sec.9-2 TheCenterof Mass
'1 Figure9-36showsa threeParticle system,with masses
mt = 3.0kg,m2 = 4.0 kg, and
mt = 8.0 kg. What are (a) the
x coordinateand (b) the y coordinateof the system'scenter
g*'
I
e"''
I
prob,em,
l"*:::.1'lji,',ili::iir:l Fis.s36
massof the systemshift towardor awayfrom that particle,or
doesit remainstationary? sstrn
3
&)
Xcorn =
E xlm ;
i .,
*
b)
a4
fn
l! f"r,
r5
j
=
;-Z,Si,*' fr-
r
g*.^: -J'
F
mL
irtt
z)
t)
*lS lct
Xcronn=
)
.\
t )[o^1+(\b5\
F-,)* t".il(,d
c [o
=
i5
)
$alr,
ril('^)]
,^)
+G
[t.-dto*)+(qr$('
= ft vt^
tnuernre-.Qr
+L
crt'{.-
{owo*-& vn3..4 What are (a) the .r coordinateand (b) they coordinate
of the center of massfor the
uniform plate shown in Fig.
9-38if L : 5.0cm?
+
rha:: w.tl
mbe.
Q,= 6f
A.= r.li
$r= $f
AY= qL'
i o , =z z f
o:t
Xorn
:
r
[-'q
*qf[.r.)+rf
,r*L]= .*[,*,,1
[-q
r-t},.Leu'
*..[..]l=- f u =
=
$".r'
-.,*t'!
- lcm
ll
+qf ( f . ) * 8iz ( -{z +,if(-r.!
#[ r * ( : . . )
*'*[- 'tJ
=- $ r
= - 3 . ( t' 4 2
f r".l
-6. Fi*ertu9-31 showsthe dimensionsof a compositeslab; half
fhe slab is madeof aluminum rdensity: 2.70 9cm3) and half is
madleof iron (density : 7.85 :m3). Whereis the centerof m,ass
-s
ofthe slab?
/
>_,^---___
l-;/rz.uo.'n
,,, (.th
vf\,xr * fiz xz
( 3, + 3 .
)
(ar,
=
Xs
a
X .-nn:
2 ' ? D- T ' 8 s
?.8S+ ?-f o
{M
.1o Two skaters,one with mass 65 kg and the other with
rnass 40 kg, stand on an ice rink hold,ing a pole of length
10 m and negligiblemass.Starting from the ends of the pole,
the Skaters pullThemselves along the pofe untiftheflE-eer
How far doesthe 40 kg skatermove?
Y\\,2H0 K;
Sgsler-, ts
hz:65 q
,,oldt.,O+
iS
X Crrn
l-€rn4141
trr +k
E4r.g
tocd,i,^
Xcr"r z
*^*l
,#.f^,*,
y'c,ovn*
tn5 tr,r'ra(tq
;
o
,to(0ttt ,,)l?
_JI.
r{o+65L
"J\.'"/.+l-A *ri, +q
ovv'_
bJl"'A +k s4r\
d
6,2 t,n
-
hJ r^ i
6.19
xr+l q x{=!, Z,".
m = t{o+6s
+- [ro+cr)
)
=)
L
r)
lc .
24
..{5 A shell is shot with an initial velocity tr6 of 20 m/s, at
an angle of 0r: 69' with the horizontal. At the top of the
oTequalmas5
inio two fragmEnts
trajectory,the shell
"*ptoa"t
afterthe
(Fig.9-a5).One fragment,whosespeedimmediately
explosionis zero,falls vertically.How far from the gun does
that the terrainis leveland
the otherfragmentland,assuming
that air dragis negligible?ssm
Fig. g-4s Problem15
Tk
*l^
rn^ss {otl*,
*nr 6,*^
a.l,olruf"{h
flarr
*;{[
Ltr:
d
n Fz
vo. 8rn z0o
q
o
x --
Ourn
T{ v.
o\
$ +t nqsso^L t^p "r[ **r^, +t"^ {L
ull*.
q
,^f ,4
oA
lJ\^^d1
) X,,,,^^
.rL
xr^lrxrJ Lt
'l
ar-
+ \.;lnab z j
+
(*)'*