9 Two bodies have undergone an
elastic one-dimensional collision
along an xaxis. Figure 9-31 is a graph
of position versus time for those
bodies and for their center of mass.
(a) Were both bodies initially moving,
or was one initially stationary? Which
line segment corresponds to the mo-
tion of the center of mass (b) before the collision and (c) after the col-
lision? (d) Is the mass of the body that was moving faster before the
collision greater than, less than, or equal to that of the other body?
10 Figure 9-32: A block on a horizontal floor is initially either
stationary, sliding in the positive direction of an xaxis, or sliding in
246 CHAPTER 9 CENTER OF MASS AND LINEAR MOMENTUM
the negative direction of that axis. Then the block explodes into
two pieces that slide along the xaxis. Assume the block and the
two pieces form a closed, isolated system. Six choices for a graph of
the momenta of the block and the pieces are given, all versus time
t. Determine which choices represent physically impossible situa-
tions and explain why.
11 Block 1 with mass m 1 slides
along an xaxis across a frictionless
floor and then undergoes an elastic
collision with a stationary block 2 with
massm 2. Figure 9-33 shows a plot of
positionxversus time tof block 1 until
the collision occurs at position xcand
timetc. In which of the lettered regions
on the graph will the plot be contin-
ued (after the collision) if (a)m 1 m 2
and (b) m 1 m 2? (c) Along which of
the numbered dashed lines will the
plot be continued if m 1 m 2?
12 Figure 9-34 shows four graphs of
position versus time for two bodies
and their center of mass. The two
bodies form a closed, isolated system
and undergo a completely inelastic,
one-dimensional collision on an xaxis.
In graph 1, are (a) the two bodies and
(b) the center of mass moving in the
positive or negative direction of the x
axis? (c) Which of the graphs corre-
spond to a physically impossible situ-
ation? Explain.xt12 3(^45)
6
Figure 9-31Question 9.
p
t
(a)
p
t
(d)
p
t
(b)
p
t
(e)
p
t
(c)
p
t
(f)
Figure 9-32Question 10.
x
t
tc
xc
A
B
C
D
5
4
3
(^12)
Figure 9-33Question 11.
x x
x x
t t
t t
(1) (2)
(3) (4)
Figure 9-34Question 12.
Module 9-1 Center of Mass
•1 A 2.00 kg particle has the xycoordinates (1.20 m, 0.500 m),
and a 4.00 kg particle has the xycoordinates (0.600 m,0.750 m).
Both lie on a horizontal plane. At what (a) xand (b) ycoordinates
must you place a 3.00 kg particle such that the center of mass of the
three-particle system has the coor-
dinates (0.500 m,0.700 m)?
•2 Figure 9-35 shows a three-par-
ticle system, with masses m 1 3.0
kg,m 2 4.0 kg, and m 3 8.0 kg.
The scales on the axes are set by
xs2.0 m and ys2.0 m. What are
(a) the xcoordinate and (b) the y
coordinate of the system’s center
of mass? (c) If m 3 is gradually in-
creased, does the center of mass of the system shift toward or away
from that particle, or does it remain stationary?
••3 Figure 9-36 shows a slab with dimensions d 1 11.0 cm,d 2
2.80 cm, and d 3 13.0 cm. Half the slab consists of aluminum (den-
Tutoring problem available (at instructor’s discretion) in WileyPLUSand WebAssign
SSM Worked-out solution available in Student Solutions Manual
- –••• Number of dots indicates level of problem difficulty
Additional information available in The Flying Circus of Physicsand at flyingcircusofphysics.com
WWWWorked-out solution is at
ILW Interactive solution is at http://www.wiley.com/college/hallidayProblems
y(m)x(m)ys0 xsm 1m 3m 2Figure 9-35Problem 2.AluminumIron Midpoint(^2) d 1
d 2
d 1
d 1
d^3
y
z
x
sity2.70 g/cm^3 ) and half consists of iron (density7.85 g/cm^3 ).
What are (a) the xcoordinate, (b) the ycoordinate, and (c) the zco-
ordinate of the slab’s center of mass?
Figure 9-36Problem 3.