Topic #1: Physics, A Mathematical Science



Topic #1(: Physics, A Mathematical Science

1. Search for Understanding

2. Measurement and the Scientific Method

3. Metric System

4. Prefixes and SI Units

5. Fundamental and Derived Units

6. Scientific Notation

7. Addition and Subtraction in Scientific Notation

8. Multiplication and Division in Scientific Notation

9. Uncertainties of Measurements

10. Accuracy and Precision

11. Significant Digits

12. Operations Using Significant Digits

Notes should include:

Search for Understanding: Physics is a science. The word science comes from the Latin word Scientia which means Knowledge. A scientist is a person that pursues knowledge.

Every subject has it’s own, unique vocabulary. Physics is no exception. Every topic encountered in this course will have additional vocabulary associated with the subject matter. This vocabulary should be written down and defined in your notes as well as studied along with all of the other information and skills you are expected to learn. It is recommended that you make flash cards to learn your vocabulary as quickly as is possible. Learning your vocabulary within 48 hours of starting a new unit is a desirable goal that will help in the case of a pop quiz.

Definition: Physics is the science that studies the nature of matter, energy and their relationship to one another.

The Illinois Institute of Technology (I I T) model of science, which looks like a pyramid, says that mathematics is the foundation upon which modern science is built. After that physics is the underlying support for the rest of the sciences because it provides the "Fundamental Rules" of the game upon which our technology is based. Physics provides us with the tools to investigate and evaluate the environment in which we live, from the tinniest virus to the largest of celestial objects. To visualize this model, think of mathematics as the foundation of a learning pyramid. Upon this foundation is placed the study of physics. On top of physics is the study of chemistry. At the apex of this study is biology. To understand biology one must understand all that its body of knowledge is based upon.

Scientific Method: Perhaps a more appropriate term is the "process of science". This process provides us with an approach to solving problems in a systematic, objective way, if we keep personal biases and prejudices out of the investigation. The process of science is a circle of knowledge that goes around and around cycle after cycle. With each cycle more knowledge is accumulated. One cycle of this process begins with studying and learning everything that is currently known about the topic at hand. From there, if new knowledge is to found, more research is to be done. If no knowledge exists, the process often begins with the formulation of a hypothesis. A hypothesis is NOT an educated guess as some textbook authors suggest. A hypothesis is a prediction that is made after all known knowledge about a subject has been (thoroughly studied (researched). In a new area of study, where the only data available is new data gathered through careful observations, a person has to make a predictive statement about any apparent pattern(s) observed and what possible reasons there are for such a pattern or patterns. A predictive statement is called a hypothesis. Next, the person or persons involved in the investigation have to do further research through additional observation / experimentation for the purpose of testing the prediction. From these results an explanation can be formulated. Such an explanation following the testing of a hypothesis is called a theory. A theory explains what is known and is based on facts. A theory is NOT a hypothesis. As an example consider that a long time ago, during the 1800’ a biologist by the name of Charles Darwin was at this point in his research when he spent years of gathering data to determine the origins of all the different species of animals and plants on earth. His hypothesis to explain the evidence he found during his research of various species of animals and plants on earth was called evolution. He did his research from 1859 to 1871. Since then literally thousands of scientists have taken up his research. The result of all of this research was to change the status of his idea from hypothesis to theory. A theory is an explanation of what is known and is not a hypothesis. So today we have the theory of evolution. This theory is based on fact and today’s research looks at the mechanism of evolution.

Any worthwhile research moves forward through an unending cycle of research from hypothesis, through observation and experimentation and finally to theory. The objective in science is to develop theories and to constantly challenge them. Theories are explanations. As new tools (technology) evolve, existing theories must be tested with the new more accurately determined data that is gathered with the use of the new technologies. That is how science progresses and theories evolve. Today scientists are more reluctant than in past centuries to call a proven theory a law, even when there are mountains of evidence supporting it. Rapidly advancing technologies offer new ways to study evolving theories at a faster than ever pace causing the theories to be refined faster than ever. When gathering scientific data moved much slower in the past due to less available technology, scientists were more comfortable with using the word law in place of the word theory.

Today, because technology is moving so fast and there are so many more people involved in research, theories are always being retested, and scientists don’t rush to put the label of law on them. On the other hand, when no new research contradicts the basic idea in a theory, such as in the theory of evolution, new technologies allow for it to better explained and reinforce previously known facts with additional new facts. So much is known about the process of evolution today, that the majority of scientists would prefer to call it a law because evolution is based on a mountain of facts. Today scientists are fine tuning the explanation of the process, but no longer dispute that evolution has and is occurring all the time on earth. As another example consider the flat earth concept. For thousands of years, it was “common sense” to accept that the earth was flat, despite evidence to the contrary. In another instance the earth was believed to be the center of the universe. Religious leaders said it was true and to believe otherwise was heresy. Heresy was punished through social disgrace, torture, and even death. Today either one of the ideas is absurd and they have been replaced through science by the factual based truths that the earth is an round and the earth is not the center of the solar system, much less the center of the universe.

Evolution is going through a similar change. It was a hypothesis in the 1800’s. Since then there has been so much factual data collected about it and research done that its status has risen to evolution being a theory. It is now understood as an explanation based on fact. Evolution like any valid theory is always challenged on the level concerning how the process works. For us to know (that the process occurs is not enough. We want to understand the exact mechanism by which it occurs. Some already call evolution a law, but others feel until we grasp the details of the process, we should stick to the term theory meaning explanation.

One problem remains for all who are scientists. Just as in the past, scientists are still challenged by the fundamentalist religious zealots who feel that science challenges their belief in a creator. This attitude has placed the Theory of Evolution at the center of debate in this country, just as the Theory of a Sun centered solar system was debated centuries ago. Does anyone actually belive that the earth is the center of the universe anymore?

The heart of the problem is that many fundamentalists believe that to accept evolution is to be an atheist. How much further from the truth could those people be? Science is NOT about the business of addressing the existence or non-existence of a creator. Science is about gathering data, data about the earth, our solar system, our galaxy, and the universe as a whole. Science uses the logic of mathematics to analyze and interpret the results of observations and experimentation. Whether you, the reader, have a belief in a creator or not is not at issue. Science is not about the business of religion and religion should not be about the business of science. That is why the United States constitution is based upon the separation of church and state. The U.S. will fail the mandate of its founding fathers if it ever adopts a state religion with its particular version of a creation story.

Get it straight now. Evolution is a scientific theory based on fact. Creationism is a pseudo-science invented by and put forth by certain fundamentalist religious groups. Creationism is prejudiced towards one particular religious point of view and against all other recognized religions and philosophical points of view. It has nothing to do with actual science. Evolution is a scientific theory based on fact and has no relationship to the belief or disbelief in a creator. That evolution takes place on planet earth is a fact. The question of whether a creator exists or does not exist is neither the realm of science, nor should it ever be. It is in the realm of Philosophy and Theology to help us answer that question. Evolution just like other scientific concepts, has been discovered and researched through the process we call the scientific method.

Metric System, Metric Prefixes, and SI units: You need to know all units encountered in this course, not just the few that you may have learned in other science courses. Previously, You should have learned about length, mass, and volume. As you should already know, the metric system uses prefixes to report multiples of and fractions of the base units. Also, you should have already been introduced to the International System of Weights and Measures, which defines the international standard unit for each category of measurement. (i.e. the SI unit for mass is the kg) This system is commonly taught in biology, chemistry and physics classes, and often in your 6th, 7th and 8th grade science classes. You need to know this well to do science, engineering and the international business community.

Fundamental and Derived Units: These are two terms you should know well. You should be able to give a few examples of each.

Scientific Notation: Very large and very small numbers in particular are written using exponential notation. This form of writing numbers such as 2.35 x 106 is very often used in science to express measurements and numerical constants in equations. This is a very important concept fundamental to all the work we do in physics as well as the other sciences.

(Addition, Subtraction, Multiplication, and Division using Scientific Notation: It is necessary that you master the basic arithmetic functions using numbers expressed in scientific notation.

Uncertainties of Measurements: It is absolutely vital that you understand the limits of measuring instruments and know how to express these limitations when writing down measurements made with them.

Accuracy and Precision: You should be able to define them and clearly describe the difference between them.

Significant Digits: When looking at a measurement recorded by someone else, it is necessary that you be able to identify the number of significant digits in the value and be able to distinguish significant zeros from those that are just place-holders keeping the decimal in the correct place.

Operations Using Significant Digits: If one or more measurements are used in a calculation it is necessary that the number of significant digits in the measurements influence the number of significant digits in the answer. If you do this correctly, you won't be trying to claim your answer is more precise than it really is.

Vocabulary: metric system, SI, base unit, meter, second, kilogram, mks system, fundamental unit, derived unit, scientific notation, factor-label method, precision, accuracy, parallax, significant digits, and the metric prefixes of tera, giga, mega, kilo, hecto, deca, deci, centi milli, micro, nano, pico, femto

Skills to be learned:

Metric System, Prefixes, and SI Units

Scientific Notation

Addition, Subtraction, Multiplication and Division in Scientific Notation

Uncertainties of Measurements, Significant Digits, Math Operations with

Significant Digits

Assignments:

Textbook: Read / Study / Learn Chapter 2 Sections 2.1 and 2.2

Workbook Exercise(s): PS#1-6, 1-7, 1-8; 1-2, 1-3, 1-4, 1-5; 1-9, 1-10, 1-11, 1-12

Activities: TBA

Resources:

This Handout and the Overhead and Board Notes discussed in class

Textbook – Chapter 2, Sections 2.1 and 2.2

Workbook Lessons & Problem Sets

- “Physics, A Mathematical Science”

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