mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M...
Transcript of mi )gX= - Rutgers Physics & Astronomygershtein/382/homeworks/hw04_sol.pdf1€, U= tzk-12 / K M M...
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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
Helix :
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
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
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
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 )
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
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,