Master SyllabusCourse: PHY 109/110, Freshman Seminar I/II

Cluster Requirement: 2A, Science of the Natural WorldThis University Studies Master Syllabus serves as a guide and standard for all instructors teaching an approved in

the University Studies program. Individual instructors have full academic freedom in teaching their courses, but as a condition of course approval, agree to focus on the outcomes listed below, to cover the identified material, to use these or comparable assignments as part of the course work, and to make available the agreed-upon artifacts for assessment of learning outcomes.

Course Overview:

Both semesters of this seminar course, PHY 109 and PHY 110, are structured identically. Each introduces first-year students to physics and the physics major through group problem-solving activities; hands-on, exploratory projects involving measurement and elementary mathematical analysis of experimental data; oral presentations by students on historical and/or modern discoveries in physics; and presentations by physics faculty members on opportunities for student participation in their research program. Fundamental concepts and analytical techniques relevant to subsequent physics-major courses are covered.

Learning Outcomes:

Course-Specific Learning Outcomes:

After completing either PHY 109 or PHY 110, students will have gained:

• an overview of the various branches of physics and their interrelationship. • an appreciation of the mathematical nature and formulation of physics.• experience in problem-solving techniques applicable to physics, in particular, those that will be useful in subsequent physics courses.• knowledge of the curriculum, requirements, and expectations of the physics major.• familiarity with the scholarly work of physics faculty and the opportunities for supervised undergraduate research in these areas.

University Studies Learning Outcomes:

After completing either PHY 109 or PHY 110, students will be able to:

• Recount the fundamental concepts and methods in one or more specific fields of science (here, physics). • Explain how the scientific method is used to produce knowledge. • Successfully use quantitative information to communicate their understanding of scientific knowledge. • Use appropriate scientific knowledge to solve problems.

Examples of Texts and/or Assigned Readings:

Various journal articles and faculty notes relevant to the particular physics topics covered during the semester. See Appendix A.

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Example Assignments:

See Appendix B.

Sample Course Outline:

See Appendix C.

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Appendix A: Sample Reading Assignments

PHY 109, Freshman Seminar

Fundamentals of Electrostatics

There are three ways to electrically charge an object:

1. Friction: two objects take on equal and opposite charge; conservation of charge applies to the two objects, i.e., one object becomes positive and the other object negative. When a plastic or rubber rod is rubbed with fur, the rod becomes negative and the fur positive. When you comb your hair, the comb becomes negative and your hair positive. See the strands stand up? Similarly, scuffing your feet on the carpet renders you negative and the carpet positive. On the other hand, when a glass or plastic rod is rubbed with silk, the glass rod becomes positive and the silk negative. In each case, the material whose atoms have less tightly bound electrons lose their outer electrons and become positive.

2. Contact: excess charge on charged object migrates to contacted neutral object, which takes on same charge polarity as charged object.

3. Induction: bring charged object close to neutral object to create charge polarization in neutral object, ground the neutral object to provide path for repelled charge to escape, then remove the charged object. Induced charge will be opposite that on the original charged object. Can also be used to induce opposite charges on a pair of neutral objects in contact.

Charge polarization: a neutral piece of paper can be attracted to a charged rod as follows. A negative (say) rod aligns polarized molecules in the paper such that the positive charges in the paper are, on average, slightly closer to the rod than the negative charges. As a result, the inverse square property of electrical force (Coulomb’s law) indicates that there will a slightly greater attraction than repulsion between the rod and the paper. Therefore, if brought close enough, the rod will pick up the paper. A similar analysis works for a positively charged rod. Charge polarization also explains why a charged balloon will stick to neutral wall; molecules in the wall will align themselves according to the balloon’s charge, creating a new force of attraction. In all these cases, excess charge eventually migrates to the neutral object (an insulator so migration takes time) and the force of attraction diminishes or even becomes a repulsive force.

Electroscope: a detector of electric charge consisting of an insulated conducting ball-and-rod connected to a pair of conducting leaves. If initially uncharged, the leaves spread when charge is detected. If initially charged, the leaves spread or come together depending on the polarity of a nearby charge.

(a) (b)

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Electroscope charged by (a) induction Previously charged electroscope can and (b) contact. be used to determine the polarity of

a charged object.

Interesting tidbit: If you placed a pair of one-Coulomb charges one meter apart, their mutual force would be about 9 billion Newtons, more than ten times the weight of a battleship.

PHY 109, Freshman Seminar

A Much Abbreviated History of Physical Science

The ancient Greeks were the first society to systematically study natural phenomena. They were not “scientists” in the modern sense of the word because they did not carry out controlled experiments. Instead they formulated explanations of natural phenomena based on logic and common sense. Prime among these early pre-scientists was Aristotle, whose pronouncements about nature were accepted virtually without criticism for the next 2,000 years. Aristotle held that the behavior of objects was due to some occult, or hidden, properties; these properties could not be revealed through observation or experimentation. Thus the urge to experiment was suppressed for a long time.

Things began to change in the mid 1500s when Copernicus proposed his highly mathematical restructuring of the cosmos from Earth-centered to Sun-centered. His mathematical arguments were compelling, even though there is no sensation that our planet is in motion. With Copernicus and his overthrow of the centuries-old geocentric system, others realized that common sense and intuition are not the best bases on which to formulate explanations of the natural world. Clearly, more detailed observations were required before any explanations could be posed.

The first person to conduct systematic, quantitative observations of nature was Galileo. In the early 1600, Galileo sought to discover the mathematical relationships underlying the motion of objects; therefore he made carefully constructed, timed experiments which revealed the interconnections among distance, velocity and acceleration. Essentially, Galileo’s mathematical approach determined the forms of experiments he conducted; experiments had to reveal quantitative data about the various parameters of motion. Unlike Aristotle’s old ways, this mathematical approach also prevented unquantifiable (and extraneous) properties, such as beauty, purpose or dignity, from being considered. Galileo explored only the subject known as kinematics, the description of motion, not the complex subject of dynamics, the root cause of motion. Newton handled that subject later in the 1600s.

Robert Boyle in the mid-1600s made a concise case for abandoning the old Aristotelian methods: “A man would be a dull fellow if, when he wanted an explanation of a watch, he was satisfied with being told it was an instrument made by a watchmaker.”

Basic timeline of scientific development:

• 1600s: basic foundations of physical science are laid out; gross observations and mathematical relationships are explored.

• 1700s: systematic measurement is conducted with more precise devices; timing devices improve tremendously.

• 1800s: even more detailed experiments are conducted; comprehensive physical theories are proposed to form the core of “classical” physics.

• 1900s: quantum mechanics and relativity point out the limitations of classical theory.

History of Electricity and Magnetism

The root of the word “electricity” comes from the Greek “electrum,” which refers to amber, an orange-tinted fossil resin observed to have unusual properties: when rubbed with a piece of fur, amber attracts bits of parchment (paper), wood, or cloth. The word “magnet” comes from Magnesia, a region of ancient Greece (now in Turkey) that was the source of an unusual form of iron ore, lodestone, that attracts bits of iron. The ancient Greeks knew about the basic properties of magnets: magnets attract iron,; pieces of ordinary iron can be magnetized themselves by other magnets, magnetic attraction passes through non-magnetic materials such as cloth, parchment, or wood.

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The Chinese discovered the magnetic compass in the 4th century A. D., noticing that a magnetized needle floating in water aligns roughly to the Earth’s north-south geographic axis (actually to the Earth’s north-south magnetic axis).

The first systematic investigations of magnets and electrified bodies was carried out by William Gilbert in England in the 1500s and 1600s. He noted that:

• magnets have two poles, north and south, which align, respectively, to the Earth’s north and south geographic poles;

• like poles of a pair of magnets repel one another, unlike poles attract;

• the Earth itself behaves like a huge magnet (it aligns compass needles) and probably has a lodestone interior.

• magnets are limited to iron-bearing materials, whereas a wide variety of materials can be electrified;

• magnets are relatively permanent, whereas electrified substances lose their power in time;

• electrified bodies always attract one another (he was wrong!).

It had been thought that the only way to electrify a body was by rubbing it, i.e., by friction. After Gilbert, Stephen Gray in England demonstrated that an electrified body could electrify another body by contact, just like a magnet. He also realized that it was possible to transfer the property of electrification through a wire as though some electrical fluid was flowing. Gray made a list of “conducting” and “insulating” materials.

The term “electric charge” was invented by Joseph Priestley, discoverer of oxygen, in the mid-1700s. The notion that there were two types of charge also came about in the mid-1700s, and Ben Franklin designated these “positive” and “negative.” It was believed that electricity was some kind of “imponderable fluid,” i.e., it co-exists with ordinary matter but has no mass and cannot be detected. (Heat was also considered to be such a fluid.) Some believed that electricity was two fluids, whereas others (like Franklin) believed it was one. In the single-fluid model, the charge on an object was determined by whether there was a deficiency or excess of this fluid relative to other objects. That is, a positively charged object would have more of the fluid than a negatively charged one. Excess fluid could be transferred from object to object through friction or contact:

• Rub glass with silk: glass acquires a positive charge and the silk a negative charge. • Rub amber (or plastic) with fur: amber acquires a negative charge and the fur a positive charge.

Ben Franklin, inventor of the lightning rod, proved through his famous kite experiment that lightning was an electrical phenomenon. Franklin also was first to notice that the interior surface of a conducting container exerted no electrical force on an object placed near it (whereas the exterior did exert a force). He informed Joseph Priestley in England who realized that the situation was analogous to that for gravity, where Newton proved mathematically that, according to the inverse square law, there is no net gravitational force in the interior of a spherical shell of matter. Henry Cavendish confirmed experimentally in the 1770s that there is no net field inside a charged sphere, hence the inverse square law holds, but he did not publish his results. The connection was finally established by Coulomb in 1785 who used a sensitive torsion balance to prove directly the inverse square nature of electrical force.

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Appendix B: Sample Assignments

The following sample in-class activity addresses Cluster 2A Outcomes 1, 2, and 4. There are a number of similar activities that cover fundamental concepts of electricity, as well as how to acquire scientific knowledge through careful experimentation and observation. The instructor conducts a guided post-activity discussion among the class. A grade is assigned to each student based on the quality and completeness of their work, participation in their group, and the correctness of their conclusions about electric circuits, insulators and, conductors.

PHY 109, Freshman Seminar

EXPLORATIONS IN ELECTRICITY (VI):

BATTERIES AND BULBS

Materials

D-cell batteries

Flashlight bulbs (if given #47 bulbs instead, you will have to use two D-cells taped

together in series, i.e., so they are end-to-end)

Wire

Small-diameter copper magnet wire (approx. 30 gauge)

Razor blade or knife

Background

Here you will investigate the fundamental properties of an electric circuit by lighting a bulb with a battery

and wire. Conductors and insulators will also be investigated.

Procedure

1. You are given a bulb, battery, and a length of wire. Find and sketch as many configurations as possible that result

in the bulb being lit. Sketch some configurations that do not light.

2. Repeat Part 1 for a bulb, battery, and two wires.

3. Describe in your own words what the illuminating configurations have in common. How do they differ from the

configurations that do not light the bulb?

4. Based on your observations, predict which of the configurations in the attached diagram will light the bulb and

which will not. If in doubt, try it! We will call the configurations that light the bulb "electric circuits."

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5. Set up a one-wire circuit that lights the bulb. At some convenient place in the circuit, insert various materials

that you find around the room, such as paper, coins, fingers, pencil tips, glass, keys, etc. Record which materials

allow the bulb to glow and which do not.

6. What do the materials that allow the bulb to glow have in common? We will call these materials "conductors,"

and the materials that do not allow the bulb to glow "insulators." Is air normally a conductor or an insulator? How

can you demonstrate this using your circuit? Can you cite a circumstance in which air is a conductor?

7. LET THERE BE LIGHT! Consult with the instructor before you try this part!

Get together with others in the class and place six D-cells in series to form a "super-battery." (What is the total

voltage of this super-battery?) Now cut a three-inch strand of copper magnet wire and scrape off the shellac

insulation with a razor blade or knife. Wind the central portion of the wire around a small cylinder to form a tiny

coil, like a lamp filament. (Do not let the individual coils touch one another.) Attach each end of the filament to an

alligator-clip lead so the filament is held upright. Then press the far end of each lead wire against a terminal of the

super-battery. Wait a few seconds. Describe what happens. Do not leave the leads connected to the super-battery

for a long time as the battery will drain.

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The following sample in-class activity addresses Cluster 2A Outcomes 1, 2, 3, and 4. The activity covers how scientific data is acquired and used is astronomy, reviews the geometry of angles and ellipses, and applies Kepler’s laws of orbits to solve a scientific problem. Students must also communicate their conclusions in a clear, concise way. Each student’s work is scored based on the quality of their graph and the answers they deduce from it.

PHY 109, Freshman Seminar

ACTIVITY: What Lurks at the Heart of the Milky Way?

We live in a vast, disk-shaped agglomeration of stars, gas, and dust called the Milky Way galaxy. The Milky Way is some 100,000 light-years across, with our solar system situated about two-thirds of the way out from the center to the rim. From the rapid orbital movement of stars near the galactic center, astronomers have deduced that a very massive object, designated Sagittarius A*, lies at the core of the Milky Way. Among its gravitationally bound, fast-moving stars is one called S2, which whirls in a tight elliptical orbit around this mysterious object. Figure 1 is a pair of infrared-telescope photographs, taken 5 years apart, that depict stars in the central region of the Galaxy. Note that during this time span the star labeled S2 (dark blob) has clearly moved relative to Sagittarius A* (open circle).

Figure 1

From Schödel, R., et al. “Stellar Dynamics in the Central Arcsecond of our Galaxy.”Astrophysical Journal, 596: 1015–1034, 2003 October 20.

Table 1 lists S2’s position coordinates on the plane of the sky, that is, where the star was found in the sky on various nights over several years. These (x, y) coordinates are expressed in arcseconds (1/3600 degree) relative to the coordinates of Sagittarius A* at (x, y) = (0,0). The uncertainties in the measured position coordinates are included as well, labeled dx and dy, respectively.

1. Construct a graph of all the (x,y) position coordinates in Table 1. You should include the data points and error bars, but not the dates of observation. Choose overall size and coordinate scales that are reasonable, that is, avoid size or scales that compress the data points. You will have to make measurements from this graph later on.

2. According to Kepler’s 1st law of orbital motion, gravitating objects orbit in elliptical paths. Carefully sketch an ellipse that best fits your plotted data points. Remember, the ellipse does not have to intersect every data point, but represents the best average fit you can make by eye. The given data does not cover an entire orbit; you will have to make an extrapolation of the given data to complete the ellipse. Note: S2’s orbital plane is inclined to our view; we do not see the orbit face-on. Therefore, the ellipse in your graph is the apparent orbit, that is, the projection of the true orbit onto the plane of the sky. More about this later.

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Table 1

(3) Draw the major and minor axes of the fitted ellipse, as indicated in the figure below. Note that Sagittarius A* is located at a focus, not at the center, of the ellipse.

In principle, we can apply Kepler’s 3rd law to deduce the mass of the central object holding S2 in its orbit. Kepler’s 3rd law is written M = a3 / P2. Here M stands for the combined mass of the system – the central object and the star S2 – expressed as a multiple or fraction of the Sun’s mass (a unit called a solar mass). The period P is expressed in Earth-years and the orbital semimajor axis a in astronomical units (AUs), Earth’s average distance from the Sun. In the steps below, you will determine first the orbital semimajor axis a, then the orbital period P, and finally the combined and individual masses of the objects in question.

4. Finding the semimajor axis a.

(a) Using the scales of your x and y axes, determine the length of the major axis in units of arcseconds. Explain how you accomplished this. (b) Now halve the number you got for the major axis to get the semimajor axis. (c) At the distance of the galactic center (approximately 26,000 light-years), 1 arcsecond on the sky represents an actual linear width of about 1.1 x 1012 kilometers, or about 7600 AUs. (1 AU is about 1.5 x 108 km.) Convert your measured semimajor axis from arcseconds into AUs. (d) The value you derived for the semimajor axis is not yet corrected for the 46-degree inclination of S2’s orbit (measured from the plane of the sky). To get the orbit’s true semimajor axis a, divide your value by the cosine of the inclination angle. 4. Finding the period P.

Imagine a line connecting the central object with the star S2. (Note: the central object sits at the graph’s origin (0,0), not at the center of the ellipse.) In one orbital period, this line sweeps out the entire area enclosed by the ellipse: A = ab, where a and b are the lengths of the semimajor and semiminor axes, respectively. In any lesser time interval, the line sweeps out a sector of the ellipse whose area is a fraction of A.

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aC

a

b

b

2a = major axisa = semimajor axis2b = minor axisb = semiminor axisf1, f2 = foci

f1 f2

(a) Determine the length of the semiminor axis b in arcseconds and in AUs, as you previously did for the semimajor axis a. (b) Compute the area A of the ellipse in both arcsecond2 and AU2. Kepler’s 2nd law expresses the change in an object’s orbital velocity as is swings around another object. This change is expressed in geometrical terms: the area swept out by the line connecting the two objects is proportional to the time spent by the connector within this area. For example, in half the orbital period, P/2, the object will sweep out a sector that is half the entire area of the ellipse, A/2. Or in general, in the time span t, the connector sweeps out a sector whose area is A = (t/P) A, from which we can determine the period: P = (t/A) A. We already have the value for A, we need to determine values for t and A.

(d) Using the scales of your x and y axes, determine the area A (in arcsecond2) of the sector swept out between any pair of data points, that is, during a time span t (in years). You may accomplish the area measurement by counting up graph boxes within the selected sector. From this data, compute P in years. Repeat the process three more times and adopt the average P of all four measurements.

5. Finding M.

(a) Compute the mass of the system from Kepler’s 3rd law: M = a3 / P2. Remember, your answer comes out in units of solar masses, where the Sun has a mass of 1. (b) Knowing that S2 is a conventional star, and given that stars never exceed a mass of about 120 solar masses, can you rule out the possibility that the central object itself is a star? Explain. Hint: no “starlike” energy is observed coming out the central object. Not surprisingly, astronomers believe the central object is a supermassive black hole.

Your report for this activity should include the graph and various well-organized tables that clearly present your data. Clarity and neatness will count toward your score.

Students should arrive at answers and a graph close to those cited in recent research papers):

Period of S2 = 15.7 ± 0.7 yearsSemimajor axis = 930 ± 70 AUsMass of black hole = (3.7 ± 1.0) x 106 solar masses

PHY 109/110, page 10

Appendix C: Sample Course Outline

PHY 109/110, Freshman Seminar I/II

Description: The Freshman Seminar is designed to involve first-year physics majors in discussions, presentations, and hands-on activities related to fundamental physics and the physics major. You will engage in group problem-solving activities; hands-on, exploratory projects involving measurement and elementary mathematical analysis of experimental data; and oral presentations on historical and/or modern discoveries in physics. There will also be “guest” presentations by physics faculty members on opportunities for you to get involved in their research programs. Some of the concepts and analytical methods you will learn here will be useful in the more technical courses you are required to take in the physics major.

Goals of the course: By the end of the term, you will have gained:

• an overview of the various branches of physics and their interrelationship. • an appreciation of the mathematical nature and formulation of physics.• experience in problem-solving techniques applicable to physics, in particular, those that will be useful in subsequent physics courses.• knowledge of the curriculum, requirements, and expectations of the physics major.• familiarity with the scholarly work of physics faculty and the opportunities for supervised undergraduate research in these areas.

Textbook: There is no textbook. You will use online, library, and instructor-provided resources for your assignments.

Grading: Your final grade will be based on participation in class discussions (20%); in-class assignments (50%); oral presentation (10%); and quizzes and homework assignments (20%). There is no final exam. Attendance is mandatory; poor attendance will result in a lowered final grade.

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