Chapter 1
Measurement and Problem
Solving
Units of Chapter 1
Why and How We Measure
SI Units of Length, Mass, and Time
More about the Metric System
Unit Analysis
Unit Conversions
Significant Figures
Problem Solving
1.1 Why and How We Measure
Physics attempts to describe nature in an
objective way through measurement.
Measurements are expressed in units;
officially accepted units are called
standard units.
Major systems of units:
1. Metric
2. British (used by the U.S., but no longer by
the British!)
1.2 SI Units of Length, Mass, and Time
Length, mass, and time are fundamental
quantities; combinations of them will form all
the units we will use through Chapter 14.
In this text, we will be using the SI system of
units, which is based on the metric system.
1.2 SI Units of Length, Mass, and Time
SI unit of length: the meter. The original
definition is on the left, the modern one is on the
right.
1.2 SI Units of Length, Mass, and Time
SI unit of mass: the kilogram
Originally, the kilogram was
the mass of 0.10 m3 of
water.
Now, the standard
kilogram is a platinumiridium cylinder kept at
the French Bureau of
Weights and Measures.
1.2 SI Units of Length, Mass, and Time
SI unit of time: the second
The second is defined as a certain number of
oscillations of the cesium-133 atom.
1.2 SI Units of Length, Mass, and Time
In addition to length, mass, and time, base units
in the SI system include electric current,
temperature, amount of substance, and
luminous intensity.
These seven units are believed to be all that are
necessary to describe all phenomena in nature.
1.3 More about the Metric System
The British system of units is used in the U.S.,
with the basic units being the foot, the pound
(force, not mass), and the second.
However, the SI system is virtually ubiquitous
outside the U.S., and it makes sense to
become familiar with it.
1.3 More about the Metric System
In the metric system, units of the same type of
quantity (length or time, for example) differ from
each other by factors of 10. Here are some
common prefixes:
1.3 More about the Metric System
The basic unit of volume in the SI system is the
cubic meter. However, this is rather large for
everyday use, so the volume of a cube 0.1 m on
a side is called a liter.
Recall the original definition of a kilogram; one
kilogram of water has a volume of one liter.
1.4 Unit Analysis
A powerful way to check your calculations is to
use unit analysis.
Not only must the numerical values on both
sides of an equation be equal, the units must
be equal as well.
1.4 Unit Analysis
Units may be manipulated algebraically just as
other quantities are.
Example:
Therefore, this equation is dimensionally
correct.
1.5 Unit Conversions
A conversion factor simply lets you express a quantity
in terms of other units without changing its physical
value or size.
The fraction in blue is the conversion factor;
its numerical value is 1.
1.6 Significant Figures
Calculations may contain two types of numbers:
exact numbers and measured numbers.
Exact numbers are part of a definition, such as
the 2 in d = 2r.
Measured numbers are just that—for example,
we might measure the radius of a circle to be
10.3 cm, but that measurement is not exact.
1.6 Significant Figures
When dealing with measured numbers, it is
useful to consider the number of significant
figures.
The significant figures in any measurement are the
digits that are known with certainty, plus one digit that
is uncertain.
It is easy to create answers that have many
digits that are not significant using a calculator.
For example, 1/3 on a calculator shows as
0.33333333333. But if we’ve just cut a pie in
three pieces, how well do we really know that
each one is 1/3 of the whole?
1.6 Significant Figures
Significant figures in calculations:
1. When multiplying and dividing quantities, leave as
many significant figures in the answer as there are in
the quantity with the least number of significant
figures.
2. When adding or subtracting quantities, leave the
same number of decimal places (rounded) in the
answer as there are in the quantity with the least
number of decimal places.
1.7 Problem Solving
The flowchart at left
outlines a useful
problem-solving strategy.
It can be used for most
types of physics
problems.
1.7 Problem
Solving
The table at left
describes several types
of examples that are
used in the text.
Review of Chapter 1
SI units of length, mass, and time: meter,
kilogram, second
Liter: 1000 cm3; one liter of water has a mass
of 1 kg
Unit analysis may be used to verify answers
to problems
Significant figures – digits known with
certainty, plus one
Review of Chapter 1
Problem-solving procedure:
1. Read the problem carefully and analyze it.
2. Where appropriate, draw a diagram.
3. Write down the given data and what is to be
found. (Make unit conversions if necessary.)
4. Determine which principle(s) are applicable.
5. Perform calculations with given data.
6. Consider if the results are reasonable.