Focus Your Learning 41
61. Most samples of matter expand when heated. Assuming that
this is the case with water at room temperature, would the
density increase or decrease as the water warmed? Show the
mathematical basis of your answer.
62. Ice floats on top of water. Using the information from Prob-
lem 61, explain how this could occur and show the mathe-
matical basis of your answer.
63. In casual food preparation, one may be directed to add a
pinch or a smidgeon or “just a bit” of a particular ingredient.
If 10 pinches equaled 2 smidgeons and 10 “just a bits”
equaled 1 smidgeon, how many “just a bits” of hot sauce
should be added to a recipe that calls for 2 pinches?
64. Consider the tongue twister “Peter Piper picked a peck of
pickled peppers.” If two dozen pickled peppers are in a peck,
and Peter Piper picked 8 pecks for his girlfriend Polly, how
many peppers did Peter Piper pick?
Section 1.5 Conversions and Dimensional Analysis
Skill Review
65. Illustrate a plan of attack (in the same manner as indicated
in the text) for converting units of miles per hour (mph) to
meters per second.
66. Illustrate a plan of attack (in the same manner as indicated in
the text) for converting units of kg·m/s
2
to lb·ft/s
2
67. Osmium (element 76) is one of the most dense elements
known. The standard density is 22.6 kg/L. What is the density
in units of g/cm
3
? What would be the mass of a 0.50-L sam-
ple of osmium?
68. Mercury has a density of 13.6 g/cm
3
. What is the density in
kg/L for mercury? Calculate the weight in pounds of 3.6 L of
mercury.
69. Convert the following into the indicated units:
a. 35 mph to kph c. 733 mi/gal to km/L
b. 22.4 L/s to cm
3
/s d. 4.184 g/°C to lb/°F
70. Convert the following into the indicated units:
a. 12 doz/lb to gross/kg c. 14.4 lb/in
2
to kg/m
2
b. 16 lb/gal to g/mL d. 3.04 °C/min to °F/s
71. In the vacuum of space, light travels at a speed of 186,000
miles per second. Indicare how many miles light travels
through space in:
a. 1 minute b. 1 day c. 1 year
72. The speed of sound varies greatly depending on the medium
and conditions. If the speed of sound at sea level and zero
degrees Celsius is approximately 1100 feet per second, indi-
cate how far sound travels in:
a. 1 millisecond b. 1 dekasecond c. 1 microsecond
73. Perform these conversions:
a. 2.0 oz to pounds d. 96 in to meters
b. 4.0 qt to liters e. 13 ft to centimeters
c. 160 lb to kilograms f. 32 mi to kilometers
74. Perform these conversions:
a. 3.0 kg to pounds d. 134 oz to kilograms
b. 7400 s to days e. 75.5 cm to feet
c. 50.34 mL to gallons f. 2.88 L to quarts
52. Determine the volumes of liquid in each of these graduated
cylinders, and report your answers with the correct number
of significant figures.
53. A fast-food restaurant wants to standardize the temperature
of its coffee. It installs a coffee machine that is specified as de-
livering coffee at 75°C
± 3°C. What are the maximum and
minimum temperatures of the coffee delivered by this
machine in °F?
54. The temperature of the hot oil bath in a fast-food restaurant
determines the quality of the french fries that are produced.
The heater on the oil bath can regulate the temperature at
350°F ± 10°F. What are the maximum and minimum tem-
peratures of the french fries delivered by this machine in °C?
55. Carbon atoms have an atomic radius of approximately
77 pm. If you drew a line that was 1 cm in length using a piece
of charcoal, approximately how many atoms of carbon
would be in this line? (For the purposes of this question, as-
sume that the atoms are touching and that they form a
straight line one atom wide.)
56. The same piece of charcoal (see Problem 55) was used to
darken a box on a survey form. The box measures 5 mm on
each side. How many atoms of carbon would be in this box?
(For the purposes of this question, assume that the atoms are
touching, that they line up into a square grid, and that they
are only one layer thick on the paper.)
57. During the 1980s, several new elements were synthesized in
Germany. These elements are made of unstable atoms. Half
of the atoms in a sample of unstable atoms will decompose
over a period of time known as the element’s half-life. One of
these newly discovered elements, Meitnerium (element 109)
has a half-life of only 0.07 s.
a. What is its half-life in milliseconds?
b. What is the length of time of four of its half-lives in terms
of microseconds?
58. Before filling, an empty, irregularly shaped container has a
mass of 0.1956 kg. When this container is totally filled with
water,the combined mass of the containerand wateris 305.6 g.
Whatis the mass of wateradded to the containerin kilograms?
59. A certain red tomato has a mass of 45.6 g. A green tomato
also has a mass of 45.6 g. However, when placed in water, the
green tomato floats and the red one sinks. (Try this. Depend-
ing on the degree of ripeness, it actually happens!) Which of
the two is denser? Explain how two tomatoes with the same
mass can have different densities.
60. Various plastics have identifiable density values. For example,
you may have heard of high-density polyethylene and low-
density polyethylene. If you had pieces of each that were
equal in volume, which would have the greater mass?
5
a