mi )gx= - rutgers physics & astronomygershtein/382/homeworks/hw04_sol.pdf1€, u= tzk-12 / k m m...

7
13.30 My , q ¥ t.it " "t' zmzxnttzkingysj . T - IT 'zm , + ' zmzttam ) mi ma U = g ( Msm , If = x. ( mitmzttzm ) =p Le= 'z( menu F) it ( mom , )gX= I = B- Le . Implant ( mz - m , )gx M ,tMzt M/z ill . m , - mz # = @ z - mpg # . ( mitmzt 'zm)** : ii. many g or P - = - X : p= ( mitmztmz ) x . 0 P M , + mz.im/z= × Tdef of generalized momentum

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Page 1: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

13.30 My,

q ¥t.it"

"t' zmzxnttzkingysj .

T - IT 'zm ,+

'

zmzttam )mi

maU = g ( Msm , )×

If = x. ( mitmzttzm ) =p Le= 'z( menu F) it ( mom ,

)gX=I = B- Le . Implant ( mz - m, )gx

M ,tMzt M/z

ill • . m,

- mz

#= @z -mpg # . ( mitmzt 'zm)** : ii.

many. g

or P •

- = - X : p= ( mitmztmz ) x.

0 P M,

+ mz.im/z= ×

Tdef . of generalized momentum

Page 2: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

Helix :

[email protected]⇐ ef

are f- ¢ p=µ→ one degree of freedom .

→ Cylindrical coordinates.

✓ Y Speed of the bead , 0r=O, sy= Rif

T= 'zm(R4e2)g°3 µ= mgcgoz=E=c•g

p=Tyt= in ( Rte ) if ⇒ go = mya ,

Flight ,+ mgc . if eyg

"

= mgc

• se if - *¥og

g.

/" " "

•p=i= math ,→ at { E=

- ,÷egor

fy= - F = m if Rio y is meaningless and E= -

gas expected

Page 3: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

1€, U= tzk -12/ K

,M

M

-⇒ M¥ T= tzmx 't Tspring

K=l ×

mudto

determinespeed of all segments cf the spring

KEEI For den which is a away

from the

( 1

1 11 left end of uncompressed spring :

f n

; \\ "

: y=a . ¥ = al it E),.

. I l '

:

I'

a > j= Eia.l¥

da.ly×

e e

Tgmig = § 'z Media . ( EDI 's Max" { a 'da=j Mya

Page 4: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

T= £ ( mt Mg ) x"2 U= tzkx

'

p=f?f= @+ of)x"

⇒ H=z(P÷m⇒ + tzkx'

0÷f=kx= - f= - @+ Mg ) ;

ii. .

k- x

mt 43

x= Acs @tts ),

w :#mtM/z

Page 5: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

130T= £miittzmig

't

'zmE2U=O

p×=Of = mioi

PY '

- T.yt.mg Le=Zpigi - L = BITE2m

pz=0I= MEat

Ypf,=xe=Em Td×= . p*=o x

"

- coast

g. anp:p;:} kits

z.=E i. I # It

m

oI=( I ,y'

,E )

Page 6: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

l3@ F= - kxxn e KJU ( x

, y ) - U ( o.O ) =

'

zkx'

- #y

L = In it 'zmj2 - tzkx 't ky

p×=f¥= mi; py : T.ft.my

Ff = mi 't my -

' zmii . 'zmg2+ 'zkx2 - Ky

fl = # ePI + tzkx

'. Ky

ZM

OH He x= Aesffatts)⇐

'=E ⇐ If.IE } ?jIIY{y= g. + attire

if = Pen

Page 7: mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M ⇒-M¥ T= tzmx 't T spring lK= × to determinemud speed of all segments cf the spring

13.130€ U='

zkr ? '

zk ( R 'tE )m

|.ge/T=tzm((Rjj+zz)Teonstataz

I L=tzmRif2+ '

zmzi'

-tzkz 2i"¥g¥lpg=mr2gp⇐mE

Tl= ftp.tP¥m +

takeor . onfp,=y=mPfg

q --o==p•y f- f. + wot

£=P÷ng?z=kI=.p:{¥z¥±mz

⇐ z.adfnt.is,