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“how far?” are usually asking a question about distance, unknown quantity, the mass (m) of that volume. Make a list
and questions about “how long?” are usually asking of these quantities:
a question about time. Such information can be very 3
ρ = 13.6 g/ cm
important in procedure step 1, the listing of quantities
and their symbols. Overlooked or missing quantities V = 10.0 cm 3
and symbols can make it difficult to identify the
m = ?
appropriate equation.
3. Understand the meaning and concepts that an equation The appropriate equation for this problem is the relationship
represents. An equation represents a relationship that exists between density (ρ), mass (m), and volume (V):
between variables. Understanding the relationship helps m _

you to identify the appropriate equation or equations by ρ =
V
inspection of the list of known and unknown quantities
(procedure step 2). You will find a list of the equations The unknown in this case is the mass, m. Solving the equation

being considered at the end of each chapter. Information for m, by multiplying both sides by V, gives:
about the meaning and the concepts that an equation _
mV
Vρ =

represents is found within each chapter. V
4. Solve the equation before substituting numbers and units
Vρ = m, or
for symbols (procedure step 3). A helpful discussion of the
mathematical procedures required, with examples, is in m = Vρ
appendix A. Now you are ready to substitute the known quantities in
5. Note whether the quantities are in the same units. A the equation:
mathe matical operation requires the units to be the same; g
_
(
3)
3
for example, you cannot add nickels, dimes, and quarters m = 13.6 (10.0 cm )

until you first convert them all to the same unit of money. cm
Likewise, you cannot correctly solve a problem if one time
And perform the mathematical operations on the numbers and
quantity is in seconds and another time quantity is in hours.
on the units:
The quantities must be converted to the same units before

g
_
( )
3
anything else is done (procedure step 4). There is a helpful m = (13.6)(10.0) ( cm )

3
section on how to use conversion ratios in appendix A. cm
6. Perform the required mathematical operations on the _ 3
g∙ cm

numbers and the units as if they were two separate problems = 136 3
cm

(procedure step 6). You will find that following this step will
facilitate problem-solving activities because the units you = 136 g
obtain will tell you if you have worked the problem correctly.
If you just write the units that you think should appear in the
answer, you have missed this valuable self-check. 1.7 THE NATURE OF SCIENCE
7. Be aware that not all learning takes place in a given time
frame and that solutions to problems are not necessarily Most humans are curious, at least when they are young, and are
arrived at “by the clock.” If you have spent a half an hour motivated to understand their surroundings. These traits have
or so unsuccessfully trying to solve a particular problem, existed since antiquity and have proven to be a powerful moti-
move on to another problem or do something entirely vation. In recent times, the need to find out has motivated the

different for a while. Problem solving often requires time for launching of space probes to learn what is “out there,” and hu-
something to happen in your brain. If you move on to some mans have visited the moon to satisfy their curiosity. Curiosity
other activity, you might find that the answer to a problem and the motivation to understand nature were no less powerful

that you have been stuck on will come to you “out of the in the past than today. Over two thousand years ago, the Greeks
blue” when you are not even thinking about the problem. lacked the tools and technology of today and could only make

This unexpected revelation of solutions is common to many conjectures about the workings of nature. These early seekers
real-world professions and activities that involve thinking. of understanding are known as natural philosophers, and they
observed, thought about, and wrote about the workings of all
Example Problem of nature. They are called philosophers because their under-
3
Mercury is a liquid metal with a mass density of 13.6 g/cm . standings came from reasoning only, without experimental evi-
3
What is the mass of 10.0 cm of mercury? dence. Nonetheless, some of their ideas were essentially correct
and are still in use today. For example, the idea of matter being
composed of atoms was first reasoned by certain Greeks in the
Solution fifth century b.c. The idea of elements, basic components that
The problem gives two known quantities, the mass density make up matter, was developed much earlier but refined by the
(ρ) of mercury and a known volume (V), and identifies an ancient Greeks in the fourth century b.c. The concept of what
1-13 CHAPTER 1 What Is Science? 13