F h ve i ce_ :l-85_ F o
rm.ula*$
h
e$t
Csnstant l-ineaf Acceler*tign Equatio4.S;
V*vo+at; X=xc+yol
+
fatz; vt-v3=?a(x-xo), X=Xo+$(v+v,)t
Anqular I Liftear VFriqhJg,*;
6=slr; ",=#=v/r;"=#
, &radiai =,jr;61s6ssn1i61
=crf
eonets nt Anqular Aceelcratign Hngptipf3c I
* }at?; n'-*f,*2*{$-{},}:
{.rEa.,o*11{, 0=0o+6,'"1
0=$n+ i{"+c,;o}t
Retatiqnal lnertiq;
|
* >:rnjrf
(point masses)
;
t = 1[r2
l"* * |MR? { solid cylinder),
l"m
{Parallel Axis Theorem); I = 1",
Kinetlc Engj'ovi
i4
=
drn
;MR'
Ang$-[arMomentuu.
i?i
lcm
= MRz (ring / haop)
;
K = |1t.",2 (rotation)
f =-rtxm?; iili =mvr(sin,,l) ;C=t?
Wqrk/Pgwer: 1ry=/rd#;
Sp.nstank.*CM
# =I?
ul
F=H= ",
C"pn.diti"pn:n-fqt$tgtip- F.qqilibriuru
1 rpm = 0.1047 rad/sec
i
=rF(sinp)
lleuderesd law Fpr&Jatrsni ? =
* 3600 = ?n rad
(sphere)
* Mh?
= ,Mv2 (translation)
-+
Torsqe: --+
7=TxF
1 rev
(continuous rna$s distributions]
IF
=0
;
f?
=o
FXN"M
SOLtffIDNS
,o"=. Konn,RD sTF tn,l
Phvsics 185 Exam # 3
Fall 2013
Show All Work in order to receive partial credit consideration.
Keep your papers covered as much as possible,
TURN OFF YOUR CELL PHONE!!!
1. A uniform plankwith a length L = 6.10 m and a weight of 445 N
rests on the ground and against a frictionless roller at the top
of a wall of height h = 3.05 m. The plank remains in equilibrium
for any value of > 70o but slips af 0 < 70o. Find the coefficient
of static friction between the plank and the ground.
I
+
ziraQ
Nf.hb)
I
ZF=o
x
J
0e
'=
l;
lr{ =
Nx
-
rr''',
n66)cDts
(*)cpso = o
+ f{= usq*sry
RorF(
f,= Ncos(9o-ol = NsrvrE
UgL srrrb cuso
;],h
N.
0+
Z[=" + [ + slsrn (qo-d -ng = o
o\
m6- Ncoso
\)H
\/=
s* /,.t=
o
o0
t
(*gL/r^,) srrio coro
Fc
F"
ULdn)pr,- Lsrns.oro]
z2-
Stnb
f'= ffi:
o
Sin o=
-- rnfl- [8tsr,,rB cDSLe
Co-tD
Sin-tzu/
lsr'ip
cr:.ns
L(+-s,rrvcosQ
cosjs)
+
,/it
=
Q
,3+
f
K. srErr/
2. A spool of wire of mass M and radius R is unwound
under a
constant force F. Assuming that the spool is a uniform solid
cylinder that doesn't slip, find (a) the acceleration of the center
of mass, and (b) the magnitude and direction of the frictional
force. (c) lf the cylinder starts from rest and rolls without
slipping, what is its speed of its center of mass after it has
rolled through a distance d?
TAKE Tl+E TDRQTTF ftaau.r fu] ttXts
G^) -il{FouaH
Tl+F forr.rf illAr 15 lrv f,DNrAor
WrTH TFF GKoulrvD
+
p(an) = rpd = (*uf+ HK)d
r(an)= €Mf/c(
+
{= ffi
g- siNcF TF|E S'foor '(0U5' t'9|r110fi sttfltNS,
Jns
a= Ro( :>
(b) Wt+€N rr+F Fr:Kcr Fo,
ftoKt?oNrpl/ TIIF CYLINDFK \OILI ROTr
R)KeftRD AND sD Yl+F l=Rtcr,o.N wru- 6F ,r./ I+r 5i+fl8 DlPFcr/'uV
As
tr
BY NEwroNk e-'d tAuv,
(c) VL rftaoA + V--\m=
\/-lt@
v- 3M
V
W
K,
STEIN
3. A uniform spherical shell ( 1., = 3MR') rotates about
a vertical axis
on frictionless bearings. A light cord passes around the equator
of the shell, over a pulley of radius r and rotational inertia l, and is
attached to a small object of mass m that is otherwise free to fall
under the influence of gravity. What is the speed of the object
after it has fallen a distance h from rest?
,il'
fu,n
WY CoNSER/AXDN
CF ENE46Y
V
AKt A% =o
0
So
[*(A nt)wl + *r*r,'+irnil+
rnflh =
vn
gh
6)(trn)(#)'r *r (ut )^
= *l3M+ %"+rn)
6Y,(Vl1
(-in6h) r
{Yl
t?
+
ernv
vl
=(aM+ Wr'fitr:) vL
o
o$
V:
(eut
6,rngh
3nn
Q
I
3r/rr)
$v
K,
SrEtl/
4. A pulsar is a rapidly rotating neutron star that emits a radio
beam the way a lighthouse emits a light beam. We receive a
radio pulse for each rotation of the star. The period T of rotation
is found by measuring the time between pulses. The pulsar in the
Crab nebula has a period of rotation of T = 0.033 s that is
increasing at the rate of 1.26x l0-s s/y. (a) What is the pulsar's
angular acceleration a? (b) lf a is constant, how many years
from now will the pulsar stop rotating? (c) The pulsar originated
in a supernova explosion seen in the year 1054. Assuming
constant a, find the initial T.
NorE i
| ,trar
:
dauls
d^v
3bS
3te
5d,
X
d_
da
(d Lt)-- + + dq=,dw-4
xEr At
,=
0
V
!t =
oo
G)
I
Slf
(o,o)3)
(1)=wo+d+
hr ., (a) trl,r-, " (uDs
W
,vr)
/cr
dA
\/
/
= 3,l5XlD *(
JT\
= -Tz\E/
E.lT
+5
Jb;(to dv)
l-Jbxr,)*5
lo,
]u,15 x,tr tD s/ }
:--,1^
lL{
.T
+ d= - A,3Xl;q rod/s'
+ e:ffi;-(r"gxff)t + t= S,eoltjos
oK {=(f.aaxtJ'tx 3ol4r
15xtfs
(c) Tt+E ftasA( wAs CKEflTED
+
t= ein
Qor3 ^ D5+)
\€ars
= q51 f EftRs ft6o,
t" (qsq.dr) x('-l#rj')=
3,Oa+xlo'o sec HAvr pArrrt srNcF
(utsffi WAi CKEATFD..
3o @,= ru. + dt - (T)+dt
=
rur=
/a0'8
sc
(r*t+ (*r,3xr;?(3uor*xrD) +
raA/s
=
T,r,^l
eT"
"4
Tt"lF
,11
IIDOE
-\.
-
t,u
-
C,OSA
5e<