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Ch 5 Homework
Name:
Homework problems are from the Serway & Vuille
L0th
edition. Follow the instructions and show your
work clearly.
1. (Conceptual questions 6.)
A skater is standing still on a frictionless ice rink. Her friend throws a Frisbee straigit
the following cases
is
to her. ln which of
the largest momentum transferred to the skater?
(a) The skater catches the Frisbee and holds onto it
(b) The skater catches the Frisbee, holds it momentarily, and throws it back to her friend.
Explain your answer.
l'a'*fr r"5 ftrrtf er r'"raf '
c han6o tn +A4. lrorllftt4r"l A{ +AoSl<^t'er i-s fha- t6ne m*,'aitaol*
5o , th,
nllrtction *o
or tAL -^ro,,ent'utc .,han$e of ft'e Fris f,ee , b*L afytor;+e"
T^ th;s
co'se
)
t"tol
2nwlnex{*4fi't of tAe Frisbee a*ol *i'v
;*n *f +k{ [r ' s {'r'e ,
tsknter
I sdfr*^or.
zl,,,1
l-t"f- Ae^., +
+t"€ direc4
?.o =/
- 'Fr,rirc
T here {we , c*te-$ ) i s the-.l^,Eies
Sihrc tk mlmtnLqrn oF fhe Vriikpe changes
s
4Fr,,,r,o =
-l\"r*tr,
'
cc"se CL'),
rQ i rt
,-{"hP*
(^r{ U) 14 Pr,ra*.I= l^Trr-^y;
*a,a
2.(Problem 1)
Calculate the magnitude of the linear momentum for the following cases
(a) A proton with mass equalto 1,.67 x 10-27Kg, moving with
P='7n1^
a speed of 5.00
x
106m/s.
I
(b) A 15.O-kg bullet moving with a speed of 10.0 m/s.
f = mV
=
l5,oVff x {o,ou7t
| 5o
Yt^/,
(c) A 75.0-kg printer running with a speed of 10.0 m/s.
P- %tw
W
(d) Theearth(mass=5.98x1024kg)movingwithanorbitalspeedequalto2.gBxT}am/s.
D%V
l-
r t;' Pfth/s
3. (Problem 15)
The force shown in the force versus time diagram in the figure below acts on a 1.5-kg object,
i
1
l
4
o r(s)
(a)
Find the impulse of the force.(Hint: The area under the curve is the impulse)
-2e
|
= F'/)L
.1
47
jLl
l
l= S t"t
(b)
Find the final
*,:,,
oY
2{2
8 ky u1t
of the object if it is initially at rest
7=
=
(c)
I
I
aP
?n.)il
on 1r+
ca
Find the Final velocity of the object if it is initially moving along the x-axis with a velocity of -2.0
m/s
T:
=
ff+=
)
4P
h',
lff -
]
m
W
*{;
?N
V;
4. (Problem 18)
A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 0=60,0" with the plain of the wall. lt
bounces off the wall with the same speed and angle (See the Figure below). lf the ball is in contact with
the wall for 0.200 s, what
is
the average force exerted by the wall on the ball?
'%=*...*
"&-'---- A
ti*.{}"#
';;.ffi
o, t,":'r'^al anx,lc
or " {;a^l t'"61e
,fu1 ,, rt4otss of 'fk batl
1r' '' initiaL lfaloci(7
'
-4''---dY"'
t'tr'"
-'" htl.tt
/
tq
1
*#-'
1
'
dm*
FIGIJHE
[ ; n^t v'locilf
t ', +iws ;n
1
86.?E
Tsntori wi tA tt{ wiil
P; : inil;"l '1^,nalq"'
f+'. hral
4^or€Trttcrl-.
(a) Define a coordinate system on the figure above and label all physical quantities in this problem
using letters you choose.
(b) Calculate the difference between initial and final momentum of the ball in the x- and y-
directions.
X-direction
value(Kg m/s)
Variable
Y-direction
va ria
x-component of lnitial
momentum:
momentum:
?nV; Jin A;
/1
x-component of Final
p.
,rt
1rcomponent of Final
momentum: P^
momentum: D
tf t'
,ty
-?q1l,5rn0"c
't'
Ap,
Pt*
-
Ap,
?;x-
f=
t
F
-+
F
I
=4
zs
?r.
t o hls * $ tn $oo
b,
Px
4
xt
u
+
: i 5 2,0
7(
4 P*il
4?* 4
:v-
Ti (;n0s
-
?r?
b Pt-- ny.w{eS -
{} l} o ';, * 'tu11f )'^ 8+- 'Nl"t/ i;,'()^
7,oov
m1t; b 50 ,
P+t
Find the average force exerted by the wall on the ball.
= - L/
m/s
VA
t'component of lnitial
l-i L
(c)
ble
\,,1
a
n
+ny?6so;
5. (Problem 21)
High-speed stroboscopic photographs showthatthe head of a 200-9golf club istraveling at 55 m/s just
before it strikes a 46-9 golf ball at rest on a tee. After the collision, the club head travels (in the same
direction) at 40 m/s. Find the speed of the golf ball just after impact.
(a) Draw a diagram and label all physical quantities
.t +t b'il
'l1r', noss
/Ylc I
l*ny
using variables you choose.
,f
t'eCl,a5
1f, . r^;tinl rrof+lcclus
/lf1 lTi,,'t tf
o{ thccl*L
/
?
1fi^:Ttitiilr\^,,
t/i1: FinJ rrat
\^,t
[r"
65
fif = 4ou/5
^ls
(b) Calculate the initial mbmentum of the club and the ball
P;= M'\;
: ll
(c)
+
"aW^
Y6h/s
Find the speed of the golf balljust after the impact.
D:
l1
ll
l'y't-y, =
o-+
Pr
ffirV+
r muWr
n"v) /^,
J= 6\,)h/s
I
4r=
?,
6. (Problem 25)
An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line
loses its attachment
to her spacecraft while she's on a spacewalk. lnitially at rest with respect to her
spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to
propel herself back toward it.
(a) Draw a diagram and label all physical quantities
in this problem using letters you choose.
,
__ E ,oo%/s.
q
---?
A-)
ULr
M=1.
0
<_
ri
A
trd=
n
u
thc
mAi 15,okb 'trl,.t s of
/'vistJ af *I"e
TtL= P 'o?.fr'
f
y,
o,st ronaqt-
f*-"
f-r
auf
ffErT
sYet} of +'*"
{, = 1
[t = fi.loon/, gPwd ut' *he f nolc.
gtl
(b) Findthespeedoftheastronautaftershethrowstheoxygentankintermsofthevariableyou
choose above.
lrf
P;
o
(c)
Using numbers
*ntn
,Oor", calculate the speed of the astronaut.
,V^= l,L8
M/s
%*
W
(d) Determine the maximum distance
she can be from the craft and still return within 2.00
min(amount of time the aii in her helmet remains breathable)
iil=
[*'t
(e) Explain in terms of Newton's law of motion why this strategy works.
pa'erd\ $uYre
tan16 e*ert's $ov(E ot1 *te
tt-e
[46{ior'},
farqit
tla
se1
$orte lushrs
6 ltfsnnu-l' bcck C Reo(1ior' )' thi s rQo'crion
Bt
/
he
lrew
(on's th;rol
bovl, to the
r
lad, i+ tl's astrar**t
sPru&cfaft
,
7. (Problem 32)
A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision,
the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without
breaking a bone is 4500 N. lf the impact time is 0.100 s, does a bone break?
(a) Draw a diagram.
!
fo"$&/s
5'o-O
'
tu/5
r t--+r tr ;
o--,
/L
*
/\
l-
l.
m
1$, o
lt1
"
s u*v/Srrn*ir''8
rr pfr #< tir<oterl
1f af *tu 5pa{re"J'
=ttf =E - $.ootrty, fin^,( rref
t = r. ro05 tl* {rrt' fin'e
'Vf
tl
(
,t c\ slatef
tuo**
0
=
:.4; = to.aw1, i,rit;uJ
'%u r'S
;r*7
'yyq
5t'e'fer
f
$*
(b) Calculatethe initial momentum of the ice skater moving at 10.0 m/s.
rtr%1
*
;*1
l-.."t
(c) Calculate the change of
\ K"1tr
the momentum of each skater.
I
t)
ft4
Zl"--
?n
=
t",
Yr^
uf
?nff6
zq s Kft,'4
l;-gYakr
L
4P, = ?rf fv
= mvf :J
(d) lf the impact time
is
0.f00
s, does a bone break?
T- F't r
!+
AP,
lr
;;;"2
F< bSaoN,
,or*Aeir
bones c^Yo;nf,
8. (Problem 38)
Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic
glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the
right at 5.00 m/s as in Figure (a) below. After the collision, the orange disk moves in a direction that
makes an angle of 37.0'with the horizontal axis while the green disk ma[<es angle of 53.0'with this axis
as in Figure (b) below. Determine the speed of each disk after the collision.
';
o
I
tJ*
ft
5,00in',i
____l
)
I
t&
*
W.
\'-l
lr
{
(b)
(a)
(a) Define coordinate system on the figure above and define variables.
of
M; = S,ooh/* tnitinl rx
1ff)
=
O.aoh/S i-ni'f,iat
*Ae &ronge oitslc
u o* *k $r{.rn lir k
f ino"( T o+
l'14' gre'tr a{irft'
1.
0l,a.fi88 dtsg
0, = }|,7,0, Fiaal ''l,.tle 0+ +k*
t
rytf --
0r= t7,o
.tn
.
P,;
Pu^
Pr(
?er
s# i/.t 6r*ev' dtlk
'o'f
*a*55 $ f' e' I r's k6;
6h3rls
A'tsV
5{ fha \l''anYe
A;s L'
+aovt1ntwrvr o{ tAe )rcert
tiol
Lri
lh;tto-l
L
fi
p.; r, rl
nar
ruatt\ont*rrt
iltncv.,rPat'a,,t
oronf,& "litA-
"f 'he
f,;sL.
*/na
*r.ol$e!Y1:euftI $f
trreen
(b) Write x- and y- components of initial and final momentum
X-direction
Values in terms of variables you
Variable
In terms of varlable you define.
Y-direction
Values in terms of variables you
variable
define
define
lnitial
ln itia
D,
lOrL
nn
P2;*
ltei
I
n
p
'a^V
D
o
I Qru
o
atr
Final
Final
I o*t
mfit C"5 0
Pg+*
ott l|oe @5 0>
lJ-
P"f
r
+n
F
-
7n+y
%t
S;n g,
"t'v1Sg S;x
0,
(c) Writetheinitialandfinalkineticenergyintermsofthevariablesyoudefine.
lnltial Kinetic Ener
?"
Final Kinetic Energy
,-
%r
2-
^%,
amuor
(d) Determine the speed of each disk after the collision.
= ?f t
=>
P^U Pr* , +>
Pr,
Ye^=l.L+
Meth.
-rrov.,
/hAT,;
=
O :
.,nafo.rc'singl
il
-bron
',
1f,+
--
S"tbs+itwle
1'ra+
rrn eg.
Q
I
I trbrt;tule e6@ tnto *bO
,, %^'= (#wf.* nir'
I u;= (,- *)qr"
trn0z
ffi, -@
ey@ ;** Qbq
n"t
lin or 1J7.,i 16+
r& =
r
Gr0r
- til'0rt trr0r(69r
F
t {r= ,+t:# *@
gr
%@
O
lt e rAo6l 2
l.
?0n O &@
co5
- ^\*tin01 -@
=) lnv,i=*"^wt' ti*'1i
t )( Ggg >'2 4; 4
''\Io1 li n0t-$+ S''0, * OP
\foy
+ h|),pC'rg* -O
/11^1fr+$5&t
,,1-'-.-
gin 0>Toi
= 6c0,fraOe
I Sin01cos0t
|
,',
-
Both
ffiwf*=ffiu;
Yelkls
5how
'tk
lffie,lffi*
'ant'
6nSwe(
'
9. (Problem 40)
A bullet of mass m =8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a
table of height h = 1.00 m. (See the figure below.)The bullet remains in the block, and afterthe impact
the block lands d = 2.00m from the bottom of the table. Determine the initial speed of the bullet.
il*uar
p6.4*
(a) Define a coordinate system and'label all physical quantities using letters you choose.
O/t
> 8,oo
*
in as1 o I 'the b'tllel'
",^^ts al rk hlock
lt1
111og
=
-h t . oo 'rq h*i6tt ,1' +Ae +aSla
4n
t2
,
,l
\o
',
-J
\
\
61,.::..Ooivt f;stane +he blocl< lrarcle/l'
.f^ot*,{lntun of +he la'alle{
D
lb
+le B lock,
lo
'irwvr?n**b1 of
of +be butleL
14
S pt t at
1rB
t p*& , oS tte B lock.
(b) Findthespeedoftheblockandthebulletafterthebullethitstheblockintermsofthevariable
defined the problem and variables you define.
p., =
t&
PF
+ Fe; = ?a; + PrS
nTur + t'l?lrl{ (\r= \r =w
o
=
mfa;t
, 5in1E
tAel Yove
(**
ta)u+
m\; a
+ogetfier )
Pa;
qyt
1ft=
| <-\;
.rnt4
(c) Findthetimetoreachthegroundintermsofthevarlablesdeflned.(Hint: theblocklsfree
fa
lling)
- h)*t -; -*t
t=
(d)
c,
"t'
ah
2.
Find the distance d from the bottom of the table in terms of the variable defined.
t
\f+
OL
.yn
. ,..?ht M
U,,
Dfu
{;r
,l
I
(e) Solvetheanswerfromthepartdfortheinitialspeedofthebulletandfindtheinitialvelocityof
the bullet.
\;
'
on+N I *-
.M {-Vh
: l+z m/s
10. (Problem 57)
Two objects of masses mr = 0.56 kg and mz = 0.88 kg are placed on a horizontalfrictionless surface and
compressing spring of force constant k = 280 N/m is placed between them as in Figure (a) below.
a
Neglect the mass of the spring. The spring is not attached to either objects and is compressed a distance
of 9.8 cm. lf the objects are released from rest, find the final velocity of each object as shown in Figure
(b)
,f}
L.
(a)
f,
1)"
I
i{-
-*"-"-"--*-----&
re
Im,t
u.;t
a
4
(b)
(a) Define a coordinate
L=
system.
t fut=
C , {){trT'tr}
o,9[PX-
)'lnn,
=o'flky
(b) Write down the initial and final total energy.
lnitial
f,r
o
Final
E
f,, +
PEs
)
K E,*
+
E
lpLrf
o
I
l<
I
v
t'
l,
x' 2 ion ,t,'*
I
h jlr,'*
I
hrt--
F'f'= h,v3+ *-f-- -e
* *.'t6*
ts
4,
(c)
Find the final velocity of each object using the law of momentum conservation.
t
p^
,f
o
= -M,V, +mrw
0
.r
1f,
S"rblti t,{{e
F*'
€b (,
qnt
fr'
= TT,-*E
i
nto
e'*
ffn'artvrl
n'9
,r:
fr:" !-
Yz'
O
W1
1t, ffi:+'rq?
r{4
e+91 irr{,a f e Q
Subs{i"[
m11
!:
4f,
=
'
n, m u+ fnf
1---^
*-0
LW
ll
r'fi..
r-,^ Q &$
Wt=
l,'/lm/s
Tr2
l,0q h/s
ta
to
-Y
v
olireclhn
S ire c"tton