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