Study Guide to accompany Physics Including Human Applications Fuller/ Fuller/ Fuller by Thomas C. Campbell Illinois Central College and Robert G.

Transcription

1 Study Guide to accompany Physics Including Human Applications Fuller/ Fuller/ Fuller by Thomas C. Campbell Illinois Central College and Robert G. Fuller University of Nebraska Harper & Row, Publishers New York Hagerstown San Francisco London All rights reserved. Printed in the United States of America. No part of this book may be used or reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews. For information address Harper & Row, Publishers, Inc., 10 East 53rd Street, New York, N.Y Standard Book Number:

2 TABLE OF CONTENTS: Introduction and Table of Contents Preface Dear Student Mathematical Skills Review (0) Human Senses (1) Unifying Approaches (2) Kinematics (3) Forces and Newton's Law (4) Energy (5) Momentum and Impulse (6) Rotational Motion (7) Fluid Flow (8) Transport Phenomena (9) Temperature and Heat (10) Thermal Transport (11) Thermodynamics (12) Elastic Properties of Materials (13) Molecular Model of Matter (14) Simple Harmonic Motion (15) Traveling Waves (16) Sound and the Human Ear (17) Optical Elements (18) Wave Properties of Light (19) Human Vision (20) Electrical Properties of Matter (21) Basic Electrical Measurements (22) Magnetism (23) Electromagnetic Induction (24) Alternating Currents (25) Bioelectronics and Instrumentation (26) Quantum and Relativistic Physics (27) Atomic Physics (28) Molecular and Solid-State Physics (29) X-Rays (30) Nuclear Physics (31) Applied Nucleonics (32)

3 PREFACE We have written this to accompany the general physics textbook, PHYSICS Including Human Applications, by Fuller, Fuller, and Fuller. This, we think, serves several purposes. It can be used along with a lecture-recitation course to provide additional study materials for the students. On the other hand, for several years we have been using the Fuller 3 manuscript as the textual material for our Keller Plan physics courses. This can be used as the student modules for a self-paced physics course. Additional Keller Plan materials to assist instructors of Keller Plan courses, using this, are available from Harper and Row Publishers. In addition, the Fuller 3 textual materials were developed for flexible use for a wide variety of physics courses, including correspondence or independent study courses. This can be used to assist students in self-study programs for personal improvement. One result of the flexibility of the Fuller3 materials is the variety of sequences available for the study of these materials. It is not necessary to go through the textual material in a linear progression by chapter number. You need only to l follow the prerequisite statements for each textbook chapter. On the following two pages we have presented the prerequisite chart for the Fuller 3 text. Please note that we have constructed a Chapter Zero for this from the Mathematical Background materials in the Appendix of the textbook. We believe it is essential for students to have sound mathematical skills before beginning a quantitative physics course. We have made Chapter Zero the prerequisite for the rest of the chapters. The charts on these two pages illustrate the prerequisite requirements for each chapter in Part I of Fuller, Fuller, and Fuller. To find the chapter which must be completed BEFORE you begin to study a later chapter, do the following: a) Locate the chapter title, b) Trace up the chart following the solid lines noting all the chapter titles encountered until you arrive at Chapter One, Human Senses. For example, to find the prerequisite chapters for Temperature and Heat (10), you would encounter chapter titles along two directions; Energy (5), Forces and Newton's Laws (4), Kinematics (3), Unifying Approaches (2), and Human Senses along one route plus Transport Phenomena (9) along the other. Each of these chapters should be completed before you begin Chapter 10, Temperature and Heat.

4 PREREQUISITE CHART FOR PHYSICS INCLUDING HUMAN APPLICATIONS BY FULLER/FULLER/FULLER PART II Prerequisite Chart (1) Prerequisite Chart (2) There are two other aspects of learning physics we would like to mention. While it is obvious that we learn by doing, it is not so apparent that we learn by interacting with other persons studying the same material. Nevertheless, our experiences as students and teachers of physics has convinced us of the importance of peer interactions in learning new subject material. Some provision which encourages people studying these materials to work together and talk to each other about these ideas seems to be essential. All the ideas and/or principles of physics cannot be presented with equal clarity in any one book. Students who want to know physics are to be encouraged to study the subject and not only a textbook. While the Fuller 3 text can serve as an introduction to the concepts of physics, it need not be the only source of physics information consulted. Students are to be encouraged to use the various references recommended in the bibliography of the Fuller 3 text. Thomas C. Campbell Robert G. Fuller June, *Please note that in several of the tables which outline the Suggested Study Procedure a dotted line appears. This line separates two levels of competency for that chapter. First, the basic level appears above the dotted line. Below the line are the more advanced Chapter Goals and the recommended study outline which accompany them.

5 Dear Student, This has been especially written for you to assist in your mastery of physics concepts. As you study each chapter, we hope you may rely on the material presented here to resolve some of the questions you may have from the many topics you encounter in the textbook. To help you use this, we have attempted to use the same format for each of the thirtytwo chapters (plus APPENDIX). In this way, you will be able to find the same "kinds" of assistance in each of the chapters. After a chapter or two, you may even anticipate the sections of the which are most helpful to you and utilize them more extensively than other sections. Generally, the make-up of each chapter is as follows: Section One - Chapter Introduction In the double page opening to each chapter we provide you with a restatement of the GOALS for each textbook chapter. This is accompanied by a chapter OVERVIEW and a SUGGESTED STUDY PROCEDURE. This information suggests a realistic study procedure for you to follow in preparing yourself on the contents of the chapter. The study procedure does not suggest that you must study everything in the chapter (although this maybe your style), but outlines an economical and straight-forward method for mastery of the chapter contents. The correspondence between the chapter GOALS and the various sections and problems in the textbook are also summarized in tabular form. Section Two - Definitions In most chapters, one of the chapter GOALS deals with Definitions of terms introduced in the chapter. Although you will find a short definition of each of these terms in the text GLOSSARY, in this section we provide an extended discussion of them. This addition should not encourage you to "memorize" our definition but to use the additional information to formulate additional examples or situations which illustrate the function of the terms introduced. Section Three - Answers to Questions Asked in the Text As you read each text chapter you will encounter numerous questions. Some of these questions will be at the end of a chapter section, other will be within the narratives themselves. In this section of the, we provide you with a discussion of these questions. We hope that you will think seriously about the answers to these questions for yourself before you look at the answers we have provided. Section Four - Examples Many examples are provided in each chapter of the Text. Physics principles are general in nature and can be applied to a multitude of circumstances and applications. In this section of the, we present additional examples which illustrate the more quantitative concepts of each chapter. These problems will help you broaden your knowledge of the major concepts. Section Five - Practice Test The final part of the chapter is a Practice Test. These tests have been included with the answers to provide you a way to test yourself on your understanding of the information included in each text chapter. All of these tests have originated from exams we have given our students while using Fuller3. We hope that you will use the tests in a real testing situation-time yourself, complete all the test in one sitting, and do not look at the answers until all the parts are finished. When you are done, check your answers against those given at the end of the test. If you have difficulties, refer back to a portion of the text, the, or seek help from your instructor.

6 Well, now it is up to you. Studying Physics is not an easy chore, but one which requires good study habits. Don't procrastinate and put off studying on a regular day-to-day basis. In writing this we hope to give you the basis for developing a regular study routine (suggested Study Procedure), assistance for potentially difficult areas (Definitions, Examples), and a self-check assessment of your understanding (Practice Test). But like any other well-planned lesson guide, it is only as good as the conscientious effort you make. Sincerely, Thomas C. Campbell Robert G. Fuller

7 Appendix MATHEMATICAL SKILLS REVIEW GOALS 0 Keywords: ; Learning Objectives; Mathematics; Arithmetic; Exponents; Exponentials; Exponential Functions; Logarithms; Trigonometry; Graphs; Dimensional Analysis; Cartesian Coordinates; Significant Digits; Powers Of Ten Notation When you have mastered the contents of the Appendix you will be able to successfully demonstrate your mathematical skills in each of the following eight areas: 1. Powers of Ten Notation 2. Significant Figures 3. Cartesian Graphs 4. Dimensional Analysis 5. Right Triangles 6. Exponents 7. Logarithms 8. Exponential Function OVERVIEW This review of basic mathematics is a good place to begin your study of introductory physics. In the Appendix you will find a helpful review of the eight basic mathematical skills which you will need during your study of this text. SUGGESTED STUDY PROCEDURE Please note that the math review is broken into eight parts: Powers of Ten Notation, Significant Figures Cartesian Graphs, Dimensional Analysis, Right Triangles, Exponents, Logarithms, and The Exponential Function. As you begin your study of this mathematical review, attempt each of the self-check exercises which begin on the next page of this. Check your answers against the answers given. If you do not score 100% on any individual part, refer to the text Appendix for help. The outline below will provide a quick reference to each of the mathematical skills. Next, turn to the Practice Test in this. Complete the practice test and check your answers with those given at the end of the test. In any of the eight mathematical areas where you did not score 100%, again refer to that particular section in the text Appendix and work through additional Example Problems and/or Exercises Chapter Goals Self- Suggested Text Practice Check Readings (Appendix) Problems Powers of Ten Notation 1 A.2 (p. 733) Significant Figures 2 A.3 (p. 734) Cartesian Graphs 3 A.4 (pp ) Dimensional Analysis 4 A.5 (pp. 740, 741) Right Triangles 5 A.6 (pp ) Exponents 6 A.7 (p. 745) Logarithms 7 A.8 (p. 748) Exponential Function 8 A.9 (p. 749) SELF-CHECK EXERCISES Keywords: Mathematics; Problems; Answers: Powers Of Ten Notation

8 Powers of Ten Self-Check Solve each of the following problems, and give the answer in powers of ten notation x / = x 103 x 5.00 x 104/2.50 x 10 5 = x x x 105 =. Powers of Ten Self-Check Answers If you had difficulty in correctly solving these problems, please study the Section A.2 on the powers of ten notation, page x x x 107 SIGNIFICANT FIGURES SELF-CHECK Keywords: Significant Digits Solve each of the following problems, and give the correct answer in the appropriate number of significant figures x 1.03/.025 = x 103 x 2.5 x 10-2/2.15 x 10-4 =. 3. Solve for A; 3x 10-4 A/4.5 x 103 = 1. A =. ANSWERS TO SIGNIFICANT FIGURES SELF-CHECK If you had difficulty in correctly solving these problems, please study Appendix Section A.3 on Significant Figures, page (3 significant figures) x 105 (2 significant figures) 3. 2 x 107 (1 significant figure) Graphing and Dimensional Analysis Self- Check Keywords: Graphs; Slope; Units; Conversion Of Units 1. The following table is taken from a drivers manual and shows data for stopping an automobile on dry pavement Velocity Thinking Total Stopping (m/sec) Distance (m) Distance (m) a. Draw a graph of thinking distance (y-axis) versus velocity (x-axis), and find the slope of the curve at the point on the curve where x = 15 m/sec. b. Draw a graph of the total stopping distance (y axis) versus the velocity (x axis), and find the slope of the curve at the point where x = 20 m/sec. 2. We can define length, mass, and time as fundamental dimensions in a system of measurement. What are the SI (System International) units for a. Length

9 b. Mass c. Time The SI units are related to each other by multiples of ten, and the units are represented by the fundamental unit with the proper prefix. What are the relationships between the fundamental unit and the following common prefixes? d. The prefix centi-means, so one tesla = centiteslas. [10-2; 10 2] e. The prefix milli- means, so one liter = milliliters. [10-3;10 3] f. The prefix kilo- means, so one watt = kilowatts. [103;10-3] Graphing and Dimensional Analysis Self- Check Answers If you had difficulty in correctly solving these problems, please study Section A.4, Cartesian Graphs, and A.5, Dimensional Analysis, on pages a sec; b. 4.8 sec 2. a. meter; b. kilogram; c. second; d. 10-2, 102; e. 10-3, 103; f. 103, 10-3 RIGHT TRIANGLES SELF-CHECK Keywords: Trigonometry; Trigonometric Functions A surveyor wishes to determine the distance between two points A and B, but he cannot make a direct measurement because a river intervenes. He steps off a line AC at a 90º angle to AB and 264 meters long. With his transit, at point C he measures the angle between line AB and the line formed by C and B. Angle BCA is measured to be 62º. What is the distance from A to B? RIGHT TRIANGLES SELF-CHECK ANSWERS Distance AB = 497 meters. If you had difficulty getting this answer, you will find additional information in Section A.6, Right Triangles, of the appendix. TRIGONOMETRIC RELATIONSHIPS While nearly all of the problems in the book can be worked using the definitions of the sine, cosine, and tangent you have seen derived for right triangles, there are some relationships between these functions that it will be useful for you to know. We will derive them below. See Fig. (0-1) From the Pythagorean theorem you learned in high school, you know the relationship between the three sides of a right triangle; i.e., the sum of the squares of the two sides is equal to the square of the hypotenuse x2 + y2 = r2 (1) Look again at Figure (0-1). Note y/r = sin q = cos a (4) x/r = cos q = sin a (5) Since q + a + 90º = 180º i.e., the sum of the angles of any triangle equals 180º, then a = 90º - q The angle a is called the complement of the angle q. From equations (4) and (5) above notice that the sine of an angle is equal to the cosine of its complementary angle and the cosine of the angle is equal to the sine of its complementary angle.

10 Example: An arrow shot into the air comes vertically down and sticks in the grass on the side of a hill inclined 68º from vertical. What portions of the arrow point down the hill and perpendicular to the hill? See Figure Now we divide both sides of equation (1) by the square of the hypotenuse, r2, x2/r2 + y2/r2 = 1 Then recall the definitions of sine and cosine, sin q = y/r; cosine q = x/r so x2/r2 cos2q; y2/r2 sin2q thus x2/r2 + y2/r2 = cos2 q + sin2 q = 1 (2) The sum of the squares of the cosine and the sine of any angle is equal to one. In a similar way we can derive a relationship between the tangent, sine and cosine of any angle. tan q = y/x. Divide both numerator and denominator by the hypotenuse, r tan q = (y/r) / (x/r) = sin q/cos q (3) The tangent of any angle is equal to the ratio of the sine of the angle to the cosine of the angle. EXPONENTS SELF-CHECK Keywords: Exponentials; Powers x 83 = = x 10-3 = =. EXPONENTS SELF-CHECK ANSWERS Keywords: Exponentials; Powers If you had difficulty with any of the above answers, you can find additional assistance in the Appendix, Section A.7, page 745. LOGARITHMS SELF-CHECK Keywords: Powers; Logarithms Use the properties of Logarithms to solve each of the following problems: 1. 3 x 5 =. 2. 3/5 = =. 4. Solve the following equation for X: 16 = 4(102X) LOGARITHMS SELF-CHECK ANSWERS If you had difficulty with any of these problems, please study Appendix Section A.8, page 746. EXPONENTIAL FUNCTION SELF-CHECK Use the properties of exponential functions to solve each of the following problems. 1. If the population of a growing country is governed by the relation, N = 100, t, where t is in years, how long will it take for the population to double?

11 2. Predict the total population of the country in 10 years. EXPONENTIAL FUNCTION SELF-CHECK ANSWERS years thousand If you had difficulty with either of the problems posed above, please turn to Appendix Section A.9, page 748. PRACTICE TEST 1. (Powers of Ten Notation and Significant Figures) Solve the following problems using the powers of ten notation. In each case write your answer with the appropriate number of significant figures. a) 731 x x 431/0.005 =. b) 4.7 x 10-7 x 2.51 x 105/ =. c) Solve for A: 795 x x 103 A = x 104 =. 2. (Cartesian Graphs and Dimensional Analysis) The following data were taken from a physics laboratory experiment Velocity of a Rolling Coin Time (m/s) (S) a) Plot a graph showing velocity and time for this rolling object. b) Calculate the slope of the curve at (4, 15). c) Give the proper dimensions to the slope. 3. (Right Triangles) To find the height of a tall building, a physics student steps 75 paces (each 1 meter) from the base of the building. Using a ruler at arm's length (1 meter), the student finds that at this distance, the building appears to be 50 centimeters when compared to the ruler. Determine the approximate height of the building. 4. (Exponents) Calculate the following using the laws of exponents. a) =. b) 108 x 10-3 =. c) x =. 5. (Logarithms) Use the properties of logarithms to solve each of the following problems. a) 7 x 4 =. b) 20 4 =. c) 93 =. d) Solve the following equation for X: 2700 = 300(103X) 6. (Exponential Function) Use the properties of the exponential function to solve the following problem: a) A biologist determines that during the month of June, the number of live frogs in a small pond is governed by the relationship N = 189e. 075t (t is the number of days). How long will it be until the number of frogs is three times its initial population?

12 b) Predict the total population of frogs by the end of the month (30 days). ANSWERS: 1. a) 6.36 x 107 b) 6 x 101 c) 1.52 x b) 10 c) m/sec m 4. a) 57 b) 105 c) a) 28 b) 5 c) 728 d) a) 14.6 days b) 1800

13 Chapter 1 Human Senses GOALS Keywords: ; Learning Objectives; Humans; Sensory Systems; Transducers; Energy; Force; Interactions; Variables; States Of Systems; Systems; Intensity When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define the following terms, which can be used to describe a relationship between you and your environment: system energy state force variable field interaction intensity transducer Stimuli List the major external stimuli that are detectable by humans. Human Responses Describe an elementary threshold measurement experiment, and interpret the data obtained. Models Use a mental construct, or model, to explain a common human experience. PREREQUISITES You may find it necessary to review your knowledge of the powers of ten notation before you study this chapter. OVERVIEW Keywords: Sensory Systems; ; Instructions Without much difficulty you can probably name the five senses of the human body. As man has learned more about his surroundings, he has learned more about himself and about his ability to interact with his environment. In this chapter you will learn about the physical nature of your human senses. SUGGESTED STUDY PROCEDURE When you begin your study of this chapter, be familiar with each of the four Chapter Goals: Definitions, Stimuli, Human Responses, and Models. (Please note than an expanded discussion of each term listed under Definitions is given on the next page of this.) Next, read Chapter Sections Be sure to attempt some of the more interesting Simple Experiments suggested and consider several of the probing questions posed at the end of most of the sections. (Answers to these questions are given in the second section of this.) At the end of the chapter, read the Chapter Summary and complete Summary Exercises 1-4. Now do Algorithmic Problems 1-6 and complete Exercises 1, 2, 3, 4, 7, and 8. Now you should be prepared to attempt the Practice Test on Human Senses found in this. This study procedure is outlined below.

14 Chapter Goals Suggested Summary Algorithmic Exercises & Text Readings Exercises Problems Problems Definitions Stimuli ,3 3,4,7,8 Human Responses ,3 2,4,5,6 1,2 Models DEFINITIONS Keywords: ; Glossary; Transducers; Interactions; Energy; States Of Systems; Variables; Force; Systems; Fields; Intensity SYSTEM A whole entity. In marked contrast to the holistic thinking that characterizes much of human activity, physics uses an analytical technique that seeks to understand complex situations by dividing them into separate parts which we call systems. We try to imagine that a system is a separate part of the universe which we can study without the system being changed either by our study or by whatever is happening in the rest of the universe. For example, if we wish to study the physics of human hearing, we will define the system of study as the human hearing system and include within it all of the parts of the body that are necessary to hear sounds. Of course, such a system is quite unreal since you cannot hear anything if the other parts of your body cease to function. Nevertheless, this mental, somewhat artificial, technique of dividing up the universe into separate systems has allowed us to make great strides in the study of nature. VARIABLE Quantity that is subject to change. Once you have picked a system for study you can analyze the ways you can change or vary the characteristics of the system. For example, you can modify the human hearing system by the use of drugs or the use of ear plugs. The properties of a system that we can change or vary we call variables. One big idea of physics is to find all of the important variables of a system and see how changes in each of the variables affects the rest of the system. You will notice once again the analytical approach, chop a system into parts called variables, and see if we can understand the whole system by finding the ways the variables influence one another. STATE Particular form or condition of a system. It is usual for physicists to define the starting point of their study of a system by attempting to give all of the important variables of the system some initial value thereby specifying the initial state of the system. For example, if you wished to

15 study the influence of various amount of cotton ear plugs on human hearing, you could define your starting condition, or initial state, as a well rested, typical human with no wax or obstructions in the ear canals. TRANSDUCER A sensor or detector that transforms a change in one physical variable to a change in another. In many cases we wish to observe the changes in the properties of a system. Often it is possible to infer a change in a system by measuring a related, but different, property. In such a situation we make use of a transducer, a part of the system that relates the change of one variable of the system to another. For example, the eardrum acts to transform the sounds that fall on your ear into vibrations of the eardrum which are subsequently transformed into the electrical messages that are sent to your brain. The eardrum serves as a transducer. INTERACTION Action or influence exerted between systems. If we wish to study the influence of one system on another we say we will study the interaction between two systems. Then we will proceed to change the values of variables of one system to see if that causes any changes in the values of the variables of the second system, e.g., if we change the noise level in the room where our human subject is located that will change the response of a typical person. ENERGY Property of a system which causes changes in its own state or state of its surroundings; measure of ability to do work (physical). One way to specify the state of a system is to compute the energy of the system. Energy is a kind of imaginary property of a system that physicists have invented to help define in a more holistic way the state of a system. We never actually measure energy directly but only calculate it from other variables that we can measure. In a sense, energy is to a system as meaning is to a poem. In general, a group of physicists think that they can objectively agree upon the energy of a system, while a group of poets are not likely to think that they can objectively agree upon the meaning of a poem. Does the fact that ten people can agree upon the same value of an imaginary quantity make it truly objective? FORCE A measure of the strength of an interaction; a push or pull; the effect of a force is to alter the state of motion of a body. A vector quantity with a magnitude measured in Newtons (N). From our earliest experiences as children we know of the interactions between systems by physical contact. From our beginnings as humans we have responded to the direct contact of another person. Throughout our early experiences of

16 collisions with walls and falling down we know of the effects of direct contact interactions. We use the term force to designate the strength of interaction between two systems. We have the idea that a greater force applied to a system is most likely to cause a greater change in the system. FIELD A region of space characterized by a physical property which has a determinable value at every point in the region, e.g., gravitational field, magnetic field, etc. Our experiences with direct contact interactions are so convincing that physicists have invented a concept of a field that can be used to bring into contact systems that may be widely separated from one another. The physicist just imagines a field exists everywhere between the two systems and the field of one system may exert a force on the second system. INTENSITY Energy transported through a unit area in one second. Another idea that is readily associated in our minds with direct contact interactions is the transfer of energy from one system to another, such as the energy of food being transferred to the energy of your body via the life processes. In a similar way we can think of a field as having a source which emanates energy to all objects in its field. We characterize the intensity of a field by the amount of energy its source emanates per unit of area in one second. If we are in the field of a light bulb our eyes interpret the intensity of the bulb in terms of brightness, the more intense the source, the greater is the brightness of the light. ANSWERS TO QUESTIONS FOUND IN THE TEXT Keywords: ; Answers; Systems; States of Systems; Humans; Anatomy And Physiology; Biology; Variables SECTION 1.2 The Human System 1. A human being is a complex set of interacting systems. To properly describe in a holistic way your present state would require you to define the different states of your basic body systems such as the skeletal-muscular system, digestive system, urinary system, respiratory system, circulatory system, nervous system, and reproductive system. You are usually not very aware of the present state of any of these systems even though your brain must continually monitor the activities that occur in all parts of your body. To determine the present state of your circulatory system you could find your pulse rate, blood pressure, and results of various tests on your blood. Even so, many details of your circulatory system would be left undefined. 2. Your present state is determined by the values of many variables of the body systems listed above. Such variables as pulse rate, blood pressure, etc., can be specified. However, there is evidence that personality features such as self-worth or

17 faith can have an important influence on many of your physiological variables. Historically such variables as faith and self-worth are classified as not being physical observables. SECTION 1.3 The Human Detector Keywords: ; Answers; Sensory Systems; Interactions; Energy; Electric Fields; Gravitational Fields; Sound; Light And Optics; Auditory Systems; Optical Systems; Human Body 3. At this moment you are interacting with your environment through a wide variety of systems. The force of the chair on your bottom is a mechanical energy interaction. Your eyes are responding to electromagnetic, or light, energy. Your ears are picking up sound energy. Your nose and taste buds sense odors and tastes by chemical energy. Your body is said to be immersed in the gravitational and electromagnetic fields of the earth and sun. The influence of these fields upon you is not well understood. 4. In general, we can think of the odor, sound, gravitational, and light or electromagnetic interactions as being interactions-at-a-distance, while taste of food and the force of the chair may be envisioned as direct contact interactions. SECTION 1.4 Direct-Contact Interactions Keywords: Answers; ; Interactions; Sensory Systems; Tactile Systems; Thermal Regulatory Systems; Human Body 5. There are areas of your back, legs, and feet that seem relatively insensitive to touch. Your finger tips, tongue, and forehead is quite touch sensitive. 6. By tasting a variety of known salt concentrations it is believed you could train yourself to be a salt water taster. Just as, after years of practice, persons are able to perfect their taste sense to become professional wine tasters. 7. Both the inside of your arm and your lips are particularly thermal sensitive while your hands and face have fewer nerves to detect heat and cold than other parts of your body. SECTION 1.5 Interaction-at-a-Distance Keywords: ; Answers; Interactions; Action At A Distance; Human Body; Electromagnetic Waves; Sound; Gravitational Forces; Sensory Systems 8. You have surely experienced sunshine, music, noise, voices, smells and food today. Have you climbed some stairs, ridden a bicycle up a hill, or hiked to the top of a mountain? 9. Sunshine (electromagnetic); music, noise, voices (sound); smells and food (odor); stairs, hill, mountain (gravitational). 10. Your ears are never shut, so the interaction-at-a-distance most common for non-deaf humans is probably sound. SECTION 1.7 Threshold for the Sense of Touch Keywords: Answers; ; Human Body; Tactile Systems; Thresholds 11. Various whole body variables such as state of restfulness, lack of influence of drugs, normal blood pressure and blood

18 sugar concentrations, etc. 12. One source of error is the inability of a subject to tell exactly when a touch is felt. Doing repeated measurements with each subject in a varying sequence of locations so that several threshold measurements are performed at each location should prove helpful in reducing this uncertainty. 13. Figure 1.3 shows a technique that can be used to determine the distance between distinct contact points. SECTION 1.8 Model Building Keywords: ; Answers; Models; Humans; Sensory Systems; Philosophical Implications 14. In each of these cases a powerful group of persons developed an explanation of the behaviors of other groups of humans that defined them as less than human, e.g., savages, enemies of progress, threats to national security. These mental constructs, or models, were used to justify a wide variety of inhumane and unjust treatments. 15. For most scientists, the subject areas of extrasensory perception, of mind-brain research, and of how the human beings develop logical thought are still not scientifically ordered. Two areas of science, molecular biology and astrophysics, have contributed new concepts to our daily language by popularizing the double helix and black holes. PRACTICE TEST Keywords: ; Problems; Answers; Transducers; Evaluation; Interactions; Thresholds; Humans; Sensory Systems; Questions; Heat; Action At A Distance; Tactile Systems; Auditory Systems; Models; Sound; Contact; Forces; Scientific Method 1. You are in a swimming pool several meters away from another person also in the pool. Name below three methods you might use to gain the person's attention. For each case, identify or describe transducer you use and mark the interaction as either a contact (C) or action-at-a-distance (A-D). Method Transducer Interaction (C or A-D) Imagine that you are taking a shower in a bath with "inadequate plumbing" and find the shower temperature difficult to control. As the water temperature changes drastically, please describe the response your body makes to this variable in terms of a. Threshold - b. Sensitivity - c. Discrimination - 3. The different parts of your body respond with different sensitivity to outside physiological stimuli. Consider the bottom of the feet and their response to four major stimuli as outlined below. Please rank each stimuli from 1- body part most sensitive

19 to stimulus to 4-body part least sensitive to stimulus. Body Part or Area Tested - Bottom of Feet Ranking Stimuli Interaction Heat Contact Visible light Action at a distance Ultraviolet light Action at a distance Low frequency sound Action at a distance 4. What is a "model" in physics? ANSWERS: 1. Shouting, Vocal Chords, A-D Making Waves, Hands & Arms, A-D Splashing Water, Hands & Arms, C 2. Threshold - Minimum temperature difference detected by the body Sensitivity - Body's receptors reaction to various incoming energy (heat) levels Discrimination - Detection of temperature differences across the shower spray or ability to tell if the temperature of the water is changing with time. 3. 1, 4, 2, 3 (other answers accepted under other physical conditions). 4. A model is a specification of a unification of ideas which help to visualize a variety of experiences. In physics, these experiences deal primarily with aspects of the physical nature of the world.

20 Chapter 2 Unifying Approaches GOALS When you have mastered the content of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and use each term in an operational definition: equilibrium restoring force conservation laws inertia oscillatory motion feedback gradient linear system natural frequency current superposition resonance Inertia Give an example of a physical system that has mechanical, thermal, and electrical inertia. Energy Transfer Explain how you would maximize the transfer of energy at the interface between two systems. Superposition Solve problems making use of the superposition principle-given the proper physical variables of the systems. PREREQUISITES Before beginning this chapter you should have achieved the goals of Chapter 1, Human Senses. If you have not recently been working with cartesian coordinate graphs and dimensional relations, you may wish to review the material on graphs and dimensional analysis in the mathematical background supplement in the appendix. OVERVIEW Keywords: ; Instructions; Inertia; Superposition Principle; Flow Of Energy As men have attempted to make sense of physical phenomena, a series of approaches have emerged. Some of these approaches are descriptive, some are mathematical, some may be both. In this chapter you will study some of the basic approaches used again and again to understand and/or explain the actions of a variety of physical phenomena. SUGGESTED STUDY PROCEDURE In this chapter, you should direct your study toward all four Chapter Goals: Definitions, Inertia, Energy Transfer, and Superposition. An expanded treatment of each of the terms listed under Definitions is given on the next page of this Study Guide. Next, read all the chapter sections, Please note the questions asked throughout your reading. Answers to these questions are given in the following pages of this. At the end of the chapter, read the Chapter Summary and complete Summary Exercises Next, do Algorithmic Problems 1, 2, 3, 4, 7, and 8. Finally, complete Exercises and Problems 2, 3, 4, and 5. Now you should be prepared to attempt the

21 Practice Test on Unifying Approaches given in this. This study procedure is outlined below Chapter Goals Suggested Summary Algorithmic Exercises Text Readings Exercises Problems & Problems Definitions 2.1, 2.2, 2.4, , 2.10 Inertia , 2 3, 4 Energy Transfer , 4 5 Superposition 2.6, 2.7, , 8 DEFINITIONS Keywords: Glossary; ; Equilibrium; Inertia; Kinds Of Force; Oscillations; Oscillatory Motion; Waves And Sound; Superposition Principle; Gradient; Conservative Laws; Feedback; Resonance; Frequency EQUILIBRIUM All the influences acting on the system are canceled by others, resulting in a balanced unchanging system. Nature is comfortable. Everything else being equal, the systems in nature tend to their lowest possible energy states and to equilibrium, a state in which all the external disturbances acting on a system are balanced or canceled out. Perhaps you are presently seated, relaxed, reading this. You are in a state of equilibrium. INERTIA Property of system that is a measure of the system's resistance to change. If you wish to stand up, the bulk of your body tends to remain seated. The tendency to stay put is called inertia and is given a numerical value of mass for systems in which motion is studied. Whereas this resistance to motion is called mechanical inertia, the resistance an object offers to the flow of electrical change is called electrical inertia and the resistance to heat flow is called thermal inertia. RESTORING FORCE Force acting to return a displaced body to equilibrium position. You may have had the task of trying to move an automobile, or motorcycle, stuck in the mud or snow. In its stuck condition, it was in equilibrium: when you pushed it you moved it from its equilibrium position. When you stopped pushing it may have rocked back and forth about its starting position. Most systems in equilibrium experience a force that tends to move them back to their original position if you only move them a small amount from equilibrium. This force is called a restoring force. OSCILLATORY MOTION Characteristic motion of systems having a linear restoring force. The action of a restoring force on a system causes the system to rock back and forth about the original position. This back and forth motion is called Oscillatory Motion. LINEAR SYSTEM A system in which the restoring force is directly proportional to the displacement.

22 Suppose you attempt to push a stuck vehicle out of the snow or mud. If you find that you must push twice as hard to move it twice as far from its original equilibrium position, this system is called a Linear System. Once this fact is established, simple addition can be used to estimate the number of pushers (each pushing the same amount) needed to get your vehicle out of trouble. If you can push it one-fourth of the way out, then four persons (all pushing the same direction) should be able to push it all the way out. SUPERPOSITION The resultant effect is equal to the sum of the individual independent effects. A principle that holds true for linear systems. When linear and independent systems interact, the total effect of their action can be found by simply adding the contribution of each. Please note that an application of this superposition principle in the definition of linear system was used in the case of a vehicle stuck in the snow or mud. When one person can push the vehicle onefourth of the way out of its position, four persons should be able to push it all the way out. Note that if five persons were to push, three one way and two the other, the vehicle would move one-fourth of the way from equilibrium. GRADIENT Rate of change of a physical quantity relative to position. What is the present temperature of your surroundings? The thermal conditions of your surroundings is one of the most important aspects of maintaining a comfortable environment. We readily notice a temperature difference when we go from inside to outside a building in winter or in summer. If a variable, such as temperature, has different values at two different locations, then we can talk about gradient, in this case a temperature gradient, existing between the two locations. We compute the size of a temperature gradient by calculating the ratio of the difference between the temperatures at the two locations to the distance between the locations. CURRENT A steady and onward movement of a physical quantity. The ratio of the change in a quantity to the change in time. Consider the wall of a home where the inside temperature is much higher than the outside temperature. Because of the difference of temperature, we can detect a flow of heat or current from the inside to the outside which occurs in response to the temperature gradient. For simple systems the current is a linear function of the gradient. CONSERVATION LAWS There is no change in a physical property with a change in time. In many life situations we get our bearings from fixed objects, whether they are the North star, the city hall, or the university bell tower. Similarly, in physics we look for fixed, or constant, properties of a system to help us understand it. A property of a

23 system which does not change is called a conserved property, or quantity. We can then formulate a conservation law for the system we are studying. A conservation law, simply put, states that even though time marches on, a particular property of the system does not change. It would be difficult to overemphasize the importance of conservation laws in the growth of physics. In systems where conservation laws seem to be violated, physicists have invented new variables to preserve conservation. Now physicists have a whole list of properties of systems that can be conserved under certain conditions, such properties as energy, mass, electrical charge, momentum, atomic number, strangeness, charm, baryon number, etc. The list seems to get longer every year, as new conservation laws are invented. FEEDBACK A portion of the output from a system is returned as input into the same system. A common result of positive feedback is the squeal that occurs when an amplifying system is not correctly used at a musical event. The result often occurs when the amplifier system speakers are placed close enough to the microphone to have the amplified sound picked up by the microphone and circulated through the system again. NATURAL FREQUENCY The frequency of a freely vibrating system, i.e., the number of vibrations per second that are characteristic of the system. If you strike the middle C key on a piano you excite the natural frequency of vibration of the stretched wire in the back of the piano. It oscillates at a frequency of 256 vibrations per second. RESONANCE Occurs when the frequency of the external force equals a natural frequency of the system. Resonance occurs when the frequency of an external interaction equals the natural frequency of the system. On a playground swing, to pump up the amplitude of the swing you must pull on the swing support chains at the proper time using a frequency of pulling equal to the frequency with which the swing goes to and fro. ANSWERS TO QUESTIONS FOUND IN THE TEXT Keywords: Answers; ; Superposition; Principle; Feedback; Systems; Equilibrium; Oscillatory Motion; Oscillations; Waves And Sound SECTION 2.3 Inertia 1. Some systems in equilibrium are your (Fuller)3 physics text resting on your study table and your head resting on your hand with your elbow on the chair arm in your physics lecture. 2. Both of the above systems may tend to move back to their original position if lifted slightly. Gravitational interaction and your muscles will provide the restoring forces. 3. Suppose you can define a lack of knowledge parameter, a misconception parameter, and a concrete reasoning parameter. In each type of property, knowledge, concept, and reasoning, your class will have a characteristic average inertial parameter.

24 The class may be slow to respond to rapid changes in knowledge, concepts, and reasoning. SECTION 2.7 Feedback 4. The input for you is the information you are taking in from your environment. If you process that information and use it to modify the information you are taking in by asking a question or writing an explanation of a comment in your notebook, then you are using feedback. For your instructor, the input is information that is gathered from the students by means of questions, smiles, nods, or snores. The instructor uses feedback from the information to change the approach being used in the classroom to respond to student input. SECTION 2.8 Superposition Principle 5. There are a number of old myths that indicate marriage is not a linear transformation. "Two can live as cheaply as one," for example is no doubt false, but it does indicate a common understanding that superposition does not apply to marriage, i.e., the total of the married couple is not the sum of the individual persons. 6. A collection of marbles is a linear system with respect to number, weight, and volume occupied. A school of fish is linear with respect to volume occupied and oxygen used. A school of children is not linear with respect to economic factors. See Fig. EXAMPLES Keywords: ; Worked Examples; Superposition Principle; Speed; Galilean-Newtonian Relativity; Arithmetic; Scalar Arithmetic SUPERPOSITION 1. An Amtrak train is roaring East through Lincoln, Nebraska, at a speed of 100 km/hr. The conductor on board is collecting tickets from the back to the front of the train while walking at a speed of 2 km/hour. Meanwhile, a dining car waiter is serving hot dishes by rushing back and forth from the kitchen at a speed of 8 km/hour. What are the speeds of the various moving objects with respect to Lincoln? What Data Are Given? The speed of the train with respect to Lincoln = 100 km/hr. East The speed of the conductor with respect to the train = 2 km/hr. to the front The speeds of the waiter with respect to the train = 8 km/hr. to the front = 8 km/hr. toward the back What Data Are Implied? The speeds of all three are assumed to be along the same East- West line, so that linear superposition holds true. What Physics Principles Are Involved? Superposition - in this case, the algebraic sum of the various numbers. What Equations Are to be Used? We can write algebraic expressions for this problem by assigning symbols; let st = speed of the train, sf = speed of object moving forward on the train and sb = speed of object moving backward on the train.

25 Algebraic Solutions The speed of an object with respect to Lincoln sl is given by sl = st + sf for forward moving objects. sl = st - sb for backward moving objects. Numerical Solutions sl (train) = 100 km/hr. East sl (conductor) = 100 km/hr. + 2 km/hr. = 102 km/hr. East sl (waiter) = 100 km/hr. + 8 km/hr. = 108 km/hr. East when he is moving toward the front sl (waiter) = 100 km/hr. - 8 km/hr. = 92 km/hr. East when he is moving toward the back of the train. Thinking About the Answers Keywords: Einstein, Albert A.; Humor; Notice that the speed of the train is so much larger than the speeds of the conductor and the waiter that their motion relative to the train does little to change their motion relative to Lincoln. Their motion does seem important to them and the other people on the train. Notice also the analytic style of problem-solving. The final question is answered by cutting it into small pieces and using superposition. See Fig. PRACTICE TEST 1. Suppose after you have accurately weighed a small sample on an equal arm balance, you accidentally touch the balance pan, what happens? Describe the initial state of the balance, and its subsequent behavior. 2. List the three kinds of inertia of an electric frying pan. Give a specific action you can perform to verify the existence of each kind of inertia. 3. On a cold day in January, the inside wall of a home has a temperature of 29ø C. Twelve centimeters away, the outside wall has a temperature of - 7ø C. What is the temperature gradient? Which way does heat flow? 4. Eight college students are deadlocked in tug of war. A ninth student joins the contest. What physical principle can you use to predict the outcome? What do you predict will happen? If your prediction does not come true, how can you explain that? ANSWERS: Keywords: Questions; ; Equilibrium; Inertia; Superposition Principle; Harmonic Oscillations; Oscillations; Oscillatory Motion; Properties Of Oscillations; Evaluations; Gradients 1. Initial state - equilibrium (no motion); subsequent behavior - restoring force causes harmonic motion about the balance position (the equilibrium position). 2. A Mass inertia - Attempt to give the pan a velocity by pulling on it with a spring balance or to stop once placed in motion. B. Electrical inertia - Apply a voltage and determine the resistance to the flow of current.