Homework#8
Physics1111
Spring2009
: Physics1111
Home-workSet#8 Solution
Problem1. A work 7q is requiredto stretcha spring2 cm ftornits equilibriumposition'How
N)ch ddditionalworkis lequted to stretchthespdngto 3 ch from equilibdum?
lil
+h" .ltft
aFaen't
I
t 1tlexc
' 'h h f, a-el+6tsn"-f bt,,7tz
+t^'1
'f 't
yeqv,;ttl,
h 4t',kl
"|d
"
I
c2-'. I*
f
f
s+*l ;";( '
e"o'6i1
7o+t"'tu'(
ofuuIc\ '
'ult *rPl
t
t
*fu
.
r
-'
uuo >FX''
t
'^
--
,
"-o-'( l*'rk
tY
.
+r^r+,{f w'k l"+A< 42e^d+#AoLB"
--o
v/,= JF]
^ol w'e'*^ o[4o
,t
Wr,
ue
hto'^
t/,
can
IJ w' Jvile 0 UOfot
k,
4
[,h^r
0
<o
W0
R
(r)
)Fx,n
), tsv:
>--
Y,'
t,'
.-\
'/
.7h" ^llt(to./ wo+ki< +tnrd4l.*
l"'(te"
nu
h,,ro^ wo
90. Altt/= VJr-w" ^
Yf
Wi+6 +4a n"^lut,'
4W=
:--r)W"
2
v
li/- . -::-
,
W"
- x,"
t",,/u ^.ol q/o
= (' -I:X , -t
t /)t4/^
-
-i
ZL
Wa
Homework#8
1111
Physics
Spring2009
Problem 2, A 1.92-kgblock slideson a rough,horizontalsutface.The block hits a springwith a
it a distanceof 11.0cm beforecomingto rcst.Tfthe
speedof2.17 m/sandcompresses
coeffcientofkinetic frictionbetweenthe blockandthesurfaceis /r'r:0.535, whatis theforce
constartofthe spdng?
I^+k^y"6te-,
b"+^a'atvJtQ
l-'<'t7'5'p'*l
,l*e) -z awbJ"
a^An^-a-srru-4:< C.fv,a:,fc
,.5 +he LJeak
- 4"e,tt a^od.en,u4 l"-r
Au.."f b6
a P + ^ t l = ( F ! ^ k ; )+ ( t 4 ^ U ; )
Wnc.-AZ.
l" +t:5 tl''14^. k
' T,
F; -- -z J n
u4
.
-lzrl
7)'-a.tl-/e
L'44!
Ll;
J',
W , ^ c =t j l - l z ;
'TA<w"tk/'-a
)
-ll"+,:""
fn
I
l,\= ti 1 Wn,
C"^A
r.ty,{eni,, 1"'-s
t
tru fct
W^," .f,.da'tho"= - firnf,x
'Tlrn
ltc*-t r
o,n wa(- e- e'yt1 '21^ft"-et^:7
Ll+^ ki
-> lkf=
=,,
\
l 7
{1
-
in -cl"t A*"vbrg.
twn<
)^u"-lrrVr
-t' - !'-0
-x"
,{
t
( t . 1 q C 2 . t 7 ) b O.tttf,1,l)1f.r t)
l<= I;rtT-
( o . t )t
dcruh
Homework#B
1111
Physics
Spring2009
Problem3. (a) ObjectA hasa rrassofn, objectB hasa massof4n, addobjectC hasa mass
kiaetic
rankthemin orderof increasing
of z/3. If all tbreeobjectshavcfte samemomentum,
thattheobjectshavethesame
asbeforc,nowassume
energy.(b) Forthesamethreemasses
momentum,
rank
them
in
order
ofincreasing
kinaic energy,and
D
\A") Nz l<uo'^t
l=m4
:)
1)-- +
ro 2
l<= )^rl" = )^ ( ;) l r
-t
a
" *
lts is +rt v!,(Jt*alif
'{r"n '
ht'{wu^ [<:^e+t<ehe-n o^ol ''io- 'n'
+he tt tms*t|u.- ** +tua cfc4C ua +U *^r,
F
-to c.2ee Lt'a nT+t Af <-oL o!<t '
f
5
^
L
9lq
Unl*^ *".{
3(
5 o .l . * = + ; . V u = DL
#, lr.=!fr
AlY"*'l,
Fu. pq< la, --.>
\b t 1k"""7^2 +\e efuJte',,(Q.
hl
f
/h
= zr'1t< .
1-
14 -- 2w1<
t .
1,./z Co- o L{"n'^ .
t:ac? +he ki^o4t,
( n = 8rl, .
50' .
?" ?o.?u
..-\
/rrl'
"na,5414a4
2
,
(" = 7^l'
.g'4 9.t"rt, l/c
Homework#8
1111
Physics
Spring2009
Problen 4. Choosewhethereachofthe following statementsis hue or false. (a) It is possiblefor
two isolatedobjectsto collide so that all the initial kinetic energyofthe systemis lost. (b) Two
carscollide a1an inte$ection, but do not "stick together"after the collision. Therefore,the
collision waselastic.(c) An objecl at rcst on a slick surfaceis struckby a secondobjeat.After
the collision, both objectsmust be moving. (d) A systemofparticles with zeromomentummust
alsohavezerokinetic energy-(e) A systemofparticles with zerokinetic energymust alsohave
zeromomentuln,
6$'als. yav,,fin offt+dpdi,ult,aeL,/ith;Jk,n;(Atl2pAs,
i{+wc aq^"(--u*
-r
I
|
l
0
I
nt
\q/ Wil
lt:::J
iaet,4t16"4;u:^, +(a^ +t^1u,\l tul ,f +t^,k +'yt".r "*A
h",rea c",1l"flelX
4t 4,,-"t;r. Tl"+. all ul +har k:,,+,,e^e.ant-;l h,*t h-0t.,k,(.
u)
I
u
lb) |T"tu1 V"* hu^uc. 4^r cor(i
s:uaiit
ue^+tnt
a-y'zkt1 e i^th<.(t
c, 6{oern't
i( h* +o hp llo*: r. Tn nay c6r crelle, 4tu @,c l- t eJ
"p n"u'.y
't
e )fu **
le+|rl.b,,'t ane lnk al +,t^,/DA1rt f"^h,9 s/r.*( Cor,y;nr
U
I
U
"],
e'1'rt!) "t*t lo"t i" +\e Co((;q"'\.
(t'fpa
As *" lr^^,lr^t'i{ i' +hzclq. l{ a 7-1"*t1 -ei*1r'<ol;^e'rozcuzs'
{
-
'
]
.
h4"an -t-" cljck, 4 +t^tg*e ua)e,.l"re-^p ;, ;,,1,lJ a+l'-"'1J
4^4 4ai -.v"77ot:'*(c"^et
\r< o+\e,f'rr ^ov;^S
, a.to^ +1.!^.'1 rnc*tt i s
-ts c A*46J A; 4$An1 ef..* u"ute'J+ . A 5:,,,:l-/ ,!*.(r'-\ (ba
Dt<'q w:eU billi*o( b^il, .
U t'i-er;l
A,-t,l+'rq1a;^
.^e o,a*dp{r,-^ l*4(at ?rl-, u,
U
I
o|1"asA'ue
^l
"y^l
lzca-.q k+h
fta\aat/e{,
lfa4t
"F4,
I
gu +wo
6'slliSto-..
)
na-utb, s" +dot,@( raetn2*+"ui1
.oo
,-l
vovt,ff, Lhe1/4a"4,,k,'"t+t<e"efi1 ;e
7p 16
lot
1z/ i
'
*? *7
nu*Lor,.'dt
^r,Xy h* b hQ^ ^'n-A7'a"$'a
Bn*-q' (a^J^"
;l
# "
nf,^
^:14 ,,',;ln,* {7+*
k"-ez+uo
l,'^"(,q
I f^,rf"r4u
aaa611a'1"4i^"U,*"J ^"*r
6a2w.urj. 9;-,* +\c
Vailos
Va,A;clae
no
nsae!++u"r.\\
Homework#8
l1l1
Physics
Spring2009
Problem 5. A small car and a largetruck aretraveling in oppositedircctions,bul with equal
magnitudesofmomentum. They collide, andtheir bumperslock together.(a) Which vehicle
experiences
the smallerchangein the magnitud€ofits momentum?(b) Which vehicle
experiences
the smallerchangein its kinetic energy?
t
(A) -Tte I.+"1 ,"*e"+.-
i
n
/
lh;t t"'/tv\ +q4
.:ll be u-u'"nd in +l"t
"Uit;en'
7,,+ft.;^7,t* P,,f=) al2'=-a(.
o,"t +l^;t
rbt =4" kt1 +' J,:5we
y^4 is to
I
.'^-1"-.
lJe c*t a.J +*"k n*ot b* st'+|"aaV . 4"
^*ta
J
r/^j.
f"4
t'""r'+',^-tr)
u,Avttu,.tt 4-"{*t
t/'
colh'"ta.
tl"
u+J /,1on€"tta
l-f."
+/"7t*ra
c,a(1,:;1",r
-fuO<
is zr," (e7"4 il tpo+r,,
Colhr;"n
4 r,
with r"tu p.^e Veb.i\,
{ta
k =*vo
i, 2ero t-/tc4nza^sslapcky
9o <.r[., o!:nof'9
; k',o(t<et"z-
lSi,* .1"J +o-,,l^^o
oJc.t:t's
l.:,u(t ewfJ. t1r,t6k,fZ_
;n,1;^,1
Ltz gb+;,""'|, lu
lvbl+^#3.
ue sLa thd- +ht ,q16r_ no", ,*
+t^<tyr ;^,{+1K-^4,.eor"d1-Tl*s,
.
--Ele flHKt
o.4S l"<+
12.,"4,,, ?neif.tt 1,.
"h^
caiE,
L,
1111
Physics
Spring2009
Homework#8
Problem6. A 4.30g bulletis fired horizontallyat two blocksrestingon a smoothtabletop,as
shownin thetop figure.Thebulletpasses
throughthefirst block,with mass1.20,tg,andenbeds
itselfin thesecond,
with mass1.80,tg.Speeds
of0.490n/s ar'd1.04nls,respectively,
are
thercbyimpartedto theblocks,asshounin thebottomfigwe. (a)Neglectingthernassremoved
fromthefust blockby thebullet,find thespeedof thebulletimmsdiatelyafterit emerges
ftom
the first block. (b) Find the bullet's original speed.
@) =Ae ncatn(w
l-
o,*t^ ul/;t;u. ie conr-9"d.
4 +b b*ttztls
An"-,'d +het,;{t-l ,.,y
.rA<i^;tJ
''lo'tnt,.a *L
"{
.
l"4r+ is {i-<:
1tr
l; = ^t'/o
bb"A,4" '"-"-t#f*"n^("Q'
+At
*'rt
ol,k,
,r
*r'"^
ft't
!z
A4"^t^6+tz
ba*t "al"<'t';'<b/'oA'"ole+"6'( '"-t''t"-"-f
t
i,
1)n
*/,nn
tfl
W14's
+t^e b*1Lf- j.,* bl*k ff+l"e^ i<
----@
fu,=''lu+^'il'
':ntp
H-0,
-+he monalt+va t4 6u9rvt/
l)o o-ol l)o
o'z
' t".
Fr ' Pf, :> ,"rt"
unkno'"t"'
|
|
= n^2j, +'',t/,
0
.
ef U6' +he frtnr&@
z a+ a t
bl"c4'
w:'h
carl"fus
uuAc^+\z [*lk'(
Ttd
+he b'tttt- Ll*kZ s74e'^ tt ca-srll,|. l**t"h
--@
'f,/
wt co'-1ft
mt*a- Q,+nry.il,-D il, _ !:#/4
= ( rfi5il.
n"^fiurr,
t" +r^r
,^
, 1)t- cft
l"tV
+a / ^/S
f
ffi)C,,,+2,
cbt
tlt = ats r"l
P,V
4*"
b * l b { .L g
to
=
;rttn qf'\o"(ttA (D,
n )t +., ,
-+4-,
vt tc."
,rr(,J
SW
T-J
t4 *#d,
+zr* fffuao,+f)
57) ^l
Homework#8
Physics
1111
Spring2009
Problem7. An artilleryshellofmass10.00kg, lying at reston the ground,accidentally
detonat€s,explodinginto tbreepiecesofshrapnel.Onepieceofmass 2.90 kg is flung in the -x
directionat 20.1m/s,while a secondpieceofmass4.00kg is propelledin the -y directionat 18.7
m/s. (a) Determinethe angleat which the remainingpieceof sbrapneltavels, relativeto the +x
axis. O) Calculatethe speedofthe third pieceof shrapnel.
Mor",tn4,Lv^W;ll bt zerc,
^ t/a/&"'
)Aonc'nt"a ;e
Qu,a-,1;1., ec 1,hr., uea.'s 2o$
J"
I
I' f",.1
A*p,nea
I
a-{ +hQ
t
,*r'"tu^ 9t"-(olbl 2<ro. p-26o*r2+k 't';'*
e-! K n.-z,at"n,
a^1,+tq *a-f pucesA"+o-! gJ
?'aa G
-+lars ,,!aae +A*t +h4 ca-f n"iz(e
"1"*(
+/,t ^",t,.tu^
(
*r,n ntnl
7,"r"
4.r"(
e:
ho,au'-tr'^ cr'-foqe';+
":
') ln,-o ^/ ft, u
?+-"
l,* *
".t'
ry*F'
P,=o )
?u*'1, =o +
= m,tj' 4 t/,r= #lf,
lr,,-(, =2ruda,<
p:l=-(, -->,rzl1 = n,'/, =>?):1.-#ir/.
- r1r-wtz, rlen nt = ta'o't<i
/ocnkd 2,for,l,^#^U = r.,rg.
?tv
i, nd,.blat,l\+^.
U
m,
u,, =#d,
= j$_r.".t ) - tr.tow./s
u'J=
#0, = +I-(/i.7).24,t3,,,/s
,0
^0
tv
c_b.a.fr
+e^I^.*^"ta
*J ,t,,,,t,"*f,*
l:
'
i: TF:.,:,-,r::,,,*.
J;"J vrl*'h +' +Lt +t"td f:xtt
.
r
I
l
^4 q0 . .
+ " ^ 0 = # _- ' tftfl .ir ) = t . f i 1 f= - 2 $ = e z . l '
Homework#8
1l1l
Physias
Spring2009
kg wadof
Problem8. A 0.484kg blockofwoodhangsfromtheceilingby a string,anda 0.0682
puttyis thrownstraightupward,stdkingthebottomofthe bloakwith a speedof 5.58m/s.The
riseabovetheoriginal
wadolputty sticksto theblock.How highdoestheputty-block-system
positionoftheblock?
-flt
1o+k bL4 ;" ^ yl-"t!
f,V:;tt6l,
6;,t[i,;^. tAe *f".-J
nane*i",'t.]
T e- \t co"s.waol, 5r wt ,^
.+
"U 7.A6-il".k
f,rr"
+t< y$X-bl"okco-bo).a
l*
bl '
m{i - Qvt+*,1,?} :}
;"ct-.+rc
ofi Lte
T"l
+U ca/19'.n..
t} =-
hd,'
1",
a
- t,l".k *-bo 's
uln- -+l,p
7*4X
^uovt5 7*d,
+)e ^u.L^,:c^.| ruor6L)\e ,el
*-*,)
e"?2r",t1/'u
*-k.9o
/".t1,a*l *
514+he i,:t,".-!yt.!-l. 'l +u il*kee +14ze,o
".fo*".e
c"-b",;.' o hf,a ( A .
Ltr^p
-tLo_:
E; = 6,
) c n + n ) 1 ) ' =@ + , ^ ) J h
^0L
- \ ,
_/h= _;?
v
::
YA-'r)
z-] tn+t)z
T"-'9. f"rt i^ a( | +Ae n*-l2tnt .
wt
h
(,0.o{t.-)'C5.58)L
.
> t l.bl) (0.oiS t + o.+34)
=-lo.o 2 zlz n
Homework#8
Physics
1111
Spdng2009
flom restat thetop ofa curved
Problem9. A smallblockofmassml : 0.5kg is released
wedgeofmass 10.0kg, which sits on a fiictionless horizontalsurfaceasin Figure P6.59a When
the block leavesthe wedge,its velocily is measuedto be 5.2 r/s to the right, asin Figure
P6.59b.(a) What is the velocity ofthe wedgeafter the block reachesthe horizontal surface?(b)
What is the heighth of the wedge?
lc.) J,'"ceno"t*lczvl.f.*" ,*,a "n +t'pLl"ch-vnfrtr*,
4,lp uo^on!,^ i+ a-snr,reel-7"
-
*f n* '"^
a'Q "^
/24
;,:{rQ roue-(u,-t
w"ty +/tte^ iv zerokca"sr t^
. 9o
[f = (; =>
7
,
h
"fu,&
r.vyJe :
u2 t.\4
1a,], +w"t\
--,;t
5o4a WI^1t '\ w.,r/.
il,=_#o, - Jz_l:t,s.,^j;
=.FiiA
--TAts n<o.e
+L,t
l-<
4
"1y^'tt
tb v.t."; n* Vr "l *,k-t,
*
!"
91* * +^r zeb wl-u 1"""[
4Lp^. E; = 7t.1'-_) kr+${/r
no u.,6 ,!;u.,,(t"^ wt-64 -eo+L, bhrl<.
sp(+4pl_,,.-_,r,(
"*W a-k1,,"4,,e...
= 11 +uy
l1.".rz
, 1", =,a. U,. _. n,SA
'K Tr -- ; l U ' , ' J
uf
9"' ,,lh =f
- \ /
I
t q
U
I
z
-,1,L
---n
n, z,l12 -f-
( t!,'+
|
"z2 )'1I ?/L,
tqt ^n L-t