Homework#5 Solution
Physics
1111
Spring2009
Physics
1111
HomeworkSet#5 Solution
is trueor false.(a) Ashonautsorbitingthe
Problen 1, Choosewhethereachofthe followingstatements
gavitational
Earth is so much less at their orbiting
the
attraction
of
th€
Earth feel w€ightlessbecause
of staticandkineticfrictionhavevaluessuchthat l\ = 2.0 pkfor
thatthe coefficients
altitude.(b) Suppose
a cratein contactwith a concr€tefloor. This meansthat the magnitud€ofthe static frictional force acting
on the crateat rest is alwaystwice the magnitudeof the kineticfrictionalforce actingon the moving
on a leveltrack.The tensionin th€ couplingbetweenthe engine
crate.(c) A fteighttrain is accelerating
andthe first ileight car would chaDgeif someofthe cargoin the last car were transfer€dto other cars.(d)
on a level track.Thetensionin the couplingbetweenthe lasttwo freiglrt
A fieight train is accelerating
to othercars.
oarswouldchangeif someofthe cargoir the lastcarweretransferred
a normrl force;it hasnothingto do
(a) Fals€:Astronautfeelweightlessbecause
thiy don't experience
gravity
at
their
altiflrde.
When
the
astronauts
are
orbitingEallh,theirnetforceis
with thestrenglhof
providedentirelyby gravity.Theyarein a "freefall", in whichtheykeepfallingtowardtheEarthasfast
them.
as it curvesawaybeneath
(b) Fals€rwhile theforceofkinetic frictionisj = pN, only the maximumforceofstaticfrictioncanbe
writtenasJ{.,"= F,N.Beforenotion, theforceofstaticfrictionli canbeanyvaluebetween0 andf,*"*.lf
to movethe crate,fbr example,
thestaticflictionalforcewill bezero.
no forceis attempting
(c) Fals€rRegardless
ofwherethe cargoweightis,theengineis stillpullingthesametotalweight,sothe
belweenit alrdthe first freightcarwon't change.
tensioD
(c) True: lfsome cargoin the Iastcarwerekansferred
to theothercars,the lastcarwill havel€ssmass,
forceis
as before.This acceleration
Deedlessforceto producethe sl,re acceleration
andtherefore
providedby thetensionit] thecoupling,so thetensiondecreases.
Homework#5 Solution
1111
Physics
Spring2009
hangingover a pulley;see
the systemknown as Atwood'sMachine(two masses
Problem 2. Consialer
Example 6-7 in your textbook). Assume the two massesn r andrn2are not equal (a)
nr andzz are increasedby the same multiplicativefactor (in other words, eaoh nass is
Suppose
multipli€d by the samenumber). What happensto the sccele@tionof the system? (b) Again, suppose
by the samemultiplicativefactot what happensto the tensionin the rope?(c)
,, uid -, un increased
Supposezrl aadzr, are increasedby the sameadditive factor (in other words, each masshas the same
amountof extramassaddedto it), what happensto the accelerationofthe system?
rQ)
--l-le
pf +U n*a"t in ot lt.Ji
oaaalal-1-v't
Vt^J:na is
J
fl,-ft1t
-
n
-nr,+".- ^
V'J
r4t
01f
ij LeL h"4it azeinaeq,p)td ^
^"n
-LL-4:' , n, -->
f., ., -u-s f -,
-LLe^
tht-hr
a'=
t44t+tta I
rL > ---.-t
hQ
I
-t!nA'*,
i^
{td
TI
l'l J--'
,&
H t
I
J+t
l^1
V\
LJ
yop4 i5
I
n,, -,
ulea
ig
\*Vu'
*Ldt +t, -t^t,.,-
\<l/
* j^'-
I ^ Cfe'&
1o
a.rc iqrtcnuol
-Lu y'autu,,t(y''v-t'uq
lJ"o'ttz, qb &./.v"
yz<v,., ^l+ 5/..9
tL& 'ha4j
t4t2
go
u.t"o- llp
n,
te:.crr"s,J
I
m, o^ol uu a,,z ^/"1""11,,1a n
"ts n,
1'6, +ut a4'b#,'*'
H
----:.--- > : ^
,., +hza
y-t (^) uz kn
a.,ele,rah;.
tC ) l"la
+ +,
f*
e _
_
1-- n' ( ^+J
p"^
///'.//'
'--1-
hrt"-*
Q n . + * 2 7 1 r r t 6 n)
:_=_:-__.___'q=
Cm ' { - ) + ( n , + - ) d
Ilt r--ln1t
74,+u11..t7ti4
-* qz^
htt )
r4tlo,
mv)
vtl?tt
Homework#5 Solution
1111
Physics
Spriry2009
Problem 3. Three identical blocks are attachedby ropes over a frictionless pulley, as shown in the
diagam, and the systemis releasedfrom rest. Rankthe magnitudesof the following forces,from leastto
grcatesf the tensionsin the ropesA and fs, andthe weight tr=mg of one block. Be sureto note if any of
theseforcesare equal.
#
,A-,";;';;"
At-col- nacta- QF,fk:
f-
*(.
44
f
-:^/
'4'l' A +L ui+-t^^J atp vll u'z[<tft
a.rle *Jl hth +u oa"l"'rlt /"-t-,
=n^ => Ta- ''/'(l+a)> 'n = vl -0
tF=Ta-ni
na':
rte
t'y
J U"'h
la +te b,4*''St'+-t'
u
= ntf 'a) <:\3 = t"'t -e
.T =r9. fs =na =) Ttz
5". P^V 1*"t''eQ a-JO 1
a
1 , ,a W
u/e o-f
!
tL' tuk"'d2
l^
r^
la
t4
4
rlq
Problem 4. Two blooksare oonnectedby a string,as shownin the figure below. The smoothinclined
andtheblockon the inclinehasa massoftt r =
surfacemakesan angleof r= 42.0owith thehorizontal,
themassofthe hangingblockthatwill causethe systemto be in equilibrium.(The
6,94kg.Calculate
pulleyis assumed
to be ideal).
-Btc^-tt
+t" ,f.k^ tt h
f
l;Ltiln , Wa l'no".s
+1,"f rfil n414'/
bl"?k ;t ,r,<4ld"dt4l.
-rla
bl"'han *-" a tyt'r.
let r! 1,7"^sfue^'er"
Auatl6 6 du c-.,l",h
\a./al^*,
-
lt
r
nt.
loi F'.4
fzfr,,r = rn,A-l
*\< 1",< t-n|;n
Y J
/
,lw4:m
T=."J - -O
^-z
n1,d2r.: O :7 T:n,f ,.:,9 -O
>F,l =N-nl7e)0 2,nta):c)
+ M= n,V.--A -_^@
zlt,x
= T-/,1'9e,'"9=
U
Ito^ y"-i'n"s O ^l
ntf =n'f a,0 :)
0-
h/z aq
/y:r
mz-=m,1.yB
+tt h'^"v4 nu,*, w.
ll"6;^
f
,*a
l*y
c|.,e"
,ont ,,,
f*
= m,ax =o :>
l r
I
, rn,=((.?+kl)sa4zo
t
v,(
-
Homework#5 Solution
Physics
1111
2009
Spring
Problem 5. The coefficentof staticftiction betweenthe floor ofa truck and a box restingon it is 0 39'
The truck is traveling at 86.0knvh. whal is the leastdistancein which the truck car stopand ensurethat
thebox doesnot slide?
, +)z b"t is al*
ir.le ern" ttu"k le /e.cvlwal"'6
't'A^t^
;s 1'7i"'+
7t'vdze+)te
duJ-,$6.T1.4.A;(Frc
loobr*{ oq
.t e hx, wd:cApeus +. +Aaoyp.tb
l-r
d;r'.6'^ "[ +ke *tut'k nok'"..
o.*.+ \ +.*'. 11l&v. )c.,
lh< mal:m*l"*;Llo
+,.^"- =l.M
^nca thts
:knA
Jr.,"4:" lt"udcc
A
Y
( N = n X ; n c h ac.se )
+tLe (,ttfel.u! ) aue'leto{','-
"l -u b'x.
ma =^ /,1"43=> a= -/k0 .
I ht0
au"br-Ana clo"s b,4t kx *1, + r*o[ /ou^ +o fzq( -f,"'r +/'a' '''f"^l tftl'
a^. ntQ l' ,ie^ott<1"o'^
Ne *u"(un
4"
l,
c.l"J<ft 'eat ol;",>Lu^-1
I
t ,'o
= ,l,L 1 ra( ax), Jon "u+
^/e
{; = 7t:y,-/d=23.t1
a =_N0
't * /
AX =-^
ui
2a
,1Y.--;-;-;-
'r" a
=
(.s.al-rt'
2 ( 0 . t 1 ) (f . s t - / s ' )
4
Homework#5 Solution
1111
Physics
2009
Spring
Problem 6. A ski that is placedon snowwill stick to the snow.However,when the ski is movedalong
the snow,the rubbingwarmsand pafiially meltsthe snow,rcducingthe coefficient of liiction and
promotingsliding. \iaxing the ski makesit waterrepellentand reducesfriction with the resultinglayer of
water.A ;agazi;e reportsthat a new t?e of plastic ski is especiallywaterrepellentandthat, on a gentle
skisto
time from 61.60r with starrdard
200rl?slopein the Alps,a skierreducedhis top-to-bottom
pair of skis
acceleration
with
each
ofhis average
40.00; with thenew skis.(a) Determinethemagnitudes
6(b) Assuminga 4.0' slope,computethe coefficient ofkin€tic friction for
.A€€€l€.eti€{-.'\.itho+
eachcase(Old modelski coefficientof friclior andnewmodelskicoeffic;entof friction).
y"bte";a t:-y'y F'te"{;es'
\0)"tlt.fitt 7."( el+1"tr
vka4
( tve,t+l^z ltopl..zwe,t
/o*" t'ht el"p L, a^
"';+t4
,-" ca! =il , 6,-l '+Q +o<J u^e t. orz ta- 5/u<
"l
I w ua:'d:
+Q a.<a(&/
X= il:t + )a+' 4
zl
_
:>a=Z
"
)
a)
lb ) tte
fl^t
t = 1);6+ !+f L= Ja( z
( ott: a =
n/Ez2
7;:,, _-a tor4
:) 1
|
t t
t,tud) qtdlrq'
lr42
t
I v*" <r,!-o'L
-l;;;Jfl
1 e , -t 5-_
o ^ /:_!_)
( a1t,,a1t- -[)-
6^d +hr cdrr'Jt^,,&
agFft_ ate (L^sn
1""<z ,&,/as ia eaoLlwu(,V^ p12.
=na'
z F = n X t ' " " g - l += ' h t t : ' q - / { l x
a\
4 ,'.
t,ke
."b/Q
f
-^-D
>fi = M- nlo.r€ = nat
1 , ^ c eA 2 = 0 , 5 " , Z - F y . - / t ' n f . " e z r 1 a 1= o ) N > n n u ' . P
nf^'"^O 8. af4'6^69. uttf,a
l,I
n6a't -nf ^'.0 ' Pu
O
/..tax +
fth9-
=) ilr.
fuAc"e ' a*
-a" .=+a,g
f,^'a
3; a /VV'6 ia +A4 0 ,J*
,("r t), otl o-l ,r{:;::,*
q"*.-@
A^ CJ^-ultLt"! c0"if':"4 of *a er"l*J d ne'"tsk;t a 4 :
ttll, ltr^+4^$0"
##.r, -FGff,
lvew.
-_
f r f-4"1+.0'
's' 12v
=
( 7 E t) C 6 ' v o
0 . 0+ + 4
--"(t
6"
-O
i,,ze
Homework#5 Solution
1111
Physics
Spring2009
across
the floor with a sfap that is at anangleof
Problem 7. At the airpoq you pull a ,7.I-kg suitcase
(a)
47.1" abovethe horizontal. Calculatethe normal force in the strap,given that the suitcasemov€swith
oonstantspeedandthat the coefficient of kinetic fiictioD betwe€ntie suitcaseand the floor is 0.352.(b)
Calculalethetensionin liat strap.
o(+ws;t"*
1il Tlz ?t6,i2.c^A!r- hl2 /'7"*
a* thq' otrf('
.r
n't*
lr"^ a,t ly^* r a b- u.ttit /o".
1*t"^t Srcw
-{-t"s al*S x aJ
I
J;rua'n- :
ZF =Tc"rs-Jv>Ta;,4- li,tr =-na.r
4)
: . 8 = T e r . r r i v ^ n J- n a )
4^c2 tto t'(6
^1,'A y /tte.ul",a*4 +tt v"t,^f,
"t7
y ltu"^na ia /m4o*(, 10, at-a)=o,
T
4s___
w1,40
Fo- {t{ ahve a.1"-t"'^. de u^ te'(:
^:JT:.":^_!
,.;::^=
(e
_i"
_?..
r._
{*',o**,
'T-lkM
G-s-,
tvb4:l^h
-bL;..I+t4,vA 7 *a e|^ao- @
-Tr:.0:-Bf -.(/ =>
-> /=
#!ra
;
-2r' :)
-/v/
lr.Ma.a.F=nf
mi
l-1llcr*0
?v4-"1;^ t\t rtu^h,.rc
h,etl1 pr= 1vtkd)(ftt 7c? - t^t olM
t|._. = /----1
IlJ'
o
!!=4
'*(07t2)ta^tt\lo-
tb)
I he +.ba4:r^
a'^l'?aol+'a"Q'l
-7=
h fuv 7,7.r-a .!#
t,: T=Q.o:)L!-')
crya7.l"
=wT4
Homework#5 Solution
Physics
l1l1
Spring2009
of 4.25kg each,corneoted
by a shing,slidedowna rampmakinganangleof
Probfem 8. Two masses
mr atrdlhe rarnpis 0.29.The
32' with thehorizontal.Thecoefficientof kinotiofrictionbetween
ofthe acceleralion
coefficientofkinetiofriotionbetweenmzandthemmpis 0.14.(a)Findthemagnitud€
of the masses.(b) What is the tensionin the strinS?
+t^t
/uy," {a ,*L 6l,A
@) Ttr.)*yar,.,t tfia elt"ws
t'x*-b/)
al*'V -u. +^*,'-,n"^-(|nq, ta*'("("^"| l-,0,o"( f,,,t,*4,t*ro.
LLr,".d4t 4 cAosr 6*,1,i/1 af,len, hle ca^ wv,'l<o"t t ue -fqe
c.z*ft*l+
l', l,U^ At-i+
1lvr- blo.F
t , t ,tlt
. - 4< >t :' F t-
- t + n ' t a , ' "-P' J ,= n ' a "
=n'a,
I7or.r,-n,fle'>o
a
l t '
f- /'l*hr" li
r,' '2'""6
-, t. -,,",
l4Fu'w, ,"3c-g- r,a,
eau,v1a4
a-) s'^<6,-6 / l T y = 1 1 6 = a )
7"^,*
;":;u:^:;:f
Jn |lvooll,t.,
n.s,
I,v 1,,t, blaAs l"wo +ts fa*e o.,.ahft.l,bna
1,. t + illlAe- f, : t\q
--l + r4Jt:u0 - -f =h^
"
*O
-O
AJd0 a*dO. u< c^^ : 2Tl^ip-"f,-l,.saa. -O
Stt
1t.l +wo
,o: $.4,,ut =p,-6*4
cJ^(&l-b1
l^ctn-t'"'", "f,r.
-1"
PtI +,il t,+'z7n,'{t"0. ," ",-y!'
zna =.zn|a:o0 ' /^, nf .ct9 1-t,nla.,g )
/k*,
->o.=re'oYt*,
t+'l
=l '/v'' /)""14"0
2rta=zrt\-
p- 04 tp";n;c,>B
o,ff,o,f
pn ,n +t, nn*b.r,: a 4f6D,,
(f,rt)/,e,2"
r", _
tbt fr"^ "1"4b-0. weca.^ :
f
3.41 n/ro
l--n"-htt\0+1, : n^- r,dr,,g1 [r nnc"ef= ,4(a+AArB+f,fc--o
S
= 4, r L ^ u'(fa)t; tz"+..(t 2 aUa,ezz
")
=Fe;71
#5 Solution
Homework
1111
Physics
Spring2009
Problem 9. A blockwith a massof 2.91kg is plac€dat reston a surfaceinclinedat anangleof45 1"
aboveth€ horizontal.The coefficient of staticfriction bets,'eenthe block and the surfaceis 0 440, anda
force of magnitudeF pushesupward on the block, paBllel to the inclined sltrface The block will remain
at rest only ifF is greaterthan a minimum value,F.i., and lessthan a maximumvalue, F *. (a) Calculate
F-.. (b) Calculate
4."".
(tt) \+ v. i'lh.l ?"a1.. s, ilwk c+ ,tt watl e[la l"a +b alo4,
"ll
,'",t P;,t1 4u rl"yt. 9o4 ,,c.o1yttr-1t,
n,Lrnn*n (
s,-d+Latf,to.
$ ,iJ^".o".f'.f tns nalJ 6 V"7* bbokn't"'-lt+ it sa;llw.A>t el,k lo*^
pf 4'.t +byr t't"|" v7 4" bt'ok ^Jg.
a-Jcr-&.
+*
{rlro" ",rl(ld,t
flo ft,r A,{Jr"y'^ *+ rf .ts'.l,aafrAtovnb"ul" *l;" r,"*-,6.
3*,,5 "" +t" d*s.?^a-din,la tl.+'-.+," r,^ "|.(*as ;^ x.1dnd*l'
N
zQ= n3e;,0-{+- 1.,,n-nax
zFy = N-un co,e= ha9
Jt"to 1'lo hln',l<is n"fn"b{, , 9o Qr = AJ =O
'l +rut-r<
<
coSt( Q-11 ,h64k p- {, -T^; =--o
-14e
41"4. ?te
M'nnc*t0 =gt
furn nely +, 94 a^ &, ,\axira'6
9o, W,^ =- r",J1.."
A- {> = raXr.,0 _
/o\,/ 1,./r 0
'
in nv-bt+
:
p =,,,/ (r."A_/^,a,ra)
ltr^/:- t,/r:.p - /),tf ?^,e
,-
F"n=YL2)(rot*/', k:,ca,t"-Q
'too)ar+t.,.
).
(b) tLv
rf -, yut^ *ii+*
"^
,r^
,tnrt.,
ad +\' at'f
+' op>+'h+k -4u^..
*
"*';I[,!':,f,|,to'
v./w "f {t..u = p, n,
k*r. ;1-,11tf,,r,up+ao4"pt.^r
.Np,,"r
{1o60_
lvtc v:tt.bn+[, (Vlat Fn"
1t,.0" _{*lurU
'u^"x;'-^
ht^<i''^^r=t^''^-.tF4,f/^^a"</-y-<.
,::^"^
2la - n6 tt p a {r*^, -T^^, = r4ax :o =S
fi,*= n6a.rg + /^, M
:> T-*= rld^rP1y'"ql c+ro= tyd (t,t +
f l^rccre )
=.,
rt *,s"tf s,,,,
ot,r "+ | o.44.)c^-4r,I, f
!-U1
=Ei-'JL
Homework#5 Solution
Physics1l l l
Spring2009
Problem 10. Two blocks,stackedoneontop ofthe other,slideon a fiichonlesshorizontalsurfaceThe
surfacebetweenthetwo blocksis rough,however,with a coefficientofstatictriotionequalto 0.52 The
topblockhasa massof 3.0kg, andthebottomblock'smassis 4 4 kg. (a)Ifa horizontalforceF is applied
to thebottomblock.whatis themaximumvalue-Foanhavebeforethetop blockbeginsto slip?(b) If the
thenthemaximumvalueofI'
massofthe bottomblockincreases,
lty-^+ $ l< eco\"f 4o +-o bl""ks(-,*h
utt tk {ta-6!
flr 4"-k l '- +.f '+ v.) a.tt sl'.-" o'( ttrt*. A/o{t <Le+
t'f-r
*\a dt.;.ltr.".f+u" {,r*'u j-< ^a.,t o- +tt +,ybl*h
tu +).t ton. o(irn
o4 +,, ^yyl;J .{_* F
fo""t,'d"+"tn
et" +to h+k*
S*
"f
zF,
H*lt . 61a a*{ra
c,^ wr;tq J*,n ltt
Pus .n +u! -Lol?b/*h i" x -,ol X ,/,t "'t,t,...
= t =- tahAy
>Fry= M -r,3 - ^,aJ=o + M - n,j
),aa -LAt.upbl."h l;.4
$lv
';lf
to, +=,PM - f+vtft :fltrAy
"+
tt'fft'',4\e
--'\.:t'
c,.^ h
Viren
i(tuori,,n^
/')
Jiwa no tut4ln ,,.oa'r^Mveau +ro +wo b/-A., +t1
Oacbt^,(tl-, A, ,t,ol^
44^, jan,":(it
el^.lr( L".a +b s^ae-
b;1:
^ .- a=
| =(-,+r,.1
+6
,t"te Ar..-a, .Zf^".(r',^(D c^^ 22 tov,ll+"
"+
u e ' r t '-Ar r , * _
:>
F
- _l , J ( n 6 r n s )
(3-ki*u.*o)rffi
l.,t\, y^ i^ thtn*Lectf =Q,t^2rt,tt)
/Voln , A'""t no rt'1."1"u4v"g4"^
n"il;*
+or,** ::7: X":.:#' r#*:m,"
+\4+.
\' '
l("A
prfr4,\
(n, +tb") . t"./e.k6o,!, tl o;+tr:,^",<t t,,reo5a4.
442_r
F = l^.f