Equation Sheet for Final Exam - Rutgers · PDF fileFinal Exam Equation Sheet Physics 116...
Transcript of Equation Sheet for Final Exam - Rutgers · PDF fileFinal Exam Equation Sheet Physics 116...
Final Exam Equation Sheet Physics 116
tαωω += 0
2
21 ttiif αωθθ +=−
tt ifaveif )(21
ωωωθθ +==−
)(220
2if θθαωω −+=
ωrv = αra =
Rolling condition
22
21
21
CMMvIK += ω
ωRvCM = αRaCM =
θsinBABAC
=×=
Fr
×=τ prL
×=
dtLd
ext
=∑τ
2ii rmI ∑=
Idisk=(1/2)mR2 Ihoop=mR2
Krot= ½ Iω2
ωIL =
ατ Iext =∑
ffii II ωω =
0=∑ extF
(static equilibrium) 0=∑ extτ
)32(95 −= FC TT
KTT C 15.273+=
kTKaverage 23
= Ideal gas
nRTNkTU23
23
int == Monatomic ideal gas
NkTnRTPV == KmolJR ⋅= /314.8
molemoleculesxNA /1002.6 23= KJxk /1038.1 23−=
MRT
mkTvrms
33==
)()( ifif TTncTTmcQ −=−= mLQ =
RCV 23
=
RCP 25
=
!
"U int =Q #Wdone by gas )( ifisobaric VVPW −=
)ln(i
fisothermal V
VnRTW =
ch QQW −=
h
c
h QQ
QWe −== 1
h
c
h
c
TT
= for a ideal cycle
h
cideal T
Te −=1
TdQdS r=
∫=Δf
ir
TdQS
)ln(i
fV T
TncS =Δ Isovolumetric Process
TmLS =Δ Phase change
)ln(i
fP T
TncS =Δ Isobaric Process
VM
=ρ
AFP =
1 atm = 1.01x105 Pa == vAIv constant
=++ 2
21 vghP ρρ constant
submergedfluid gVB ρ=
3310mkg
water =ρ
32.1mkg
air =ρ ( ) ( )φω += tAtx cos
ωπ2
=T
Tf 1=
mk
=ω (spring)
Lg
=ω (pendulum)
( ) ( )φωω +−= tAtv sin ( ) ( )φωω +−= tAta cos2
2
21 kAEtotal =
221 kxUspring =
Fspring=-kx ( ) ( )vtxftxy ±=,
µTv = (taut string)
( ) ( ) ( )tkxAvtxAtxy ωλπ
±=⎥⎦
⎤⎢⎣
⎡ ±= sin2sin,
kfv ωλ ==
λπ2
=k
Tπ
ω2
=
( ) ( )tkxstxs ω±= cos, max
Threshold of hearing: 2
1210mWIo
−=
⎟⎟⎠
⎞⎜⎜⎝
⎛=
0
log10II
β
24 rPI av
π=
fvvf L ⎟⎠
⎞⎜⎝
⎛+=ʹ′ 1
Listener moving toward source.
fvvf L ⎟⎠
⎞⎜⎝
⎛−=ʹ′ 1
Listener moving away from source.
f
vvfS ⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+=ʹ′1
1
Source moving away from listener.
f
vvfS ⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−=ʹ′1
1
Source moving toward listener.
fvvvvfS
L⎟⎟⎠
⎞⎜⎜⎝
⎛ ±=ʹ′ ffbeat Δ=
)cos()sin(),( 0 txkstxs nnnn ω=
If both ends are open or closed,
2nnL λ
= , ,...3,2,1=n
1nffn = , ,...3,2,1=n If one end is open and one is closed,
4nnL λ
= , ,...5,3,1=n
1nffn = , ,...5,3,1=n