Prof.
Clements Notes/Hints for Physics Courses
Introduction:
Chapter 1 Open Stax College Physics or Most Introductory Physics
Courses
I
highly recommend that you go
to the web site https://openstax.org/details/books/college-physics
to access the free OpenStax College Physics textbook and resources.
My
notes are meant to help you understand the textbook, understand
physics, and succeed in your physics course, or help you review
physics as you prepare to take another course. These notes/hints are
not a substitute for reading the textbook or attending lectures.
YouTube
videos of my (usually short) lectures and example problems are
indexed at http://www.physics.gpclements.com/
. There are also a few videos that give review of basic math tools
that are used in an introductory physics course.
Terms
you should know after this unit: law, theory, metric units, English
units, significant figure, uncertainty
I
agree with the author for the OpenStax
College Physics textbook that one of the
outcomes of a physics course is that the student is able to apply
physics
principles to a wide variety of situations. After you complete a
physics course you should be better able to understand concepts and
solve problems in a wide variety of science courses and careers.
Many
fields of study (e.g. engineering, medical school, PT school,
optometry, etc.) list physics as a required course to give students
basic understanding about forces, matter, energy, properties
of light, atoms, etc., and to help
students develop their problem solving skills.
As
soon as one experiment agrees with a hypothesis the hypothesis is not
called a theory. A
hypothesis gains the label of “theory” after repeatedly being
tested and not found to be untrue. A theory cannot be proven true by
an experiment but it can be proven to be false by an experiment. A
theory becomes accepted after experiments have verified its
predictions.
A
theory can be given the name “law” when it has simple language
and broad application.
Some
would simplify the description of the scientific method to these
steps:
1.
Observe some process 2. Make a hypothesis 3. Perform a controlled
experiment 4. Revise the hypothesis if necessary based on the
outcome of the experiment, and perform more controlled experiments.
It
is common to discover book titles from the 1700's and 1800's titled
"Natural Philosophy." This title matches the title of
“Physics” we use today.
(Optional:
View https://books.google.com/?hl=en
and search for natural philosophy.)
The
era known as classical physics starts with Galileo's experiments
(around 1600) and ends around 1900. The era known as modern physics
starts around 1900. From around 1900 through the 1930s physicists
became aware of the nature of the atom, the dual nature of light
(particle and wave), consequences of moving at high speed, electrons,
protons, neutrons, the quantum nature of the universe, the nature of
the nucleus of atoms, and many more topics.
Almost
100% of physics courses use metric units
(meters, kilograms, seconds, etc.). You
may encounter a few problems that contain
English units. You may convert the units
of metric results into English units (if you live in the USA) so
you can get a better understanding of
the reasonableness of a result. You
need to know how to convert units from English to metric and metric
to English. Your textbook likely has a
page in the front cover or at the end that has a table of conversion
factors. You ask your instructor for help if you have trouble
converting units from English units to metric units. There are also
YouTube videos (see the end of this document) that will help you
review this process.
The
second is defined in terms of vibrations of a particular atom. The
Earth's rotation is slightly variable and has a long term trend of
slowing so it is no longer used to define the unit of time.
For
the unit of the meter, the French surveyed a distance, determined the
change in latitude (angle), and used a proportion to determine the
distance from the North Pole to the equator in 1791. The distance
between two marks on a platinum-iridium bar in Paris used to be “the
meter.” This physical item survived World War II. But, this
standard is not very portable and the distance is not accurately
transferable to secondary standard bars for other countries. The
meter is now defined using the equation distance = rate * time, where
the rate is the speed of light and the time is a small fraction of a
second (see the textbook). This definition bypasses the need for a
physical object to define the distance of one meter.
The
kilogram is set by a physical object that is kept in Paris. The
statement in the OpenStax Physics text that an "exact replica"
of the standard kilogram is kept by the NIST is perhaps a little
bold. Exact measurements are not possible. The NIST kilogram is
extremely close to the same mass as the standard kilogram in Paris.
You
should memorize the power of ten values for these prefixes: mega,
kilo, centi, milli, micro.
Two
numbers called "the same order of magnitude" when they have
the same “power of ten.”
You
should view Table 1.3 in the OpenStax Physics text, or your own
textbook, for examples of powers of 10 for distances, masses, and
time intervals.
It
is worth your time to perform a search
on the Internet for …. Powers of Ten
video .
In
2017 the Google search engine listed several sites that have this
video. The video will give you some appreciation for the extremely
wide range of sizes from the very small (nucleus of an atom) to the
very large (large scale structures in the universe).
Conversions....I
would recommend that you take the starting quantity and divide it by
1 so you have a numerator (your original number) and a denominator.
Write the appropriate units on the numerator and denominator. e.g.
For 80 meters/second you would have 80 meters / 1 second. This will
help you to see which units are in the numerator and which are in the
denominator. If you are trying to change the distance unit, the
conversion factor has to have the meter unit in the denominator to
cancel the meter unit in the numerator.
Converting
units is a critical skill that is needed to succeed in a physics
course. Review example problems in your textbook or see my YouTube
videos if you need help with this.
Self
Test ... Convert 1 microCentury into minutes.
Your
answer should be about 52.6 minutes. This may be about the length of
your lecture class in physics in the USA. So, if you think you were
in class a long time, it was not really as long as a century, it was
only as long as a microCentury!
Ask
your instructor whether he/she makes a distinction between the terms
precision and accuracy.
Uncertainty
is an important concept. Scientists want to communicate how much
confidence they have in a result. e.g. 6.07 cm + or - 0.02 cm
represents a better known result than 6.07 + or - 0.08 cm. The first
result is firmly believed to be between 6.05 and 6.09 cm. The second
result is firmly believed to be between 5.99 and 6.15 cm.
Ask
your instructor for guidance on handling the reporting of uncertainty
for your work in the lecture part of the course and the lab part of
the course. Ask your instructor for guidance on how to determine
the number of “significant figures.”
A digit is significant when it occurs
in the placement in the number where the uncertainty starts. In the
paragraph above, the 7 is significant and the number has three
significant figures (6, 0, 7). The number 200 has 1 significant
figure if the uncertainty is 100; it has 2 significant figures if the
uncertainty is 30, and it has 3 significant figures if the
uncertainty is 4. The number 0.000034 (with no uncertainty given)
has two significant figures, the 3 and 4. Leading zeros for a
decimal number are not significant. A basic rule is that the result
of a calculation has the number of significant figures equal to the
fewest number of significant figures in any data used in the
calculation.
Approximation
is a valuable skill. Sometimes approximation calculations are called
"back of the envelope" calculations. This implies a quick
calculation with little concern for precise answers. A very famous
person who used this method was Enrico Fermi. He worked on the
development of the atomic bomb in World War II.
Some
examples of approximation can be found at
http://en.wikipedia.org/wiki/Fermi_problem .
You
should download the student solution manual from the OpenStax College
Physics web page and work through several example problems for every
chapter.
Scroll
down until you find the Student Resources section.
In
future notes/hints you
may find references to the Mechanical Universe videos. These videos
are freely available online on
YouTube (as of 2017)
YouTube
videos of my “short” before-class lectures and example problems
are indexed at
Copyright©
2017 by Greg Clements Permission is granted to reproduce this
document as long as 1) this copyright notice is included, 2) no
charge of any kind is made, and, 3) the use is for an educational
purpose. Editing of the document to suit your own class style and
purposes is allowed.
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