First considerone-dimensionalcollisions. Sincetotal linear momentumis alwaysconservedin
collisions,nearlyeveryproblemsolutionbeginsby writing the equationfor conservationof
linearmomentum.Thereis only one suchequationfor a one-dimensionalcollision. Always use
symbols,not numbers,evenfor given quantities.Make a list of the quantitiesgiven in the
problemstatementanda list of the unknowns.Ifthere is only oneunknown,the linear
momentumconservationequationcanbe solvedimmediatelyfor it'
For two-dimensionalcollisionstherearetwo linear momentumconservationequations,one for
eachcomponent.Selecta coordinatesystemandwrite the linear momentumconservation
equationsin termsofthe masses,speeds,andanglesbetweenthe velocitiesanda coordinateaxis.
Questionsand ExampleProblemsfrom Chapter 7
QuestionI
Al ice boat is coastingalonga frozen lake.Friction betweenthe ice andthe boatis negligible'
andso is air resistance.Nothing is propellingthe boat.From a bridge,someonejumps straight
down andlandsin the boat,whiqh continuesto coaststraightahead'(a) Doesthe horizontal
momentumofthe boat change?(b) Doesthe speedof the boat increase,decrease,or remainthe
same?Explain your answers.
(.)
XF.,t,*=ot bP-=o
^*'*
Problem 1
A 0.150kg baseballis droppedfrom rest.If the magnitudeof the baseball'smomentumis
0,680kg m/sjust beforeit landson the ground,from what height wasit dropped?
b" bdl +^c"'\-fvp rw'.erx"+'ftnrr
) fl\
) |t"fi 4;J Jn" ,*Wdl
to$^;,l #' 9\i'4t^t
uap .e""^r,.a^t^"hta
t - l, 5 J q / s
O-tsoP7
V" = Dn/:
V=-4,53nfs
v*= V"'*).o(y-y.)
Y,= 3
vt=
Y= O"t
A, = - 9.Xo,/s^
40
)o
..b
?.o (_y,) -
yo
I
\ Jgra A
""t4"Zl^X;/,
',
i
S^^tt-;,)' ,I.'^rJld'^A
= -u/ao
= - (-q.st,/t)Zgr."o,,r1 -----) Yo= l,o5tq
Problem2
A 5.0 kg cat is running northwardat 4.50 m/s, while at the sametime a 20.0 kg dog is running
eastwardat 3.00 m/s. Their 70.0kg ownerhasthe sarnemomentumasthe two petstaken
together.Find the magnitudeanddirection ofthe owner'svelocity.
-)
4
"-^,
I'1'>unl5
-*q.T' ^n^'.
(
9x= O
),vl
W
)
@;"r.
= t o..Kr,,r/s
fu)e A^-a ?x=Nv, = (Ao"orxX3.oo,f5)
1
t*,
)
?y=hVy=(E.or2)(r.sonls)=)a.Syx,
11oo',mq -tra^o,&,
D,= Go_oyzrls ----)
-ao..",., .r{\rrvntyJFnl uJl -!r"^-a
)
Vr=Py'.=
I
p u = A l . 5 K en / a
X!q*
60'oY6'q,/s
= O.75?,,r/s
, 70 . o p 2
V, = Pr/, = _3h:[ = o.z^tntfs
'l0,oYg
l'
V = ,*/V'i.v, = oo9A./s e= f^n-,(+r)= AD.s.
Problem 3
A 0.14 kg baseballmoveshorizontallywith a speedof 35 m/s towardsthe bat. After striking the
bat the ball movesvertically upwardwith half its initiai speed.Find the direction andmagnitude
of the impulsedeliveredto the ball by the bat.
\--.,
I r,t.5l'ls
o ------)
?Sn/s
-
l-
|\:
--+
e'
M"4^'41,'.
1\)t*it!rra "r:z^tth
aulll,
M"u
o -^
-v"*
.^
^.J-l
J ttvurl
tte
"
o . l ' -l c ?
Vr* - 25nfs
ufx
- u\l9
YD Y
= o"lr
Y $.'
-4,9 Ns
- l?.5nis
rJ*Z
A..t5 l.\s
{-
-f l'rr
Jx +JY
1,.^.
rlzn,.-^,rJ.
I C"l,1Ns) +(a'1)N5/
{,
A
(, =
=
5.5NS
b^ (*)
Q
\---/
<
q2o
1 .J.J
t
T
--
,t I
- a b , br D
Problem4
A truck of mass104kg is initially traveling at 35 m/s when it hits the brakes.If the brakesare
appliedfor 2.0 i, what is the averageforcerequfuedto bring it to rest?
ra = lojKg
'
ttlo = 3 5 -n, .l .
f
,f,n"l
--i
rv,avefi*n
)2t,yr-e'
*wq
---)
^r/J L
rc\V.-nV
_T.
V+ - L/rq/S
r/
P']4'!,t\',
I
75f : ].os
l-^A.=(
o
--1
F",ant - -.",4
Rr =
-+
ltA Vo
AZ
'I
= -(lolYs)(:s./s)
a.Ds
= '-'l;?g*
/D5 N
Problem 5
Two blocksof massesM and3M areplacedon a horizontal,frictionless
surfaceasshownin the figure below. A light springis attachedto oneof
them, andthe blocks arepushedtogetherwith the springbetweenthem
A light cord initially holding the blockstogetheris bumed;
compressed.
after this, the block of mass3M movesto the right with a speedof
2.00 m/s. Find the speedof the block of massM.
'l
@,
r)
^-)
10,V,{ + t{)+v;{
?t o
-t
fn,\/
+
lr l1 VyO
--1) .
--= Vao
Vo
\
10,il4* rnodl=.o
+(
(am)qa.oo*is)
M
--a
VrJ.= -f,oom/s
t@
zQ
Problem 6
A l0 kg block is slidingwith a velocityof 5.0m/s to the right on a
frictionless lurface when it explodesinto two pieces.After the explosio4
pieceA, with a massof 7.0 kg, is traveling2 rnls to the left asshownin
the figure below. Find the velocity of pieceB assumingthat no massis
lost in the explosion.
I
let=lo K+
V..= + 5.o*
pwn cd M-Mhrb d6^il\2,^fr;t,",,t,.P, =
[
nnv-irt\.4 = 1.q
4a",.0:
nq= ?.ofg
-i
---i
Vo = -J.o,.,/s
VB
= lnvo - t0*V,r
mp
lfla = 3'o Fg
Vu = ( loFtXs.o",/i)- ("t.oh)Ga-o-lr)
V"= (
(3i &)
\/
vB
--
\r
dl"5
n
I
t)/5
Problem7
A 0.150kg projectileis fired with a velocityof+715 nr/sat a 2.00kg woodenblock thatrestson
a frictionlesstable.The velocity ofthe block, immediatelyafter the projectile passesthroughit,
is +40.0 m/s. Find the velocity witl which t}le projectile exits from the block.
1u!t
--)
Ve,o"r=o
pfl
l-qb= O. l5of+
ro
' ' b l . c X- 2,,"oDH
t t2 Fl'
Y E t"or,
o
i7
v
-
v Br.I,
{
L,f
Vu1.1={ o m/r
Z E"t='
-->
o---+ {a=?
f,=f"--;
* No-*il-r,r
= lr)04,*
fqJon
Nr,*fi''.
q ,o-
fnb
(
--t
;
t(
lf\
' ' b ' r/
b,o
/!9r,a<Vgr,.x,4
mb
= 10.6"1E
vb,f
( o. t5Dfe)
Vu,f - l?q,rF
P=p
r{
lo
z.O
DoVt,* *,Dgo.,{,*,
-o
--)
ProblemI
I-nthe frgurebelow,block 2 (mass1.0kg) at rest on a frictionlesssurfaceandtouchingthe endof
an unstretchedspringof spring constant200 N/m. The otherendofthe springis fixed to a wall.
Block 1 (mass2.0 kg),travelingat speedvr = 4.0 m/s,collideswith block 2, andthe two blocks
stick together.when the blocks momentarilystop,by what distanceis the spring compressed?
-,oA;" frwJ P\opb,a ,, tt ,wv""t"r"a 4&/w14
/,\^In C)^4*4 to
,\^yLl m.rft ,'-ta
^JJA'J),9]ur<
)
Problen 9
A completelyinelasticcollision occursbetweentwo balls of wet putty that move directly toward
eachotheralonga verticalaxis.Justbeforethe collision,oneball,of mass3.0kg, is moving
upwardat 20 m/s andtheotherball, of mass2.0 kg, is movingdownwardat12mJs.How high
do the combinedtwo ballsofputty riseabovethe collisionpoint?
to, . = a . o K g
et
io
-l*n
1r=3
l?-",ls
I
?o.r/s
(-
Y=Y
rt
cau,-o^^,r#'^ 4d \1.211v4'lul'1):
ri\
tP
--t
-)
( rrr +r"nr;V+ = $, V' o * fOnV"o
n- 3"DKz
Va
-
. *5
__>
r a t , V , u* O t V r o
(m, " r'1")
Yo
\-
/ , d , ^I t
o\
..'
o^ls
vLvj"t, (r-1.)
C)rn
O =vi?ey
/
q= -7,Tonlgt
Y'
v"/ac
('7,^r/5)^
f
:-----
g Cq,xo t"1/5'
)
ftn- J-AA*;'**tr
t /" "€jl4
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