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Problems 333

*41. Figure 10.30 shows the shape of a nitric acid (HNO ) mole- z
3
cule and its dimensions. Treating the atoms as particles, find
the center of mass of this molecule.
O

y

0.141 nm
y
H O N 130° x

0.100 nm x
0.141 nm
FIGURE 10.32 Three square pieces of sheet
metal joined together at their edges.
O

FIGURE 10.30 Atoms in a nitric acid molecule. *46. A box made of plywood has the shape of a cube measuring
L L L. The top of the box is missing. Where is the
center of mass of the open box?
1
*47. A cube of iron has dimensions L L L. A hole of radius L
*42. Figure 9.13a shows the positions of the three inner planets 4
has been drilled all the way through the cube so that one side
(Mercury, Venus, and Earth) on January 1, 2000. Measure
of the hole is tangent to the middle of one face along its entire
angles and distances off this figure and find the center of mass
length (Fig. 10.33). Where is the center of mass of the drilled
of the system of these planets (ignore the Sun). The masses of
cube?
the planets are listed in Table 9.1.
*43. The Local Group of galaxies consists of our Galaxy and its
nearest neighbors. The masses of the most important members
of the Local Group are as follows (in multiples of the mass of
11
the Sun): our Galaxy, 2 10 ; the Andromeda galaxy, 3
10
11
10 ; the Large Magellanic Cloud, 2.5 10 ; and NGC598, L
9
8 10 .The x, y, z coordinates of these galaxies are, respec-
tively, as follows (in thousands of light-years): (0, 0, 0); (1640,
290, 1440), (8.5, 56.7, –149), and (1830, 766, 1170). Find the
coordinates of the center of mass of the Local Group. Treat all
the galaxies as point masses.
*44. A thin, uniform rod is bent in the shape of a semicircle of radius
1

R (see Fig. 10.31). Where is the center of mass of this rod? L
4
y FIGURE 10.33 Iron cube with a hole.
*48. A semicircle of uniform sheet metal has radius R (Fig. 10.34).
R Find the center of mass.
x
O

FIGURE 10.31 A rod bent in a semicircle.

*45. Three uniform square pieces of sheet metal are joined along their R R
edges so as to form three of the sides of a cube (Fig. 10.32).The
dimensions of the squares are L L. Where is the center of FIGURE 10.34 Semicircle of sheet metal.
mass of the joined squares?