b8 b8 b8 b8 b8
b8 10th Edition By Resnick, Walker and Halliday
b8 b8 b8 b8 b8 b8
b8 Chapters 1 - 44
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,Chapter 1 b8
1. Various geometric formulas are given in Appendix E.
b8 b8 b8 b8 b8 b8 b8
(a) Expressing the radius of the Earth as b8 b8 b8 b8 b8 b8
R b 8 b 8 6.37 b8 106 m103 km m 6.37 103
b8 b8 b8 b8 b8 b 8 b8 b8 b 8 km,
its circumference is s 2 R 2 (6.37 103 km) 4.00104 km.
b8 b8 b 8 b8 b8 b8 b8 b8 b8 b8 b8 b 8 b8 b8 8
b b 8
(b) The surface area of Earth is A 4 4 6.37 103
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 5.10
b8 b8 km2.
R2 108
km
b8 2 b8
b8
4 4
6.37 103 km
3 b8 b8 b8
(c) The volume of Earth is V R3 1.08 1012 km 3 .
b8 b8 b8
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8b8 b8 b8 b8 b8b8
3 3
2. The conversion factors are: 1 gry 1/10 line , 1 line 1/12 inch and 1
b8 b8 b8 b8 b8 b8 b8 b8 b8 b 8 b8 b8 b8 b8 b8 b8
point = 1/72inch. The factors imply that
b8 b8 b8 b8 b8 b8 b8 b8
1 gry = (1/10)(1/12)(72 points) = 0.60 point.
b8 b8 b8 b8 b8 b8 b8
Thus, 1 gry2 = (0.60 point)2 = 0.36 point2, which means that 0.50
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b 8 gry 2 = b8 b 8 0.18 b 8 point 2 .
b8
3. The metric prefixes (micro, pico, nano, …) are given for ready reference on
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
the insidefront cover of the textbook (see also Table 1–2).
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
(a) Since 1 km = 1 103 m and 1 m = 1 106 m,
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
1km 103 m b 8 b8 b8 b 8 b 8 103 m m
b8 b 8 b8 m.
109
m106
b8
b8
The given measurement is 1.0 km (two significant figures),
b 8 b 8 b 8 b 8 b 8 b 8 b 8 b 8 b 8 which
implies our resultshould be written as 1.0 109 m.
b 8 b 8 b 8 b8 b8 b8 b8 b8 b8 b8 b8
(b) We calculate the number of microns in 1 centimeter. Since 1 cm = 102 m,
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
1cm = 102 m = b 8 b8 b8 b8 b 8 102m106 b8 m b8 m.
b 8 m 104 b8 b8
We conclude that the fraction of one centimeter equal to 1.0 m is 1.0
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
,b8 104.(c) Since 1 yd = (3 ft)(0.3048 m/ft) = 0.9144 m,
8
b b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
1
, 2 CHAPTER
1
b8
1.0 yd = b8 b 8 b8 0.91m106 m b8 b8 b 8 m 9.1 m. b8 b8
105
b8 b8
4. (a) Using the conversion factors 1 inch = 2.54 cm exactly and 6 picas =
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
1 inch, weobtain
b8 b8 b 8
6 picas
b8
= 0.80 1.9 picas.
b8 b8 b8 b 8
0.80 cm 1 inch
cm
b8 b8 b 8
b8 b8 b8
1 inch
b8 b8
2.54 cm b8 b8
b8 b8 b8 b 8
(b) With 12 points = 1 pica, we
b8 b8 b8 b8 b8 b8 b8
have
b8
=
0.80 cm 0.80 1 6 picas 12 points
cm 23 points.
b8 b8 b8
b8 b 8 b8 b8 b 8 b8 b 8
b8 b8
b8 inch
2.54 cm 1 inch
b8
b8 1 pica
b8
b8
b8 b 8
b8 b 8
b8
b 8 b8
5. Given that 1 201.168 m , 1 rod
b8 b8 b 8 b8 b8 b 8 b8 b8 and 1 chain 20.117 m , we find
b8 b8 b8 b8 b8 b8 b8 b8
furlong
b8 5.0292 m b8 b8
the relevant conversion factors to be
b8 b8 b8 b8 b8
1 rod
1.0 furlong 201.168 m (201.168 40 rods,
b8
b8 b8 b8 b8 b8 b8 b 8 b8
m)
b8 b8
5.0292 m
and
1 chain
1.0 furlong 201.168 m 10 chains .
b8
b 8 b 8 b8 b8 b8 b8 b8
(201.168 m )
b8 b8 b8
20.117
m b8
Note the cancellation of m (meters),
b 8 b 8 b 8 b 8 b 8 b 8 the unwanted unit. Using
b 8 b 8 b 8 b 8 the
given conversionfactors, we find
b 8 b 8 b8 b8 b8
(a) the distance d in rods to be
b8 b8 b8 b8 b8 b8
40
d 4.0 furlongs 4.0 furlongs
b 8 b8 b8 b8 b8 b 8
160 rods,
b8 b8
rods
b8
1 furlong
b8
(b) and that distance in chains to be
b8 b8 b8 b8 b8 b8
10 chains
d 4.0 furlongs 4.0 furlongs 40 chains.
b8 b 8
b 8 b8 b8 b8 b8 b8 b8
1 furlong b8
6. We make use of Table 1-6.
b8 b8 b8 b8 b8
(a) We look at the first (―cahiz‖) column: 1 fanega is equivalent to what amount of
b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
cahiz? We note from the already completed part of the table that 1 cahiz equals a
b8 8
b b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8 b8
dozen fanega. Thus,
b8
12
1 fanega = 1 cahiz, or 8.33 102 cahiz. Similarly, ―1
b8 b8 b8 b8 b8 b 8 b 8 b8 b8 b8 b8 b8 b 8 b8
cahiz = 48 cuartilla‖ (in the
b8 b8 b8 b8 b8 b8
already completed part) implies that 1 cuartilla =
b8 b8 b8 b8 b8 b8 b8
b8
1
b8 cahiz, or 2.08
48
b8 b8 b8 b 8 102 b 8 cahiz.
b8 Continuing b 8 in b 8 this b 8 way, b 8 the b 8 remaining b 8 entries b 8 in b 8 the b 8 first b 8 column b 8 are