1
Chapter 1
Measurement and Vectors
Conceptual Problems
1
•
[SSM]
Which of the following
is not
one of the base quantities in the
SI system? (
a
) mass, (
b
) length, (
c
) energy, (
d
) time, (
e
) All of the above are base
quantities.
Determine the Concept
The base quantities in the SI system include mass, length,
and time. Force is not a base quantity.
)
(
c
is correct.
2
•
In doing a calculation, you end up with m/s in the numerator and m/s
2
in the denominator. What are your final units? (
a
) m
2
/s
3
, (
b
) 1/s, (
c
) s
3
/m
2
, (
d
) s,
(
e
) m/s.
Picture the Problem
We can express and simplify the ratio of m/s to m/s
2
to
determine the final units.
Express and simplify the ratio of
m/s to m/s
2
:
s
s
m
s
m
s
m
s
m
2
2
=
⋅
⋅
=
and
)
(
d
is correct.
3
•
The prefix giga means (
a
) 10
3
, (
b
) 10
6
, (
c
) 10
9
, (
d
) 10
12
, (
e
) 10
15
.
Determine the Concept
Consulting Table 11 we note that the prefix giga
means 10
9
.
)
(
c
is correct.
4
•
The prefix mega means (
a
) 10
–9
, (
b
) 10
–6
, (
c
) 10
–3
, (
d
) 10
6
, (
e
) 10
9
.
Determine the Concept
Consulting Table 11 we note that the prefix mega
means 10
6
.
)
(
d
is correct.
5
•
[SSM]
Show that there are 30.48 cm per foot. How many centimeters
are there in one mile?
Picture the Problem
We can use the facts that there are 2.540 centimeters in
1 inch and 12 inches in 1 foot to show that there are 30.48 cm per ft. We can then
use the fact that there are 5280 feet in 1 mile to find the number of centimeters in
one mile.
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2
Multiply 2.540 cm/in by 12 in/ft to
find the number of cm per ft:
cm/ft
48
.
30
ft
in
12
in
cm
540
.
2
=
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
Multiply 30.48 cm/ft by 5280 ft/mi to find the number of centimeters in one
mile:
cm/mi
10
609
.
1
mi
ft
5280
ft
cm
48
.
30
5
×
=
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
Remarks: Because there are exactly 2.54 cm in 1 in and exactly 12 inches in 1 ft, we
are justified in reporting four significant figures in these results.
6
•
The number 0.000 513 0 has
significant figures. (
a
) one, (
b
) three,
(
c
) four, (
d
) seven, (
e
) eight.
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.
)
(
c
is correct.
7
•
The number 23.0040 has
significant figures. (
a
) two, (
b
) three,
(
c
) four, (
d
) five, (
e
) six.
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.
)
(
e
is correct.
8
•
Force has dimensions of mass times acceleration. Acceleration has
dimensions of speed divided by time. Pressure is defined as force divided by area.
What are the dimensions of pressure? Express pressure in terms of the SI base
units kilogram, meter and second.
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 Spring '09
 Pythagorean Theorem, Energy, Mass, Orders of magnitude, numerical values

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