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Chapter 1
Systems of Measurement

Conceptual Problems

*1 \u2022
Determine the Concept The fundamental physical quantities in the SI system include
mass, length, and time. Force, being the product of mass and acceleration, is not a
fundamental quantity. correct. is )(c

2 \u2022
Picture the Problem We can express and simplify the ratio of m/s to m/s2 to determine
the final units.

Express and simplify the ratio of
m/s to m/s2: s
sm
sm
s
m
s
m
2
2
=\u22c5
\u22c5= and correct. is )(d

3 \u2022
Determine the Concept Consulting Table 1-1 we note that the prefix giga
means 109. correct. is )(c

4 \u2022
Determine the Concept Consulting Table 1-1 we note that the prefix mega
means 106. correct. is )(d

*5 \u2022
Determine the Concept Consulting Table 1-1 we note that the prefix pico
means 10\u221212. correct. is )(a

6 \u2022
Determine the Concept Counting from left to right and ignoring zeros to the left
of the first nonzero digit, the last significant figure is the first digit that is in doubt.
Applying this criterion, the three zeros after the decimal point are not significant figures,
but the last zero is significant. Hence, there are four significant figures in this number.
correct. is )(c

Chapter 1

2
7 \u2022
Determine the Concept Counting from left to right, the last significant figure is
the first digit that is in doubt. Applying this criterion, there are six significant
figures in this number. correct. is )(e

8 \u2022
Determine the Concept The advantage is that the length measure is always with you. The
disadvantage is that arm lengths are not uniform; if you wish to purchase a board of \u2033two
arm lengths\u2033 it may be longer or shorter than you wish, or else you may have to physically
go to the lumberyard to use your own arm as a measure of length.

9 \u2022
(a) True. You cannot add \u2033apples to oranges\u2033 or a length (distance traveled) to a volume
(liters of milk).

(b) False. The distance traveled is the product of speed (length/time) multiplied by the
time of travel (time).

(c) True. Multiplying by any conversion factor is equivalent to multiplying by 1.
Doing so does not change the value of a quantity; it changes its units.

Estimation and Approximation

*10 \u2022\u2022
Picture the Problem Because \u3b8 is small, we can approximate it by \u3b8 \u2248 D/rm
provided that it is in radian measure. We can solve this relationship for the diameter of
the moon.

Express the moon\u2019s diameter D in
terms of the angle it subtends at the
earth \u3b8 and the earth-moon distance
rm:

mrD \u3b8=
360
\u3c0\u3b8

Substitute and evaluate D: ( )( )
m1051.3
6×=
=D

Systems of Measurement

3
*11 \u2022\u2022
Picture the Problem We\u2019ll assume that the sun is made up entirely of hydrogen. Then we
can relate the mass of the sun to the number of hydrogen atoms and the mass of each.

Express the mass of the sun MS as
the product of the number of
hydrogen atoms NH and the mass of
each atom MH:

HHS MNM =
Solve for NH:
H
S
H M
MN =

Substitute numerical values and
evaluate NH:
57
27
30
H 1019.1kg101.67
kg101.99 ×=×
×= \u2212N

12 \u2022\u2022
Picture the Problem Let P represent the population of the United States, r the rate of
consumption and N the number of aluminum cans used annually. The population of the
United States is roughly 3×108 people. Let\u2019s assume that, on average, each person drinks
one can of soft drink every day. The mass of a soft-drink can is approximately
1.8 ×10\u22122 kg.

(a) Express the number of cans N
used annually in terms of the daily
rate of consumption of soft drinks r
and the population P:

trPN \u2206=
Substitute numerical values and
approximate N:
( )
( )
cans10
y
d24.365y1
people103
dperson
can1
11
8
\u2248
\u239f\u239f\u23a0
\u239e\u239c\u239c\u239d
\u239b×
×\u239f\u239f\u23a0
\u239e\u239c\u239c\u239d
\u239b
\u22c5=N

(b) Express the total mass of
aluminum used per year for soft
drink cans M as a function of the
number of cans consumed and the
mass m per can:

NmM =
Chapter 1

4
Substitute numerical values and
evaluate M:
( )( )
kg/y102
kg/can108.1cans/y10
9
211
×\u2248
×= \u2212M

(c) Express the value of the
aluminum as the product of M and
the value at recycling centers:
( )
( )( )
dollars/ybillion 2
y/102\$
kg/y102kg/1\$
kg/1\$ Value
9
9
=
×=
×=
= M

13 \u2022\u2022
Picture the Problem We can estimate the number of words in Encyclopedia Britannica
by counting the number of volumes, estimating the average number of pages per volume,
estimating the number of words per page, and finding the product of these measurements
and estimates. Doing so in Encyclopedia Britannica leads to an estimate of
approximately 200 million for the number of words. If we assume an average word
length of five letters, then our estimate of the number of letters in Encyclopedia
Britannica becomes 109.

(a) Relate the area available for one
letter s2 and the number of letters N
to be written on the pinhead to the
22
4
dNs \u3c0= where d is the diameter of the

Solve for s to obtain:
N
ds
4
2\u3c0=

Substitute numerical values and
evaluate s:

( )
( ) m10104 in
cm54.2in
8
9
2
16
1
\u2212\u2248
\u23a5\u23a6
\u23a4\u23a2\u23a3
\u23a1 \u239f\u23a0
\u239e\u239c\u239d
\u239b
=
\u3c0
s

(b) Express the number of atoms per
letter n in terms of s and the atomic
spacing in a metal datomic:

atomicd
sn =
Substitute numerical values and
evaluate n:
atoms20
atoms/m105
m10
10
8
\u2248×= \u2212
\u2212
n

*14 \u2022\u2022
Picture the Problem The population of the United States is roughly 3 × 108 people.
Assuming that the average family has four people, with an average of two cars per
Systems of Measurement

5
family, there are about 1.5 × 108 cars in the United States. If we double that number to
include trucks, cabs, etc., we have 3 × 108 vehicles. Let\u2019s assume that each vehicle uses,
on average, about 12 gallons of gasoline per week.

(a) Find the daily consumption of
gasoline G:

( )( )
gal/d106
gal/d2vehicles103
8
8
×=
×=G

Assuming a price per gallon
P = \$1.50, find the daily cost C of
gasoline:

( )( )
dollars/dbillion \$1d/109\$
gal/50.1\$gal/d106
8
8
\u2248×=
×== GPC

(b) Relate the number of barrels N
of crude oil required annually to the
yearly consumption of gasoline Y
and the number of gallons of
gasoline n that can be made from
one barrel of crude oil:

n
tG
n
YN \u2206==
Substitute numerical values and
estimate N:

( ) ( )
barrels/y10
gal/barrel 19.4
d/y24.365gal/d106
10
8
\u2248
×=N

15 \u2022\u2022
Picture the Problem We\u2019ll assume a population of 300 million (fairly accurate as of
September, 2002) and a life expectancy of 76 y. We\u2019ll also assume that a diaper has a
volume of about half a liter. In (c) we\u2019ll assume the disposal site is a rectangular hole in
the ground and use the formula for the volume of such an opening to estimate the surface
area required.

(a) Express the total number N of
disposable diapers used in the
United States per year in terms of
the number of children n in diapers
and the number of diapers D used
by each child in 2.5 y:

nDN =
Use the daily consumption, the
number of days in a year, and the
estimated length of time a child is in
diapers to estimate the number of
diapers D required per child:
ilddiapers/ch103
y5.2
y
d24.365
d
diapers3
3×\u2248
××=D

Chapter 1

6
Use the assumed life expectancy to
estimate the number of children n in
diapers:

( )
children10
children10300
y76
y5.2
7
6
\u2248
×\u239f\u239f\u23a0```
ÓTIMO MATERIAL
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