Alfred Bennick
Robert Costello
David Lavallee
Ezra Shahn
Fred Szalay
Hunter College of the City University of New York
INTRODUCTION
This course is a recently implemented addition to the Hunter curriculum which may be used by our undergraduates in partial fulfillment of Category I (Sciences and Mathematics) of the College's distribution requirement. Briefly, it was conceived as a one year introductory course for non-science majors which would begin their exposure to "Science." Because it is introductory, it was felt that a lab component was essential. Because it was anticipated that it would be followed by a more intensive science course experience, it was felt that it was not critical that the frontiers of any area be explored. And for both of these reasons we felt that an attempt at surveying the entirety of science would be misdirected; there is really too much to know for a comprehensive survey to be justified. Rather, we decided that an introduction to a limited number of the broad concepts that lie at the foundations of science should be made in a moderately rigorous manner. This would enable our students to leave the course with the background information needed to appreciate "how we know what we know, why we believe what we believe."
GOALS
The primary goal of this course is to provide the non-science major with an introduction that will both lead to the appreciation of science, and facilitate its understanding. This introduction will emphasize the nature of scientific reasoning and will include illustrations of the scope of the material, the nature of scientific questions (and answers), the similarities and differences in the approaches to questions raised in the different areas, and the common features which tie many of these areas together. When considered in the context of these different areas, "science" is defined by both its methodology (involving an approach to "truth" that is continually subject to revision, and is thus "self-correcting") and its subject matter (the study of the "outside world"). This course is conceived as the beginning of the students' formal experience with science; it is expected that upon completion of this course they will take at least one subsequent course that will involve studying "science in depth." In this introduction students are exposed to
Because today science is assumed to deal with an outside world, the course has, as an integral part, "laboratory" periods devoted to extending the students' experience and providing an understanding of how nature and natural phenomena can be critically observed, measured, analyzed and tested. That is, the role of appealing to nature to define the nature and limits of scientific inquiry and to test the validity of predictions which follow as necessary conclusions of proposed explanatory models are explored.
An additional goal is that students learn to see science as a human activity that, in part, deals with the variety of problems that society faces as it interacts with (manipulates?) its environment. While this is not a course in the philosophy of science as such, the philosophical foundations which govern scientific practice are highlighted, especially as they distinguish science from other human endeavors. Beyond that, the relationship of science to social and industrial needs and the technology of a given period are indicated by appropriate references throughout the course.
FALL SYLLABUS
| Lecture Topic | Reading | Lab No. | Laboratory Topic | Writing Assignment (Essay #) |
| 1 Course Introduction | Preface, Shahn: Intro. | 2 | Celestial Phenomena of the Night Sky | |
| 2 The Year and the Calendar | Bennick: Chapter I | 2 | (Celestial Phenomena of the Night Sky) | I Assigned |
| 3 A Closer Look at the Sky | Bennick: Chapter II | 2
3 |
(Celestial Phenomena of the Night Sky)
Archimedes' Principle |
|
| 4 A Geometrical Approach | Bennick: Chapter III | 3 | (Archimedes' Principle) | I DUE |
| 5 Aristotle's Laws of Motion | Bennick: Chapter IV | 3 | (Archimedes' Principle) | |
| 6 Aristotle's Astronomy | Bennick: Chapter V | 3 | (Archimedes' Principle) | I Returned
Open Lab Discussion |
| 7 A New View of the Universe--Aristarchus and Hipparchus | Bennick: Chapter VI | 4 | Open Lab Discussion
Measurements in Space |
|
| 8 An Experimental Physics--Eratosthenes and Archimedes | Bennick: Chapter VII | 4 | (Measurements in Space) | I Revised DUE |
| 9 The Different Approach of Ptolemy | Bennick: Chapter VIII | 4 | (Measurements in Space) | |
| 10 Aristotle is Reexamined | Bennick: Chapter IX | 4
5 |
(Measurements in Space)
Models and Their Consequences |
II Assigned |
| 11 Copernicus Changes the Game--Retrograde Motion Explained | Bennick: Chapter X | 5 | (Models and Their Consequences) | I Revised Returned |
| 12 Tycho & Kepler | Bennick: Chapter XI | 5 | 5 (Models and Their Consequences) | |
| 13 Kepler's Laws | Bennick: Chapter XII | 5
6 |
(Models and Their Consequences)
Galileo I: Uniform Acceleration c.1990 |
II Due |
| 14 Galilean Astronomy | Bennick: Chapter XIII | 6 | (Galileo I: Uniform Acceleration c.1990) | |
| 15 Galilean Mechanics | Bennick: Chapter XIV | 6 | Galileo I: Uniform Acceleration c.1990 | |
| 16 Galileo Applies his Theory | Bennick: Chapter XV | 6 | Galileo I: Uniform Acceleration c.1990 | II Returned |
| 17 Motion and Collisions: A Prologue to Newton | Bennick: Chapter XVI | 7 | Galileo II: Uniform Acceleration c.1990 | |
| 18 Newton's Laws I: Inertia | Bennick: Chapter XVII | 7 | (Galileo II: Uniform Acceleration c.1990) | |
| 19 Newton's Laws II: Forces and Reaction | Bennick: Chapter XVIII | 7 | (Galileo II: Uniform Acceleration c.1990) | |
| 20 Newton's Law of Gravity | Bennick: Chapter XIX | 8 | Newton: The Second Law | II Revised DUE |
| 21 The Consequences of Gravity: Motion at a Distance Tides | Bennick: Chapter XX | (Newton: The Second Law) | ||
| 22 EXAM: Lectures 1-20 | 8 | (Newton: The Second Law) | ||
| 23 Work and Energy | Bennick: Chapter XXI | 9 | Conservation of Mechanical Energy | II Revised Returned |
| 24 Heat and Conservation of Energy | Bennick: Chapter XXII | 9 | (Conservation of Mechanical Energy) | |
| 25 Satellites | Bennick: Chapter XXIII | 9 | (Conservation of Mechanical Energy) | III Assigned |
| 26 Space Travel | Bennick: Chapter XXIV | 10 | Hooke's Law and the properties of matter | |
| 27 Conclusion Theme I | Bennick: Chapter XXV | 10 | (Hooke's Law and the properties of matter) | |
| 28 Bridge; Intro Theme II | ||||
| 29 On the Nature of Matter--I | Singer: pp 41-61 | 11 | Pressure of the Atmosphere: Boyle's Law | III DUE |
| 30 On the Nature of Matter--II | Singer: pp 731-752 | 11 | (Pressure of the Atmosphere: Boyle's Law) | |
| 31 Properties of Air: Torricelli & von Guericke | MacKenzie: Chapt 5 | 11 | (Pressure of the Atmosphere: Boyle's Law) | |
| 32 Properties of Air: Boyle | Conant: pp 3-11 | 12 | The Release of "Fixed Air" | III Returned |
| 33 Identification of Gases | MacKenzie: Chapt 8 | 12 | (The Release of "Fixed Air") | |
| 34 Physical and Chemical Properties of Air | Lowry: pp 64-101 | 12 | (The Release of "Fixed Air") | |
| 35 Measurements of Gases | Lowry: | Open Lab Discussion | III Revised DUE | |
| 36 The Atomic Theory of Dalton | Dalton: 144-148, 162-168 | 13 | The Relative Weights of Particles in Gases | IV Assigned |
| 37 The Kinetic-Molecular Theory | Lowry: pp 291-359 | 13 | (The Relative Weights of Particles in Gases) | III Revised Returned |
| 38 Numbers of Particles--Avogadro | 13 | (The Relative Weights of Particles in Gases) | ||
| 39 Composition of Gas Particles | 14 | Combining Weights of Metals | ||
| 40 Atomic Weights of Gases: Guy-Lussac and Combining Volumes | 14 | (Combining Weights of Metals) | IV DUE (no revision) | |
| 41 Atomic Weights of Solids: Cannizzaro and Specific Heats | 14 | (Combining Weights of Metals) | ||
| 42 Mendeleyev's Periodic Table | Posin: (selections) | Open Lab Discussion |
SPRING SYLLABUS
| Lecture Topic | Reading | Lab No. | Laboratory Topic | Writing Assignment (Essay #) |
| 1 Kinetic-Molecular Theory of Gases I | Shahn: Kinetic-Molecular Theory | 1 | Separation of Molecules | |
| 2 Kinetic-Molecular Theory of Gases II | Bigelow: 135-142 | 1 | (Separation of Molecules) | 1 Assigned |
| 3 Atoms and Molecules: Inorganic Substances Electrical Theories | Benfy: 5-13 / Lavallee: 1-10 | |||
| 4 The Architecture of Molecules--Do the same ideas apply to organic matter? | Benfy: 14-18, 23-29 / Lavallee: 2-5 | 2 | Capillary Action | |
| 5 Natural and Synthetic "Organic" Substances Molecules from Living Beings and the Lab | Young: 240-250 | 2 | (Capillary Action) | 1 DUE |
| 6 Molecular Attractions and Polar Molecules | Jones: 100-105 109-112 / Benfy: 21-23 / Lavallee 5-7 | |||
| 7 Structural Models, Symmetry Dyssymmetry, and Water | Zumdahl: 102-103 / Lavallee: 7-10 | 1 Returned | ||
| 8 Monomers and Polymers | Lavallee: Atomic Sizes | 3 | Molecules in Solution | |
| 9 Atomic and Molecular Sizes | Jones: 44-59 | 4 | Molecules in Three Dimensions | |
| 10 Structure of the Atom--Electrons and Nuclei | Shahn: Atomic Structure and Radioactivity 1-8 | 4 | (Molecules in Three Dimensions) | 1 Revised DUE |
| 11 Structure of the Atom--Electrical Experiments and Spectra | Young: 84-94 | |||
| 12 Radioactivity | 4 (Molecules in Three Dimension) | 5 | Monomers and Polymers | 1 Revised Returned |
| 13 Summary/Conclusion/Review | 5 | (Monomers and Polymers) | ||
| 14 Bridge/ Intro to Theme III | 2 | Assigned maleen horkowitz | ||
| MIDTERM EXAM: Lectures 1-12 | 5
6 |
(Monomers and Polymers)
Rocks I: A Classification |
||
| 16 Ideas and concepts in the "historical sciences" | Bock: 199-207 | 6 | (Rocks I: A Classification) | 2 DUE |
| 17 Ancient accounts of diversity of life and earth history | Rook: (Aristotle): 41-47 / Futyma: 2-3 | |||
| 18 The Middle Ages and natural history | Futyma: 3-6 | 6 | (Rocks I: A Classification) | |
| 19 Origins of geological science | Blinn: Chapter 2 | 7 | Rocks II: Land Forms (Transformation I) | |
| 20 The Neptunists and Plutonists | Blinn: Chapter 2 | 7 | (Rocks II: Land Forms (Transformation I)) | 2 Returned |
| 21 Catastrophism vs uniformitarinaism | Blinn: Chapter 3 | 7
8 |
(Rocks II: Land Forms (Transformation I))
The Diversity and Classification of Life (Transformation II) |
|
| 22 Origins of Scala Natura | 8 | (The Diversity and Classification of Life (Transformation II)) | 2 Revised DUE | |
| 23 The Age of Discovery and the need for taxonomies | Rook (Linnaeus): 242-253 | |||
| 24 The development of concepts of species | Mayr: 1-26 | 8
9 |
(The Diversity and Classification of Life (Transformation
II))
(Homology and Phylogeny (Transformations III)) |
|
| 25 The early evolutionists and near-evolutionists: Lamarck, Cuvier, and Erasmus Darwin | Rook (Lamarck): 254-267 / Darlington: 60-66 | 9 | (Homology and Phylogeny (Transformations III)) | 2 Revised Returned
3 Assigned |
| 26 Darwinian Evolution: Natural selection, Sexual selection | Mayr: 68-100 | |||
| 27 Darwinian Evolution: Descent | 9
10 |
(Homology and Phylogeny (Transformations III))
Natural Selection (Transformation IV) |
3 DUE | |
| 28 Opposition to Darwin | Mayr: 35-68 | 10 | (Natural Selection (Transformation IV)) | |
| 29 The evolution of species in the Darwinian Synthesis | ||||
| 30 Problems with heredity and var iation: Genetics before Mendel | Mayr: 90-132 | 10
11 |
(Natural Selection (Transformation IV))
Genetics I. Mendel's Ratios |
3 Returned |
| 31 Mendel and Heredity | Shahn: Cell Division | 11 | (Transformation V) | |
| 32 The chromosomal theory of heredity | Shahn: Genetics / Schwartz & Bishop | |||
| 33 The rise of population genetics | 11
12 |
(Transformation V)
Genetics II. Populations (Transformation VI) |
3 Revised DUE | |
| 34 Origins of The Modern Synthesis of evolution in the early 20th century | Mayr: 133-141 | 12 | Genetics II. Populations (Transformation VI) | |
| 35 The merging of ideas 1930-1940 | Mayr: 142-166 | |||
| 36 Molecular revolution in biology | Shahn: Molec. Genetics | 12
13 |
(Genetics II. Populations (Transformation VI))
Central Park Geology |
3 Revised Returned |
| 37 (Continued) Watson & Crick | 13 | (Central Park Geology) | 4 Assigned | |
| 38 Werner and moving continents | Nance: 72-79 | |||
| 39 Plate tectonics: revolution in modern geology | Crum | 13
14 |
(Central Park Geology)
Biostratigraphy and Patterns of Evolution |
4 DUE |
| 40 Catastrophes and mass extinctions in modern paleobiology | 14 | (Biostratigraphy and Patterns of Evolution) | ||
| 41 Darwinian Evolution, Society, and Politics | ||||
| 42 Course Conclusion | 14 | (Biostratigraphy and Patterns of Evolution) | 4 Returned |
REQUIREMENTS
In each term, there is a midterm and a final exam. In addition, students are required to write four short to medium length essays (1000--2000 words) per term. The grade breakdown for each term is: 55 points for the essays (10 + 15 + 15 + 15), 40 points for the exams (15 + 25), and 10 points for the lab.
Midterm and final examinations consist of a choice of 25 of 30 or so questions which can be answered in one or two sentences. The exam questions are selected from a larger number which have all been distributed at the beginning of the term. In all, we have prepared about four questions per lecture which comprise this set. By design, the answers to these questions summarize the content of each lecture. We hope that students will direct their attention to preparing answers to this small number of questions. Since these are all available, students may check their answers with their peers; if a group agrees on the substance of an answer it is highly likely to be correct. For these reasons, our expectations of the answers to these questions are fairly high. Also, on the final exams, students are asked to write longer essay questions in response to questions that they have not previously seen.
Students are required to write four short to medium length essays (1000--2000 words) per term. Three of these are returned to the students with extensive comment/criticism which they can use as the basis for a revised version. The revised paper is then used for grade determination in the course. In addition, beyond the three revised and one unrevised papers that are prepared at home, the final includes an essay question that is written under traditional exam conditions. The exact wording is not distributed beforehand, and there is no opportunity for revision.
Within this general format, we try to make the specific essay assignments increasingly sophisticated. Thus the first essay asks students to define, describe and give examples, but not to explain. The second essay asks for summaries of the use of models in explanations. The third essay asks that lab work be related to concepts that have been covered in reading and class contexts. And so on for subsequent assignments. Thus, we start with facts dealing with what the students actually observed, and descriptions of phenomena in terms that do not require explanation. We then proceed to use more complex relationships, and eventually to require that students evaluate their evidence to justify their conclusions. In the most common example, lab data must be examined from the point of view of reproducibility to establish its validity. By the end of the year, when we ask students to discuss the way in which different geological theories have been supported in the past, or for the type of evidence that supports the theory of evolution, we are expecting a much higher level of performance. We do not accept simple statements that a fact supports or is consistent with a conclusion; we want students to evaluate the evidence and lay out the reasoning that makes it relevant.
Clearly, the bulk of the student's grade is writing dependent (the only part that isn't is a 10 point contribution from lab work) over which the student has a considerable degree of control. By making writing important, we believe that students are shown that they should take it seriously.
In the following, samples of exam study questions, and essay topics are presented. A complete set of exam questions and essay topics can be obtained from Dr. Ezra Shahn.
Sample study and exam questions (Fall term)
1. Describe a method for determining the length of a year.
2. In any method for determining the length of a year, there is always some uncertainty in the result. How can we reduce this uncertainty and thus have a better estimate of the length of the year using the same method as before? Why does this work?
3. What is a major problem with constructing a solar calendar? How did Sosigenes solve this problem?
4. What is the: celestial pole, celestial equator, ecliptic, vernal equinox?
5. a. Describe the daily motion of the sun relative to i) our horizon. ii) the celestial sphere.
b. Describe the yearly motion of the sun relative to i) our horizon. ii) the celestial sphere.
6. Describe the motion of the planets relative to the celestial sphere. In what ways are the motions of Mars, Jupiter and Saturn similar to those of Mercury and Venus and in what ways are they different?
7. What is a model? What purpose does it serve?
8. How did Anaxagoras explain lunar eclipses? Why don't we get an eclipse every full moon?
9. What were Plato's basic assumptions about the motion of heavenly objects? What led him to adopt those assumptions?
10. What model did Plato use to explain the motions of the planets? In what major way did the model predict motions different from what is observed?
11. According to Aristotle, where was the center of the universe? How did this tie in with his ideas of natural motion and natural place?
12. What is forced motion? What is the requirement for forced motion to occur? What problem does this cause in trying to explain projectile motion?
13. Explain in words the relationship that Aristotle found amongst force, resistance, weight and velocity.
14. Aristotle came to some conclusions about how objects fall. Describe how he came to those conclusions.
15. Why did Aristotle modify Eudoxus' model of the universe? In what way did he modify it?
16. How did Aristotle's model of the universe explain the large diversity of matter on the earth?
17. State briefly four reasons that Aristotle gave for believing that the earth was a sphere. Describe one of these reasons in enough detail so that we can understand his reasoning.
18. How does Aristotle account for the phases of the moon?
19. What proposal did Heracleides make to modify Aristotle's model for the universe? In what way did it simplify the scheme?
20. What reasoning did Aristarchus use to get the relative sizes of the sun and moon?
21. What reasoning did Aristarchus use to conclude that the sun rather than the earth was at the center of the universe?
22. State three arguments that the ancient Greeks (before 200 AD) used to argue against a moving earth?
23. On what observations did Eratosthenes base his calculation of the size of the earth?
24. A necklace weighs 30 grams when weighed in air and 28 grams when weighed while immersed in water. What is the specific gravity of the necklace?
25. A bar of metal has its specific gravity determined by weighing it in water and in air. Its specific gravity is found to be 6.4. A piece of the bar amounting to 1/4 of the original bar of metal is cut off and its specific gravity is determined by the same method. What specific gravity will be obtained?
26. Are the results of a given measurement "exact?" Why? If not, how can you determine the "best" value for that measurement?
27. How does a major epicycle account for retrograde motion?
28. Describe "precession of the equinoxes." What information did Hipparchus use to discover this effect?
29. In his theory of the motion of the planets, Ptolemy used epicycles, eccentrics and equants. Describe two of these.
30. In what way does the use of equants violate Aristotle's basic assumptions?
31. How did astronomers of the middle ages calculate the size of the universe? How is it that different astronomers could get different results for this calculation?
32. What were two experiments that Buridan of Paris proposed that showed that there were flaws in Aristotle's theory of projectile motion?
33. Nicholas of Oresme showed that Aristotle had not proved some of his contentions concerning whether the earth was stationary or in motion. What was one of Oresme's counter-arguments?
34. Describe the universe according to Copernicus.
35. What information about the planets could Copernicus calculate from his model that could not be done from Aristotle's model? What interesting pattern emerged from these calculations?
36. According to Copernicus, how can we account for the fact that Mercury and Venus are never seen very far from the sun?
37. How did Copernicus account for retrograde motion?
38. In order to account for the fact that he could not detect the effect of parallax, Tycho proposed a combination model of the universe. Describe it. How does it account for the fact that there was no detectable effect of parallax?
39. How did Tycho's observations of a nova and a comet cast additional doubt on Aristotle's/ Ptolemy's astronomical system?
40. What major contribution did Tycho make in astronomy that ultimately led to the downfall of Aristotle's/Ptolemy's astronomy?
41. How did Kepler conclude that the equant was a better model for the earth's motion around the sun than the eccentric?
42. How did Kepler conclude that the orbits of the planets were ellipses rather than circles?
43. How did Kepler's first two laws conflict with Aristotle's basic assumptions?
44. Why was Kepler so pleased with his third law?
45. How did Galileo's observations of the earth's moon conflict with Aristotle's theory of astronomy?
46. In what way did Galileo's observations of the moons of Jupiter conflict with Aristotle's theory of astronomy?
47. How did Galileo's observations of Venus cast doubt on Ptolemy's theory of the motion of Venus?
48. What are sunspots? What were three things about sunspots that Galileo discovered?
49. Give one example of why it is not useful to define uniform acceleration as having the velocity proportional to the distance traveled?
50. a) Define: uniform motion.
b) Define: uniform acceleration.
51. If an object moving from rest with uniform acceleration travels one unit of distance in one unit of time, a) how far will it travel in 5 units of time? b) how long will it take to travel 64 units of distance?
52. How did Galileo conclude that in the absence of resistance, the velocity that any falling object acquires depends only on the height it falls and not on the path through which it falls?
53. How did Galileo conclude that a ball in motion on a frictionless horizontal plane will continue its motion forever?
54. What were Galileo's assumptions to account for projectile motion?
55. How did Galileo's theory of resisted motion differ from that of Aristotle?
56. What argument did Descartes give for modifying Galileo's law for motion in the absence of forces?
57. Show how a straight line trip of 4 miles followed by a straight line trip of 3 miles can add up to a straight line trip of 5 miles from the starting point.
58. What is "conservation of motion?" Describe what happens during a collision in which both objects are in motion before the collision.
59. a) Define: inertia.
b) What characteristic of an object measures its inertia?
60. State Newton's first law of motion.
61. Discuss the concept of absolute, universal time. What are three difficulties in trying to discover this absolute, universal time?
62. In an air track experiment, a hanging weight of 6 paper clips causes a glider to accelerate.
a) If a weight of 2 paper clips is now used on the first glider, how will its new acceleration compare with its original acceleration?
b) If a weight of 6 paper clips is used on a glider which is 3 times heavier than the first glider, how will its acceleration compare with the first?
63. According to Newton, what is an object's weight?
64. Team A is in a tug-of-war with team B. Team A is winning since it is causing team B to accelerate in the direction of team A. Compare the force that team A is exerting on team B with the force that team B is exerting on team A. Is it larger, the same size or smaller? Explain.
65. An object is traveling around a horizontal circular path of radius r with a speed of v.
a) Is this object accelerating?
b) If your answer is yes, what is the magnitude and direction of the acceleration? If your answer is no, explain.
66. What did the moon and the falling apple have in common that led Newton to his law of gravity?
67. Show that inertial motion satisfies Kepler's law of motion.
68. Write an expression for Newton's law of gravity and state what each of the symbols represents.
69. In what way did Newton modify Kepler's three laws?
70. What were two unexplained problems in Newton's gravitational theory?
71. According to Newton's gravitational theory, why are there two high tides each day?
72. A person walking at a uniform velocity while carrying a heavy package does no work on that package. Explain.
73. a. Define energy.
b. Write a mathematical expression for potential energy.
c. Define kinetic energy.
74. An object at rest 6 feet above the floor has 24 units of potential energy. It is allowed to fall. When it is 2 feet above the floor, what is its a) potential energy? b) kinetic energy?
75. When an object is in a circular orbit, what is the relationship between its potential energy and its kinetic energy?
76. What observational evidence convinced Count Rumford that heat was a form of energy?
77. Two equal masses of chewing gum traveling towards one another collide, stick together and come to a halt. The kinetic energy that they had before the collisions disappears. Is this a violation of conservation of energy? Explain.
78. Assume that you are an astronaut in a circular orbit around the earth. What must you do in order to overtake (using a minimum amount of fuel) a satellite which is in the same orbit as you but located ahead of you?
79. Assume that you are an astronaut in a circular orbit around the earth.
a. What should you do to go into a larger circular orbit around the earth? (You may draw a diagram to help your explanation.)
b. How does the speed of your rocket in the larger orbit compare with its speed in the smaller orbit?
80. If you were on the outside of an orbiting shuttle and were pushed off of it, it would be better for you if you were to be pushed sideways to the motion of the rocket rather than in the direction of its motion. Explain.
81. Explain why a rocket can work in a vacuum where there is no air to push against.
82. Concerning a trip to Mars,
a. in which direction relative to the earth's orbit should the rocket be traveling at the "edge of the earth's gravitational field."
b. For most of the trip, in which gravitational field is the rocket traveling?
c. When it arrives at Mars, how does the speed of the rocket compare with the speed of Mars?
83. How can we use Jupiter as a slingshot to help launch a rocket out of the solar system?
84. Although the nearest star is over 250,000 times farther from us than the sun, it is easier to send a rocket to the nearest star than to the sun. Explain.
85. Consider an experiment in which three different masses, m1 = 1, m2 = 2, and m3 = 3 are subjected to accelerating forces by connecting them to paper clips that are strung over a pulley. If m2 is observed to accelerate at a rate of 24 cm/sec/sec when 4 paper clips are used, construct a table of the expected results for all three masses for 1, 2 and 3 paper clips.
86. In the laboratory in which Newton's second law was investigated, we used an apparatus consisting of an air track, a spark generator, gliders, and paper clips. Briefly, state the functions of three of these, and tell how each relates to the second law.
87. In the laboratory exercise involving the concept of conservation of energy, the actual masses of the gliders were ignored, but the height of the blocks under one end of the air track was not. Tell why this was so, and indicate how the height of the blocks figured into the calculations.
88. In the laboratory concerned with conservation of energy it was necessary to determine the actual velocity of the glider at a specific point. We did this by using a spark tape that recorded the positions of the glider at fixed time intervals while it was accelerating. Describe the procedure that you used to determine the velocity.
89. The following data were obtained when increasing numbers of pennies were added to a cup at the end of a spring:
Length of spring: 27.1 29.2 31 33.1 35 36.9 39.1
Number of pennies: 15 20 25 30 35 40 45
What conclusions can you draw from this data? What would the expected length of the spring be for a weight of 55 pennies? How many pennies would you find in a cup attached to a spring 31.9 cm long?
90. How are added weight and extension of a spring related? What is the algebraic form of Hooke's Law? Draw a graph of hypothetical results obtained with a spring that is initially 10 cm long.
91. The following pairs of data points were obtained with a gas enclosed in a syringe when weights of different magnitudes were added to the top of the plunger. The barrel of the syringe has a 5 cm2 cross-section area. The data for no weight added was lost. How would you determine the most likely volume of the gas with zero added weight? What is that volume?
Added weight (kg): 0 1 1.5 2 2.5 3 4 6 8
Volume of gas: ??.? 41.7 38.5 35.7 33.3 31.3 27.8 22.7 19.2
92. In a particular laboratory dealing with Boyle's Law, weights were added to a syringe with a 5 cm2 cross-section area until a predetermined set of volumes were reached. Unfortunately, these data were recorded on a scrap of paper towel, and mixed up with other scraps of paper dealing with Hooke's Law. Our job is to determine whether the following data, found on such a scrap of paper were obtained with a compression spring or a syringe. What would you do to find out which apparatus was used? Which piece of apparatus was used for these data? (You must answer both parts for full credit.)
Length (or volume): 60 50 40 30 20
Added weight: 1.2 1.64 2.3 3.4 5.6
93. When vinegar is added to 1 gram of baking soda until no further reaction takes place, it is found that 450 ml (cc or cm3) of gas are given off. Draw a graph for the expected results of a series of similar experiments in which 2, 3 and 5 grams of baking soda are used. Label the axes of the graph.
94. In your lab experiments you observed that the weights of 50 ml samples of the noble gases helium (He), neon (Ne), argon (Ar) and krypton (Kr), with atomic weights 4, 20, 40 and 84, had weights of 9, 45, 90 and 189 mg (milligrams).
a. In milligrams, how many times the atomic weight of a monatomic gas does a 50 ml sample weigh?
Hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and chlorine (Cl) have combining weights (atomic weights) of 1, 12, 14, 16 and 35.5.
b. What are the molecular weights of the gases carbon dioxide (CO2), hydrogen chloride (HCl), ammonia (NH3), water (steam) (H2O), and nitrogen dioxide (NO2).
c. If the weight of 50 ml of oxygen is found to be 72 mg, what is the formula of oxygen gas?
d. The gas nitrous oxide is found to be made up exclusively of nitrogen and oxygen. If the weight of a 50 ml sample is found to be close to 65 mg, what is a likely formula for this gas?
95. Our lab results showed that the periodic table results for the atomic weights (combining weights) of magnesium and calcium are correct. They are 24.3 and 40.1 We found these values from our observation that 1 gram of magnesium released 912 ml of hydrogen gas from hydrochloric acid (hydrogen chloride in a water solution), and 1 gram of calcium released 553 ml of hydrogen.
a. If barium, with an atomic weight of 65.5, is known to combine with chlorine in the same manner as magnesium, how much hydrogen would you expect 1 gram of this metal to release from hydrochloric acid? (You do not have to perform the arithmetic, just indicate what you would do.)
b. 40.1 gm of calcium combine completely with 71 gm of chlorine. How much sodium would combine with that amount of chlorine? (Use your periodic tables.)
c. How much hydrogen gas would be liberated by 1 gram of sodium? (Again, a detailed answer is not needed, only show the operations you would perform with which numbers.)
d. 1 gm of an unknown substance releases 349 ml of hydrogen. If this substance is in the same column of the periodic table as magnesium, what would be its atomic weight?
SAMPLE ESSAY TOPICS (Fall term)
Essay topic 1: The Roots of Science
Length: Approximately 750 words. The paper must be readable, typing is preferred. Use at least 1 inch margins and double space. If a hand-written paper is not readable, it will not be accepted. If it is hand-written, there must be room left for comments.
Revision: If the paper is submitted when due (see above), it will be returned to you on Wednesday, September 14, (by your lab instructor, at lecture), with comments and a tentative grade. If you choose, you will then have until September 21 to prepare a revised version to be submitted for regrading. This grade will be included in the determination of your final grade. Late papers will be graded without opportunity for revision. Papers submitted after September 22 will be subject to a penalty.
Context: "Science" has been defined as the attempts to account for human experiences with the "outside world." The first of these experiences which gave rise to the earliest science concerned such natural phenomena as were encountered in living in a primitive world. Also included as subject matter for "science" and as grounds for analogical reasoning are the craft and technological processes or recipes that were developed by emerging civilizations.
Topic: Distinguish among (i.e., define) episodic, periodic and craft-based phenomena which might be the subject matter of early "science." Give examples of at least five such phenomena, including three which are periodic (cyclic). (You need not limit your examples to those mentioned in class.) Describe two of the cycles in enough detail to tell someone unfamiliar with them what they are. Be sure to include in your descriptions some characteristics that distinguish your choices from the other phenomena you named. (Be sure that your examples are appropriate for early science.)
Essay topic 2: Early Models of the Universe
Length: Approximately 1200 words. The paper must be readable, typing is preferred. (See comments on Essay Topic I)
Revision: If the paper is submitted when due (see above), it will be returned to you on Wednesday, October 12. If you choose, you will then have eight days in which to prepare a revised version to be submitted for grading. This grade (which may count for up to 15 points) will be included in the determination of your final grade. Late papers will be graded without the opportunity of being revised, and will be subject to a penalty if submitted after 10/20.
Context: The emphasis of the course so far (through Lecture 10 and Chapter 9) has directed your attention to observations, models and the differences in approach that may motivate the construction of these. In this essay you are asked to integrate your thoughts in these areas.
Topic: Write an essay** in which you discuss our use of the word "model" and identify three models (proposed after 400 BC) which have been considered in this course. For each, (i) associate it with the name of the person who proposed it, (ii) provide a brief account of what "problems" or observations it is dealing with, and (iii) discuss whether it is designed to account for particular observational evidence ("empirical") or based on reasoning from some ideal ("speculative"). For one of these, show how the model solves the problem or accounts for the observations.
Feel free to include mention of relevant observations which are not accounted for. If appropriate, diagrams of the model may be used. (Remember, while a picture may be worth a thousand words, it cannot be used instead of them. The words are what are important in conveying meaning.)
** An essay should be a coherent discussion of an idea; it is not enough to give brief sentences or paragraphs directed to each of the points noted. The essay should include a title that gives you a focus, an introduction that sets your theme, a body that develops your ideas, and a conclusion that ties your thoughts together.
Essay topic 3: Discovering Laws of Motion
Length: Approximately 2000 words (not including tables and diagrams). The paper must be readable, typing is preferred (see comments on first assignment). This paper will count for up to 20 points toward your final grade.
Revision: If the paper is submitted when due (see above), it will be returned to you on Thursday, November 17 (by your lab instructor, at lecture). If you choose, you will then have one week in which to prepare a revised version to be submitted for grading. The higher of your two grades will be included in the determination of your final grade. Late papers will be graded without the opportunity of being revised, and will be liable to a penalty if submitted after November 23.
Context: In "classical times," Aristotle and Ptolemy developed a comprehensive description of all motion. Aristotle proposed that the earth was the center of all natural motion, and that objects fell toward their natural positions at speeds proportional to their weights. Ptolemy accounted for the observed motions of the planets in the sky in terms of an elaborate theory using deferents, epicycles, eccentrics and equants.
In the 15th-17th centuries, Copernicus, Kepler, Galileo and Newton introduced a new way of looking at the world and the universe together with a new way of studying them which is essentially the modern view.
Topic: Write an essay (with title, introduction, development and conclusion) that covers the following two parts:
Part I: (10 points) Discuss the developments leading to the modern view of the universe during the 15-17 centuries, including at least one contribution of each of the four men mentioned above. Indicate the nature of each accomplishment in terms of how it represented a change of point of view, methods of investigation, or conclusion.
Part II: The four labs from lab 6 to lab 9 have all been concerned with the experimental study of motion as well as with the process of gathering and interpreting data. At the same time you should have become familiar with the nature of experimentation, the limitations of exactness in experimentation, the interaction between available technology and experimental approach, and the three different roles experimentation plays in a) introducing you to phenomena, b) allowing you indirectly to verify a general law, and c) assisting you in the direct verification of a specific relationship. In Part II of this paper you should:
(2.5 points) Summarize the general conclusions arrived at in each lab separately, indicating those that reflect the work of more than one lab.
(5 points) For "the second law of motion" (from lab 8), and one other conclusion from the labs listed above,
- describe the design of the experiment and the procedure used to collect data (use diagrams if you wish)
- present your data in a useful form, and
- develop the line of reasoning that takes you from your data to your conclusion(s).
(2.5 points) Discuss the role of experimentation in the process of verifying laws or theories. (In this part, you might want to consider the following questions: Were your experimental results reproducible? Did the calculations based on your results agree exactly with your theoretical expectations? If not, does the lack of agreement mean that you did not verify your hypothesis?)
Length: 1500 to 2000 words, not including data or diagrams, if used. It is very difficult to specify length; sometimes a few well chosen words will do, and other times extensive (excessive) verbiage gets nowhere. The paper must be readable, typing is preferred. (This is the last year that typing will not be required.) N.B. This paper is worth up to 15 points towards the final grade.
Revision: Unlike the previous papers, this paper will not be returned for revisions. Do your best to avoid the pitfalls that your instructor has pointed out to you on your previous papers.
Context: The modern study of gases began in the 17 century with people working in several European countries: von Guericke (Germany), Torricelli (Italy), Pascal (France), and Boyle (England). (Note, modern geographical names have been used.) The relationships between "theory" and experiment were different in the approaches used by these four men.
The analogy of a spring has been used to explain many of the observations made by all four of these men.
Topic: In an essay (which includes a title, introductory comments and a conclusion) present a consideration of the early study of gases. DO NOT SIMPLY COPY OR PARAPHRASE THE READINGS. In this essay,
A. Describe the observations made by each of these men. (4 points)
B. Briefly characterize the approaches used by each of the men mentioned above, and in more detail compare the approaches of any two. (Note: some key words that might be appropriate to the characterization are hypothesis testing, discovery, demonstration, qualitative or quantitative. 9 points)
C. Discuss the ways in which a spring may or may not be an appropriate model for understanding the behavior of gases and vacuums. Include one example of a phenomenon that is not adequately addressed by this model. (2 points)