= j

d

L &

=

S π(2

=

1 5 5 =

i + +

= be

de det

be

+ +

=

Noto H CIR del disco:

S

(t j Wr

jc we

we =

= -

=

-

= = R + 2

&

Wr

Ü -

= R + e

Ho 2 incognite: a(t) e beta(t)

Sistema posizione:

=&

per

S e

Velocità:

biße (ije

i + =

S bisiß

: -jsn)

=

- - ,

i

=>

braß jag

=

Accelerazione:

bie-be -je

ijet

+ = -

S -bisiß-breß -ja

-jay

= - ,

i

=>

braß-buß jg--jang

=

Vs s

:

i ·

= = Essendo a terra non da

&

= lavoro

Mr

W Vi

Mj majus

. V

i + + +

mj

= L

Wr(6-B)

=+ --

=

W &

= MVmWImum

Er 2 2 V =

Il generico termine di velocità può essere visto come: F F c

w i

E =

.

= .

Mr

Mxwi Ja

m

der wie +

+ mi à

+

+

= 2

dt B))

Wir (t1(6 B

(sn(t +

-

B) BIj

i

Es

a +

+ = -

- -

-

=

+ Er

↓ t

WemMiwimm

M My

+ Mu

Ricavo

A

Considero ancora il sottoinsieme asta AB+corsoio e scrivo 2 equilibri di F, in direzione orizzontale e

verticala:

contro Ha

& Ha T

T 0

mai +

= +

mi

-max max

=

- =

-

Matteo N

E Va-my-mea Va

N 0 +

my

= mean mag

-Mag + +

= -

=

Il moto è diretto

1

Wr Or Wr

= JeWrWr)

(1-ya) (1-ya)CrWr-

Wor Wee -

=

-

= -(1-y)/(Gewn-Trunwalyes Intinua]

yes-Eww

(1-ye (We

(1-ya)We

No -

=

-

=

-

= (1-ya)((rWr-Inwrwales-Ju Jiunwa]

-(1-yed) (Galn-IrwmWa)-

Wo Wor Woz

+ =

=

Wu magRWr

RWu +

-meg

= Wu

Dato che: Moto diretto

&

mi =

ma

[zWr Ez

Wo Wr

=

= [2 Wi

Win Te

= -might

Wu magREs

Te

=> Te

Wr We

+

=

WWWImIm

Fo = 22

RWu RE

5 Ent V

;

;

Wr

Wr Wa Wr

Wo

= 1 = =

= Jwei

=...

51]

(Je [ (me

[c ci "

ma) R

Ju

1 Je

Er T We

+ +

+ +

= 2

We Wr

Wo =

+

+ [ mari]

Ersr(r) Ticiu]-migh tewe

yx)(((Jr- (m

(1- Wawelges-Ju Joi

-ye))(Wr- Gui

-( In we

magheur we

+

+ +

+ +

=

-

-Trinwa)-(e-In + /(da - In [5]

[Si

Eurw-(me-magR

Walges Wi mi) we

(me

via 5

In i Wi

er +

+

+ +

=

-

S(50 mi)R] Tige3Wa

Ti

(me (n-(me-mclgRET

Joyeyes Ev

E + +

+ + you

=

Siamo allo spunto => Cm=C0

(me-mi)gRET

Wr Co-

ye

= m2)9]["Ti

(50 (me Since

Jr

Eryeye

+ + +

+

2 (mi migr

(me Moto diretto

milgri (r

yx(n 0 -0

= -

- =

- = ge

www

=

(1- Wi

C =

0

=

Wr Cr Wr

=

Wu Moto retrogrado

Wr-magREat

megR5z O

Was

= yerya)(me

(1 mz)gRT

(1-yeeyce)

Wo We We

-

= -

-

= -

Er 0

=

t

↓

Wr Wo Wr 0

+ + = (ma migRewr

yor)(me

(1 mi)grTWr

G 0

Wr +

ye

- =

- - -

yeryz (me mz)gRi

Gr -

= - We

(1-

C =

1 (Wor w)

War

Was i

Was 0 W

0

cost =

= =

= =

=

( wπ1(A wi

a) win(j

A)

(1(G

Va + = =

- -

=

-

= (1(win(j)

(tass(6 win(wan(A d)

A))

Wis1(G Win(A win(j

d

1) ulj

w(i

a Wasn

a +

+ +

=

+ - =

= -

-

- -

= -

v

& NOTO

2 -

& B

b

Uo

(D

(B d

G B) (D

+ = -

- -

be e

de + =

S braß

rosh -rag

· + =

asndthemp song

=

(2) ir)

( berp

+ =

+

:

ade je

+ =

S ahsind-bisin rosy

- = 2 j

B

w =

= ,

braß

edad jsij

+ =

pulti +

ben( + be B

i jet

& + =

-

S and-ared-bisuß-braß Greg

- = 2 B

w j

=

= ,

dand

·d -bisuß sug

+

- = =

= Es -

;

; i

i s = =

2 P

I

M dE &

+ = =

dt Fr

Mj1

I Mag15

Wor Fe

= (rw

1 +

+

+ = -

W

1Mr Jo

1

Er ;

1Mar 1 Es Wi

+

+ +

= 2

2

2 MlwiMIMMLwis

Mr Jewo

WWMs

= Ve l = 2

By

2

(fop Mol

Mi wi

A

= +

.

3 Uguale a prima per derivata energia cinetica e tutto il resto

M T =

+

I Nel Wel

= -

A

Considero il disco, BD è un’asta scarica => Biella

[Ex 0

=

EFT 3 equazioni

0

=

EMs 3 incognite => N Ra

T

0 ;

;

= IT1

Aderenza: GIN)

-

I Nul Wal

= - Mlw

( Nu

= +

+ Legami cinematici:

Ve WaRe

We Wa =

= =

V [waRz Va

Twi

We = =

=

=

1

M3 in salita; M1 in discesa

Wr We

Wa +

+ = s

dt

Wr Mag Ve

Cr Wr +

=

Wa MageiaVa-Je/Mageand)

-MagsindV 2Va-MaVada-MaVara-tanala O diretto

moto

+

=

Wa Win deguT

- + = dt

-Mag (and 2jacash) Tware-Mariwen-MatRewan-Ja WrWe

Wr [warMagent

+

=

We Je

Meghe-Me

Wr-ErwrWm

Cr Win

Vor-

+ we

= MegrWr-Meriwewn-Jewelr

(1-y))(rWr-

Wo JerWr +

= - 2 fac2)Trz

Mag(an Magrind[R

Migr

Gra

Wr y +

+

Y + -

= (1) 55

y(Jr (3

ymri M1)pr

+

+

+

+ +

2 Magand Mag

Mara

5 cos

f

= - -

3

Salita M4, discesa M1 300-100

(300

(Masind-2ja Maral-MaswalgeWar

Wa MagsindV-2MagagrahVs

-Maganda -2

+ = = .

= .

(g5war-o

(150 Moto diretto

3008

= - :

(Masind-2Macaod-Masna)f[Rz yMigR

Cr -

= z

=

cro-AW

Cr We

=

=

1 G v

&

b d

& o B

b

· j

pr j

d NOTA

C x

=

~ a j =

Posizione:

S

Reebo L

=> P

,

Velocità:

ibe

ide =-

+

S

e ( B y)

f() x)

f(x

=> = =

, , ,

Accelerazione:

ae ibpeP-bpe

e =

is +

S

e = x)

[ f(x

B x

=> =

, , ,

[

W

W I ; =

=