SI Prep - Science - Curriculum

Physics Honors Curriculum

Last modification July 6, 2008 10:07 AM by Byron Philhour

Department Mission

Our mission is to teach students the scientific method so they can understand modern scientific descriptions of the universe and come to objective conclusions about the natural world. Like all members of the SI community we aim to educate the whole person, emphasizing the academic, extracurricular, and spiritual development of our students.

We would like to see graduates of SI ...

knowledgeable about a broad range of scientific topics
confident and proficient in the use of the scientific method
able to use core science knowledge to assimilate new ideas and discoveries
aware and appreciative of the universe and its inhabitants
effectively able to communicate scientific principles, theories, and historical discoveries
comfortable with laboratory techniques and experimental apparatus
conscious of the environmental and ethical consequences of scientific progress
dedicated to acting as a "person for others" in accordance with Catholic faith, Jesuit tradition and our school's mission
well prepared for future study in any academic discipline
... and eager to continue to enjoy, learn about, and practice science throughout their life.

To this end, we strongly advise students to take all three of our core classes (Biology, Chemistry, and Physics) as well as a 4th year elective course.

Course Outcomes

Wiggins and McTighe describe four criteria which “serve as filters to select ideas to teach for understanding. The idea, topic, or process (1) represents a big idea with enduring value beyond the classroom, (2) resides at the heart of the discipline, the ’doing’ of the subject in context, (3) requires uncoverage, and (4) offers potential for engaging students.” One can also ask: suppose in twenty years our students have forgotten specific pieces of content -- what should they remember?

Course-wide topics for enduring understanding

Physics is the study of the most fundamental laws of nature. Physicsts are concerned with the behavior of the universe and its constituents ranging from the smallest subatomic particles up to enormous galaxy clusters.

Physics is an experimental science, meaning that all theories -- no matter how elegant -- can be rejected if in conflict with the results of a single experiment. To quote Karl Popper: "Science may be described as the art of systematic over-simplification...In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality."

Physicists should "get their hands dirty." Laboratory work allows us to interact with the world in a simplified, controlled way. There is a place for calculations and abstract mathematical manipulation, but this kind of effort should lead to a deeper understanding of the real world.

As important as the content of physics is the method: students with a physics education are expected to repeatedly ask and answer the fundamental question 'How do we know?'. Physics is not a dogmatic discipline: everything is up for grabs.

Physics is more than just the memorization of content: it is a framework for understanding the world as it is. To quote Nobel prize-winning physicist Richard Feynman: "You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... So let's look at the bird and see what it's doing — that's what counts. I learned very early the difference between knowing the name of something and knowing something."

The rational world-view taught in a physics class will be more important to our students in their future lives than any specific course content.

Wiggins and McTighe describe essential questions that “(1) have no one obvious right answer, (2) raise other important questions, often across subject-area boundaries, (3) address the philosophical or conceptual foundations of a discipline, (4) recur naturally, and (5) are framed to provoke and sustain student interest.” What questions might our students still be grappling with twenty years from now?

Course-wide essential questions

Galileo Galilei once said "Mathematics is the language with which God has written the universe." Some modern physicists are proposing that the universe is "made of mathematical equations." Is it true? Is the universe made of math?

Are all the physical laws in the universe potentially understandable by humans? In other words: dogs will never understand algebra; is there some theory out there we ourselves could never understand? Or is the scientific method sufficient to understand everything we want?

Will physicists announce a complete "theory of everything" in your lifetime?

Is there more than one complete, consistent description of the laws of physics? Could an alien civilization create laws of physics as good as ours at describing the behavior of the world but which is fundamentally different in its approach? Do we ourselves work with more than one set of separate & consistent laws of physics?

Is there a "center" of the universe, or any absolute reference frame or priveleged position?

How predictable is nature? Are unpredictable events simply too complex, or does nature exhibit fundamentally random behavior?

Important resources

The People's Physics Book (this is the course textbook)
Physics Laboratories
California state physics standards (for comparison)
Conceptual Physics 9th Edition by Paul Hewitt / 8th / 7th (this is a recommended text for the course)
The Cartoon Guide to Physics
YouTube: SI Physics (please add your own physics-related videos)
Understanding by Design (this is the design method for this curriculum)

Course Framework

The course consists of nine interrelated units:

I.      Introduction and Kinematics

II.     Newtonian Mechanics

III.    Conservation Laws

IV.   Thermodynamics and Fluids

V.     Harmonic Motion and Waves

VI.    Modern Physics (Atomic, Nuclear, Quantum, Particle)

VII.   Electricity

VIII. Magnetism

IX.    Electric Circuits

Methodology (all units)

Typically, units I – III are taught in the first semester, IV – VI in the 3rd quarter, and VII – IX in the 4th quarter.

Note: Topics in light grey font are optional -- these are taught at the discretion of the instructors of the course depending on time, resources, student interest, etc.

I. Introduction and Kinematics

Topics

We will study the ways in which the analysis of motion invented by Galileo allows us to deeply understand everyday experience. At the same time we’ll learn the vital skills needed for problem solving: a clear understanding of the question being asked; an interest in drawing sketches & making notes whenever they are needed; the ability to perform proper unit analysis; and familiarity with basic algebra and trigonometry.

We also set the tone for the manner in which the class will be taught. A variety of novel experiences we associate with high school physics – the physics demo, the hand-waving derivation, “two trains approach each other” problems – are introduced in this early unit.

Questions

How do math and physics relate to one another? How are conceptual physical ideas translated into the language of math?

How is the “Galilean” idea of motion – concentrating on position, velocity, acceleration, and important acts of observation & measurement – better than the one our naïve experience has taught us?

What is a ‘dimension’ – how can we tell we live in three dimensions? How do the dimensions communicate with each other? Is time a dimension?

What is the procedure for studying physics? How do I approach lectures, labs, problem sets, reading assignments, and exams so I end up understanding everything and achieving a good grade?

Knowledge and Skills

By the end of this unit, students will be able to

Identify the position, displacement, distance traveled, speed, velocity, and acceleration of an object undergoing uniform accelerated motion (UAM)

Consult position vs. time graphs to determine the direction of motion, speed, and velocity of an object in UAM. Draw such graphs when prompted.

Consult velocity vs. time graphs to determine the direction of acceleration, speed, and velocity of an object in UAM. Draw such graphs when prompted.

Use basic kinematic equations to predict the motion of an object in UAM.

Qualitatively describe the motion of a projectile near the Earth’s surface and in the absence of air resistance.

Use vector analysis to describe the motion of a projectile fired with a certain speed and at a specific angle.

Easily transform between one set of units (say, miles per hour) to another (meters per second)

Attack two-dimensional motion problems from many perspectives; solving for a variety of parameters when provided with a set of initial conditions.

Identify the two components of a two-dimensional vector when the vector is described (i) graphically, as drawn; (ii) as a magnitude and angle with respect to a given axis; (iii) as two components in an (x,y) coordinate system.

Add two vectors graphically or numerically.

Decide when and why air resistance can be neglected in a problem.

Qualitatively describe the effect air resistance will have on an object’s motion.

By the end of this unit, students will understand that

Objects in free-fall accelerate at the same rate.

Velocity is the time rate of change of position. The direction of velocity is determined by the direction of the rate of change of position.

Acceleration is the time rate of change of velocity. The direction of acceleration is determined by the direction of the rate of change of velocity.

Speed and velocity are two different notions. One is a scalar quantity, the other is a vector quantity.

Acceleration is a vector quantity.

The acceleration due to gravity on the surface of the Earth, 9.8 m/s2, is different from the acceleration due to gravity at other locations in the solar system.

Projectiles in motion follow a parabolic path under the influence of gravity.

Position, speed, acceleration can be described in a variety of units.

Air resistance produces an acceleration that opposes motion; under certain conditions air resistance can be neglected.

Air resistance will decrease the range, maximum altitude, and hang time of a projectile.

Everyday types of motion are understandable and predictable.

To understand and predict how things move, you need to study the rate of change of position and speed.

Motion in one direction is independent from motion in a second (perpendicular) direction. To say we live in three dimensions is simply to notice that there are three independent directions in which we can move.

Kinematics problems can be fully described with basic trigonometry and algebra.

By the end of this unit, students will be familiar with the following vocabulary words

Position, distance, displacement, speed, velocity, acceleration, linear motion, parabolic motion, scalar, vector, magnitude, direction, uniformly accelerated motion (UAM), air resistance, range, hang time

By the end of this unit, students will be familiar with the use of the appropriate equations for UAM as expressed in the course textbook

Wiggins and McTighe describe performance tasks as involving “complex challenges that mirror the issues and problems adults face. The challenges are authentic … they differ from academic prompts in that they (1) use real or simulated settings with the kinds of constraints, background noise, incentives, and opportunities an adult would find in a similar situation; (2) require students to address an identified audience; (3) are based on a specific purpose that relates to the audience; (4) allow students greater opportunity to personalize the task; and (5) are not secure; the task, criteria, and standards are known in advance and guide student work.”

Performance Tasks

Students will measure the position, speed, velocity, and acceleration of real objects in a real environment using distance measures and timers. Examples of possible subjects of study include: cars driving down the street or students running, crawling, jumping. Activity will include unit conversions, discussion of accuracy of measurement, and comparison of results.

Students will engage in short activities designed to explicitly challenge misconceptions about motion. (For example, they can measure the free-fall motion of a vertical ruler based on reaction time. Then, after attaching a lead weight to the bottom of the ruler, many students will predict a faster drop for the ruler. The results, however, will be the same as without the lead weight.)

Students will use computer-based measurements of position, speed, velocity, and acceleration of real objects, producing graphs of position, speed, velocity, and acceleration as functions of time. In the past we have used sonic range finders with a data acquisition system.

Students will predict the motion of a projectile with sufficient accuracy in a “performance task” environment. In the past we have used rolling marbles and asked students to place a cup (based on mathematical predictions) so that the marble will fall precisely into the cup. In this case grade has been based on nothing more than whether the marble made it in the cup – this distinguishes between effort and results.

Students will use the measured projectile motion of a ball shot from a Nerf Ball Blaster (or similar launcher) in order to measure the exit speed of the ball. Students will then predict range and hang-time for projectiles shot from the same launcher at different angles.

II. Newtonian Mechanics

Topics

A physicist sees everyday motion as understandable and predictable. He or she also knows that the Galilean and Newtonian ideas of motion are exceptionally accurate in predicting what is happening in most of the universe. In this unit, we explore the central notion that acceleration is caused by forces and resisted by mass. Underlying our study is the space-time concept of the inertial frame.

Questions

How can we say what is moving and what is not? How can we feel that we are not moving, but at the same time know we are rotating about the Earth, orbiting the Sun, and flying through the Milky Way galaxy? Is there an "absolute" frame of reference from which we measure all motion?

Why do things fall? Why do only some things break when they hit the ground? How can a bird fly? How does my heart pump blood through my veins?

Are Newton’s Laws “right” in the sense that they actually exist in the universe, or are they just a useful description? Is there such a thing as physical law, or physical truth?

Knowledge and Skills

By the end of this unit, students will be able to

Qualitatively describe Newton’s Three Laws of motion.

Use Newton’s Three Laws to qualitatively and quantitatively predict motion.

Draw accurate free body diagrams (FBDs) where lengths and directions of arrows are consistent with predicted motion

Break a vector force into its horizontal and vertical components (i) graphically, as drawn; (ii) as a magnitude and angle with respect to a given axis; (iii) as two components in an (x,y) coordinate system.

Add vector forces graphically or numerically.

Describe and analyze static and kinetic frictional forces.

Describe and analyze normal and other contact forces.

Describe and mathematically analyze the forces on an object on an inclined plane.

Describe and mathematically analyze centripetal forces and accelerations, including the use of banked turns in centripetal (“racetrack”) motion.

Describe and mathematically analyze Newton’s Universal Law of Gravity; make qualitative and quantitative analyses of inverse-square laws in general.

Calculate the period of a geosynchronous orbit from first principles.

Describe and mathematically calculate the force of air resistance. Calculate the terminal velocity of an object given a specified force of air resistance.

Easily convert between different units for mass (kg, “lb”, etc.) and force (N, lb, “g”, etc.)

Identify action/reaction pairs in accordance with Newton’s Third Law.

Solve a variety of “typical” mathematical problems, including but not limited to “elevator” problems, “Tarzan” problems, pulley problems, etc.

By the end of this unit, students will understand that

Accelerations are always caused by a net force; for motion at constant speed in a straight line, no net force is required.

FBDs should only include forces acting on the body in question; net forces, accelerations, and velocities have no placed on an FBD

Static friction forces have varying magnitude depending on the force they are resisting – in this sense they ‘rise to the occasion’; the direction of static friction force always opposes motion.

Kinetic friction coefficients are typically lower than static friction coefficients; hence the problem with a stuck drawer slipping when pulled with sufficient force.

Friction forces depend on the magnitude of the associated normal or contact force.

‘Centripetal’ forces are center-pointing forces in circular motion; in every circumstance, one must analyze what real forces (tensions, gravity, contact forces, etc.) are providing the centripetal force in question.

Objects in motion in constant speed are experiencing a net (centripetal) force.

Mass and weight are two different concepts; the first is a property of matter, related to the amount of matter, and the second is a gravitational force that depends on the gravitating body.

Newton’s Laws are not accurate when describing the universe on small size scales, at very high speeds, or in the presence of very strong gravitational fields.

Newton’s Laws can describe an incredibly broad range of everyday phenomena

By the end of this unit, students will be familiar with the following vocabulary words

Force, free body diagram, normal force, weight, mass, air resistance, contact force, tension force, tension, Newton (the unit), gravitational force, spring force, spring constant, static friction, kinetic friction, coefficient of friction, force probe, accelerometer, air track

By the end of this unit, students will be familiar with the use of the appropriate equations for forces as expressed in the course textbook

Performance Tasks

Students will be asked to make qualitative and quantitative predictions about motion of real-life objects based on a force analysis. They will then compare their predictions with the observed/measured motion and account for discrepancies. Examples include pulley systems, elevator problems, and the like.

Students will verify all three of Newton’s Laws using force probes, accelerometers, air tracks, fan-propelled (constant force) carts, inclined planes, and other real, hands-on devices.

Students will analyze the static and kinetic friction properties of a variety of materials and decide which would serve best as material for a set of automobile brakes. Write up will mimic the style and flavor of actual engineering reports.

III. Conservation Laws

Topics

“You can’t get something for nothing.” There are things in the universe that seem to stay the same no matter what happens. We study two of these “conserved quantities” in this unit. One is a simple number – the total amount of energy in an isolated system. The other is a vector quantity – the total momentum of an isolated system.

Questions

What is energy? How many different forms can it come in? Are there more efficient and less efficient ways of transforming energy from one type to another?

Why is energy conserved? Who says? Are there any branches of physics where the law of conservation of energy seems to be violated?

What is momentum? Do all things have momentum? Does the momentum of something depend on your inertial frame?

Why is momentum conserved? Who says? Are there any examples of violation of this law?

How, specifically, can I use energy and momentum conservation to my advantage when solving physics problems? Under what conditions is a conservation approach preferable to a Newtonian approach?

How do we describe motion? Why do we have two ‘kinds’ of motion: kinetic energy and momentum? Why use a scalar and a vector, at different times, to describe motion?

Does energy “really” exist or is it some kind of accounting system with no actual attachment to the real world other than its usefulness?

Knowledge and skills

By the end of this unit, students will be able to

Describe the conservation of energy as a “zero sum” game: the total amount stays the same, it is just divided up differently.

Make calculations of kinetic energy given the mass and velocity of an object; also, students will be able to invert the equation and solve for mass or velocity.

Calculate the gravitational potential energy of an object near the surface of the Earth.

Estimate the speed of a dropped or thrown object at some height based on the conservation of energy.

Calculate the energy stored in a compressed or stretched spring.

Confirm that energy conservation leads to the same results as Newton’s Laws for important problems.

Solve “roller coaster” problems and recognize that they are much more difficult to solve with Newton’s Laws.

Calculate the work done by a force applied in a certain direction. Recognize which types of forces (i.e., centripetal forces) do no work due to their direction.

Solve “frictional braking” problems in which dissipative work is done to an object through a frictional (nonconservative) force.

Make calculations of momentum (in vector form), including calculating the two components of a two-dimensional momentum vector.

Analytically and numerically solve typical one and two-dimensional inelastic collision problems using momentum conservation.

Analytically and numerically solve typical one and two-dimensional elastic collision problems using both momentum and energy conservation.

Recognize that force is the time rate of change of momentum, and calculate forces and momentum changes (impulses) based on this relationship.

Solve “impulse” problems in which one of the following is missing: force, change in momentum, or collision time.

Convert easily between energies and momenta in different units.

Accurately sketch momentum vectors for various masses and speeds; analyze a collision graphically using just drawn momentum vectors.

Calculate the change in momentum of an object that is losing or expelling mass; use momentum analysis to understand the motion of rockets.

Numerically solve “ballistic pendulum” problems and be able to describe the solution in depth.

Calculate the time rate of transferal of energy and recognize this rate as power.

Calculate the power delivered to a moving object by using the product of force and velocity.

By the end of the unit, students will understand that

There are conservation laws in the universe that appear to govern all behavior.

Conservation laws are “zero sum games”: the total amount of energy in an isolated environment is always the same. Same for momentum.

Conservation laws provide an alternative approach to problems that are too hard or complicated to solve with Newton’s Laws. They provide a different perspective for looking at the world.

Energy conservation allows students to solve problems that cannot be easily solved with Newton’s Laws. Both energy conservation and Newton’s Laws are complete and complimentary perspectives on motion.

In all collisions, momentum is conserved. In all collisions, energy is conserved. In elastic collisions, kinetic energy is separately conserved as well. In inelastic collisions, kinetic energy is transformed into other (usually dissipative) types of energy.

Work describes the transfer of energy into or out of a system. (In later units we’ll describe Heat and Radiation as other ways in which energy can be transferred.)

Power is the rate at which energy is transferred into or out of a system.

Momentum conservation only occurs in the absence of a net force. A net force will change the momentum of an otherwise isolated system.

The relationship between momentum and force is what is “behind” Newton’s Laws.

By the end of the unit, students will be familiar with the following vocabulary words

Conservation, energy, momentum, kinetic energy, gravitational potential energy, spring potential energy, momentum, impulse, power, Joule, Watt, collision, elastic collision, inelastic collision, ballistic pendulum, work, system, isolated system, net momentum

By the end of this unit, students will be familiar with the use of the appropriate equations for energy and momentum conservation as expressed in the course textbook

Performance tasks

Use a low-friction track (air track or wheeled carts) to create a variety of collisions in the laboratory; predict how the speeds of the carts will change as a result of a collision; verify the prediction by measuring the speeds and masses accurately, and account for any discrepancy.

With a limited set of materials, build an apparatus that will allow an egg to survive a drop from a building. Describe the use of materials in terms of the conservation laws discussed in class.

With a limited set of materials, build a trebuchet that will propel a tennis ball as far as possible. Describe the action of the trebuchet in terms of the conservation laws discussed in class.

IV. Thermodynamics and Fluids

Topics

Until now, the class has focused on the physics of solid objects. We aim to extend this understanding to the physics of liquids and gases – fluids. We have to move our attention from individual things to large collections of things. We will study fluid mechanics (fluids at rest) and fluid dynamics (fluids in motion). We will study the practical applications, including engines that convert thermal energy to useful work and refrigerators wherein work can be done to reduce temperature.

Questions

How do things float? Why does putting helium in a balloon make it buoyant? How can a submarine control its depth?

How can we extract random thermal energy and use it to do work? That is, how do engines work?

How do refrigerators and air conditioners work? How can we do work on something in order to change its thermal energy?

How can an airplane fly? What properties of a wing allow it to do so?

Knowledge and Skills

By the end of this unit, students will be able to

Calculate the thermal energy of a system of particles with a specified temperature.

Calculate the force exerted by a uniform pressure over some area.

Calculate the pressure at a certain depth in a liquid in a gravitational field.

Easily convert between density, mass, and volume. Recognize mass as the product of density and volume.

Qualitatively derive the ideal gas law PV = NkT.

Derive the relationship W = P∆V starting from the definition of work and the definition of pressure.

Sketch isobars, isochors, and isotherms on a P-V diagram. State which of these will do work, and estimate the amount of work done by the area under the graph.

Use Bernoulli’s Principle and Conservation of Flux to qualitatively describe the behavior of ideal fluids.

Calculate the efficiency of an engine that does work W by extracting heat Q.

Describe the Carnot cycle and why it was invented.

Calculate the ideal efficiency of a Carnot engine.

Recognize high entropy and low entropy states.

Recognize and work with the laws of thermodynamics in any of the following formats

First Law

In any process, the total energy of the universe remains constant. [Wikipedia]

“You can’t win.” [Allen Ginsberg]

The total energy of the universe always stays the same. Energy can only be converted from one form to another. [common]

Second Law

There is no process that, operating in a cycle, produces no other effect than the subtraction of a positive amount of heat from a reservoir and the production of an equal amount of work. [Wikipedia]

“You can’t break even.” [Allen Ginsberg]

During exchanges of energy, some amount is always converted into a random form (thermal energy). [common]

The entropy of a closed system is statistically bound to increase. [common]

Third Law

As temperature approaches absolute zero, the entropy of a system approaches a constant. [Wikipedia]

“You can’t quit.” [Allen Ginsberg]

If all thermal and kinetic energy is removed from a system, the system’s temperature is absolute zero. Thanks to the Second Law, this state is impossible to achieve. [common]

“Zeroth” Law

If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other. [Wikipedia].

(Note that the “Zeroth” Law is a common-sense notion that was introduced as an axiom for philosophical reasons. We will not dwell on it.)

By the end of this unit, students will know that

Energy is a “zero sum” game.

Like work, heat describes the transfer of energy between two systems.

Heat tends to flow from high temperature to low temperature systems.

Entropy is a measure of the amount of disorder in a system.

The ideal gas law written as PV = NkT and as PV = nRT are one and the same; the latter is written in molar quantities.

The density of water is about 1000× higher than the density of air

Entropy is a statistical description of the degree of disorder in a system.

The increase of entropy in a closed system is a statistical prediction.

By the end of the unit, students will be familiar with the following vocabulary words

thermodynamics, aerodynamics, hydrodynamics, heat, work, thermal energy, Boltzmann constant, pressure, density, buoyancy, temperature, entropy, ideal gas, fluid, liquid, displacement, Bernoulli’s Principle, flux

By the end of the unit, students will be familiar with the relevant thermodynamic equations as detailed in the course textbook

Performance Tasks

Students will build a working heat engine from supplied plans.

Students will build a boat from supplied parts that can hold the largest possible weight without sinking.

Students will verify the inverse relationship between pressure and volume for an ideal gas at constant temperature using a pressure gauge and a syringe.

V. Harmonic Motion and Waves

Topics

Oscillatory (back-and-forth) motion helps to explain much of what we see, hear, and feel. A familiar example is ocean waves. It is important to realize that waves are not ‘things’ like electrons or cars. Waves are oscillatory phenomena; when sound, light, or water waves carry energy from one place to another, it is not necessary that any matter moves between these locations.

In this unit we’ll study, in depth, the motion of sound and light waves after building some conceptual experience using ropes, springs, and water.

Questions

When a water wave travels through a pool, how does the water itself move?

How does the study of wave motion relate to our previous study of Newton’s Laws and the conservation laws?

How can we tell that something (like sound, or light) is a wave if it is invisible, or too small for us to see?

How can we predict how an object can resonate, and to what uses can we put its resonance?

How do musical instruments work? What’s the difference between a woodwind and stringed instrument?

How does a laser work? What’s the difference between regular light from a light bulb and laser light?

How does my reflection in a mirror (or image through a lens) depend on the shape of the mirror (or lens)? How do I design a mirror or lens system that magnifies something so I can study it in more detail?

Knowledge and skills

By the end of this unit, students will be able to

Qualitatively describe simple harmonic motion (SHM) of a pendulum and a mass on a spring. Solve simple problems involving the period of motion of these types of systems.

Quantitatively describe SHM using trigonometric functions of time.

Calculate the frequency, wavelength, or speed of a wave given the other two parameters. Explain why the product of frequency and wavelength is speed.

Identify the amplitude, frequency, wavelength, speed, and period of a sketched or photographed wave.

Calculate the speed of sound at different ambient temperatures, and explain why the sound speed increases with temperature.

Explain how waves interfere. Calculate destructive and constructive interference patterns from existing waveforms.

Explain how standing waves form. Calculate the wavelength and frequency of a standing wave on a string. Calculate the same for a standing sound wave in open and closed tubes.

Predict the resonant frequency of a pendulum or mass-on-a-spring system. Predict the resonant frequency of a bridge with several supports.

Explain how musical instruments produce sound.

Use Snell’s Law or the Law of Refraction to calculate the change in direction of a light ray incident on a lens or mirror.

Calculate the angle of total internal reflection at an interface between two media.

Calculate the position of an image upon reflection or refraction.

Discriminate between real and virtual images. Predict the orientation of real and virtual images formed by mirrors and lenses.

Explain and calculate the interference pattern produced by shining light through two or multiple slits.

Explain and calculate the diffraction pattern produced by shining light through a single hole or slit.

Measure the wavelength of a laser using a diffraction grating and a ruler.

Explain and calculate the Doppler shift that occurs when the source of a light or sound wave is moving with respect to the observer.

By the end of this unit, students will understand that

SHM occurs when a linear restoring force is applied.

Longitudinal and transverse waves can be described with the same mathematical models, but are different physical processes.

Light dispersion by color occurs when the index of refraction of a material depends on wavelength.

Two-slit interference is a fundamental property of waves.

Ray optics is a simplification of wave motion that allows us to do problems: a full treatment of the theory of light, however, must always implement its wave properties.

The index of refraction of a medium determines the speed of light in the substance.

The principle of least time lies behind Snell’s Law.

Many objects have resonant frequencies. Near resonance, the efficiency of power transfer increases enormously.

Musical instruments rely on standing waves to produce sound in a resonant chamber.

By the end of this unit, students will be familiar with the following vocabulary words

Simple harmonic motion, pendulum, physical pendulum, sine wave, oscillation, frequency, period, wavelength, wave speed, amplitude, wave amplitude, angular frequency, sound speed, medium, dispersion, reflection, refraction, total internal reflection, Snell’s Law, angle of incidence, angle of refraction, angle of reflection, normal to a surface, interference, diffraction, index of refraction, longitudinal wave, transverse wave, principle of least action, real image, virtual image, resonance, resonant frequency, laser

By the end of this unit, students will be familiar with use of SHM and wave equations as detailed in the course textbook

Performance tasks

Students will be guided to discover the relationship of pendulum period to length. Students will also verify the standard pendulum equation experimentally, and account for any discrepancies (particularly for large initial angle).

Students will measure the index of refraction of an unknown substance by passing light rays through it then use the measurement and Snell’s Law to identify the substance from a table of indices.

Students will verify the lens/mirror equation and create real and virtual images, demonstrating an understanding of the difference between these concepts.

Students will measure the wavelength of a provided laser by passing the ray through a diffraction grating and measuring the interference pattern.

Students will use graduated cylinders filled with water to make musical instruments via standing sound waves. A song will be played and graded based on how “in-tune” the song sounds.

VI. Modern Physics

Topics

Despite the variety we see in our everyday lives, only four fundamental forces dominate the universe: gravity, the electromagnetic force, and the strong and weak nuclear forces. These forces and the fundamental particles that experience them follow the seemingly bizarre rules of quantum mechanics.

Scientific research into the nature of the atom has led to a profoundly dangerous world-wide proliferation of nuclear weapons. Physics has therefore become a political and moral, as well as scientific, subject of study.

Questions

What is matter? How can matter have both wave and particle properties? How can energy have both wave and particle properties?

Is there an objective reality?

Can science harness the power unleashed by study of the nucleus without risking the destruction of civilization?

How will the Standard Model be modified or scrapped in the future? What theories will dominate 21st century physics? String theory? Something totally new?

Knowledge and skills

By the end of this unit, students will be able to

Describe atomic energy level transitions due to the absorption and emission of photons.

Calculate the wavelength of a photon emitted or absorbed in an atomic transition.

Calculate the decay rate of a radioactive substance using its measured half-life. Use this type of calculation to analyze radioactive carbon dating problems.

Explain how the radioactive decay rate changes with time, and how this phenomenon is related to the randomness (uncertainty) of the decay process.

Distinguish between alpha, beta, and gamma decay, and analyze complex nuclear reaction equations representing real decays

Determine, using a chart of the Standard Model, which particles can interact with one another via which forces (or exchange bosons).

Use charge, lepton number, and other conservation laws to analyze particle interactions with Feynman diagrams

Calculate the energy released when matter is converted in a nuclear reaction.

Calculate the wavelength and frequency of a photon based on its energy.

Demonstrate that the intensity of radiation decreases as the square of the distance from the source. Make calculations using the inverse-square law to determine radiation intensity.

Calculate the uncertainty in the position and momentum of a particle (or the energy and lifetime of a virtual particle) based on the uncertainty principle.

Explicate the wave and particle properties of matter.

Speak knowledgeably about the destructive yield of a variety of nuclear weapons, and the number and types of nuclear weapons that exist.

By the end of this unit, students will understand that

Atomic energy levels are quantized.

Radioactivity arises in the tension between forces in the nucleus of an atom.

All matter, all energy, displays both wave properties and particle properties. All these things are known as quanta.

Matter and energy are interchangeable.

There is an uncertainty principle that prevents an observer from knowing both the exact position and exact momentum of a quantum particle.

Physicists feel a responsibility to technically and morally educate the public about the dangers of nuclear weapons and the risks and opportunities inherent in nuclear power.

The Standard Model of Particle Physics attempts to categorize all matter and interactions in the universe. This Standard Model has some significant problems that need to be sorted out in the future.

The four fundamental forces vary enormously in their relative strength.

Nuclear fission is the splitting apart of heavy nuclei; nuclear fusion is the joining together of light nuclei; both release energy.

The intrinsic randomness in time of radioactive decay leads to the half-life equation; the intrinsic randomness in direction, coupled with the geometry of space, leads to the inverse-square relation.

Radioactive carbon dating allows us to determine the era in which dead organic material lived.

The intensity of radiation decreases as the square of the distance from the source.

A small amount of matter can be converted into an enormous amount of energy.

Planck’s constant is the ‘fundamental constant’ of quantum mechanics.

Antimatter particles shares the same mass as their corresponding matter particle, but have opposite electric charge, lepton number, or quark number. Matter-antimatter annihilation releases energy.

The properties of fundamental particles are often determined through collisions in high-energy accelerators.

Study of fundamental particles and high-energy interactions is intimately related to the study of the early universe when these particles were created.

Virtual particles, predicted by the uncertainty principle, lead to such phenomena as Hawking radiation.

Nuclear disarmament and nuclear power are extremely important technical, moral, and environmental issues.

String theory attempts to address discrepancies between Einstein’s theory of gravity and quantum mechanics. The theory has not been fully accepted or established due to the difficulty in experimental verification.

The correspondence principle relates quantum mechanical effects to our non-quantum macroscopic world

By the end of this unit, students will be familiar with the following vocabulary words

Nucleus, isotope, gamma ray, beta particle, alpha particle, alpha decay, beta decay, gamma decay, neutron, proton, quark, electron, electron neutrino, lepton, fermion, boson, half-life, inverse square law, particle, interaction, charge conservation, Feynman diagram, matter & antimatter, annihilation, Hawking radiation, virtual particles, uncertainty, quantum, warhead, kiloton, megaton, wave-particle dualit

By the end of this unit, students will be familiar with the relevant modern physics equations as detailed in the textbook

By the end of this unit, students will be familiar with the Standard Model of Fundamental Particles and Interactions produced by the Particle Data Group at the Lawrence Berkeley National Laboratory.

Performance tasks

Students will measure the half-life of a radioactive substance and use the measurement process to reason about radioactive carbon dating.

Students will measure the inverse-square dependence of radiation intensity and use their results to speak knowledgeably about radiation safety procedures.

Students will analyze the Nuclear Non-Proliferation Treaty and the worldwide stockpiles of nuclear weapons and make informed arguments about the process of nuclear arms reduction.

Students will measure the wavelength of a standard “pointer” laser to high accuracy.

VII. Electricity

Topics

Of the four fundamental forces, the most important (and strongest) in our everyday lives is the electrostatic force. This is the mutual repulsion and attraction of subatomic particles. We feel this force whenever we attempt to put one solid object through another.

Most macroscopic objects (like a table) are electrically neutral, but only because huge numbers of positive and negative electric charges are in balance.

Electric forces bind electrons to protons to form atoms, bind atoms together to form molecules, and bind molecules together to form solids and liquids.

In this unit, we also introduce the abstract concepts of vector and scalar fields, which are important for further study in this domain.

Questions

How does matter hold itself together? Why can’t I pass my hand through a table?

What is electric charge? Is it something an object “obtains” or is it more fundamental?

Why do mathematical models work so well in describing the physics of electricity?

How can I produce a large electric spark? To what uses can I put this spark?

How is electricity stored?

Knowledge and skills

By the end of this unit, students will be able to

Calculate the number of fundamental charges in a macroscopic charge.

Determine the charge state of an electroscope based on the charging process and the position of the electroscope leaves.

Reason about how static charges are generated when two materials are brought in contact. Understand and comment on a triboelectric sequence.

Determine the net charge of a collection of charged objects.

Describe the processes of charge by induction, polarization, and conduction.

Calculate two-dimensional vector forces using Coulomb’s Law for a set of three arbitrarily placed charged objects.

Sketch the electric field of a small collection of positively and negatively charged objects.

Calculate values of the two-dimensional electric field in the presence of a set of three arbitrarily placed charged objects.

Reason about the strength of the electric field based on the density of field lines.

Relate electric potential to electric potential energy, and make calculations based on this relationship. Also, solve problems using potential and kinetic energy based on charged particles moving through simple electric potentials.

Relate electric potential to electric field. Be able to reason about equipotential diagrams … in particular, be able to locate regions in an equipotential diagram where the electric field is strongest or weakest, and be able to determine the direction of the electric field from this diagram.

Likewise, be able to sketch an equipotential diagram if given an electric field pattern.

Calculate simple (one-dimensional) electric field values from electric potential functions, and vice versa, using algebra.

Determine the electric charge of two leaves in an electroscope from the angle at which they are hanging and the masses of the leaves.

Calculate the capacitance of a parallel-plate capacitor given its geometry and dielectric. Make educated guesses about the storage capacity of a capacitor given its geometry.

By the end of this unit, students will understand that

Like mass, electric charge is a property of fundamental particles, and cannot be created or destroyed.

The fundamental unit of electric charge can be determined through Millikan’s oil drop experiment.

Neutrally charged objects can experience an attractive electric force when polarized by a nearby charged object.

The storage capacity of a capacitor depends only on its geometry and the additional capacity provided by a polarizable (dielectric) substance.

A useful but limited analogy can be made between electric potential and height.

Seen from an energy perspective, differences in electric potential are the cause of the motion of charged particles.

Seen from a force perspective, electric fields cause the acceleration of charged particles.

The electric field, acting as a “mediator” of force, gets rid of the messy “action at a distance” problem Newton associated with the inverse-square law of gravity.

Electric fields obey the “principle of superposition” which means the electric fields surrounding individual particles can be added together like vectors to create the electric field of the aggregate.

Inside conductors (such as metals), the electric field must equal zero. Thus conductors are equipotentials, and can act as “cages” that block externally applied electric fields.

Electric potential, like electric potential energy, is only important in differential or relative terms. That is, you could add a constant to the total amount of electric potential possessed by any or all objects in the universe and the subsequent behavior would be identical to what we see now.

Electric current is a measure of the net amount of charge which passes by some location in a certain amount of tim

By the end of this unit, students will be familiar with the following vocabulary words

charge, positive, neutral, negative, fundamental charge, electric force, inverse-square law, vector field, scalar field, superposition, charge by induction, charge by conduction, charge by polarization, capacitor, dielectric, permittivity of free space, dielectric constant, parallel-plate capacitor, Millikan oil drop experiment, current

By the end of this unit, students will be familiar with the relevant equations from the course textbook concerning electric forces, fields and potential

Performance tasks

Students will make conclusions about the triboelectric sequence by measuring the electric charge transfer between two objects using an electroscope.

Students will conduct experiments that directly demonstrate the ability of a neutrally charged object to experience an attractive electric force via polarization. Such experiments might involve small paper fragments, a comb, rabbit fur, water, etc.

Students will charge and discharge a capacitor through an ammeter and light bulb, demonstrating the relationship between current, charge, and time.

VIII. Magnetism

Topics

The motions of charged particles give rise to magnetic fields. These fields can, in turn, affect the motion of charged particles. The tiny, aligned motion of electrons within atoms can generate macroscopic magnetic fields.

Magnetism bears a special relationship to electricity. Changing electric fields give rise to magnetic fields, while changing magnetic fields give rise to electric fields.

A wave (or quantum, really) of mutually inducing electric and magnetic fields is called a light wave.

Electric motors convert electricity into motion; electric generators to the opposite; both rely on the principle of electromagnetic induction.

Questions

What is the relationship between magnetism and electricity? Are they just two different aspects of a single entity?

How can I harness electricity to make a useful, moving object?

How can I harness motion (or other forms of energy) to make electricity?

What is the nature of light? If light is a wave, what exactly is waving?

Knowledge and skills

By the end of this unit, students will be able to

Measure and sketch the magnetic field of a bar magnet, a horseshoe magnet, a straight current-carrying wire, and a current loop.

Explain how a magnet can stick to a refrigerator.

Calculate the magnetic field in the region of a current-carrying wire.

Use the right-hand-rule to calculate the direction of magnetic force on a moving, charged particle.

Use the Lorentz Law to calculate the magnitude of a particle moving at an angle through a magnetic field.

Sketch the magnetic field of the Earth.

Calculate the radius of circular orbit for a charged particle moving within a uniform magnetic field.

Calculate the magnetic flux through a surface.

Use Lenz’s law to determine the direction of induced current in a wire loop due to a changing magnetic flux.

Use Faraday’s law to determine the induced emf in a current loop.

By the end of this unit, students will understand that

The magnetic field of the Earth acts as protection from the solar wind. The interaction of the solar wind with the atmosphere at the magnetic poles is known as aurora.

Permanent magnets are made from iron, nickel, or cobalt.

So far as experimental science is concerned, magnetic monopoles do not exist. Only magnetic dipoles (with two arbitrarily named ‘north’ and ‘south’ poles) seem to exist in nature.

Magnetic fields can be induced in metal alloys containing iron, nickel, or cobalt.

Magnetic fields can do no work because the force always acts at a right angle to velocity.

Changing magnetic flux causes an induced emf. Emf, at the level of this course, behaves as an electric potential, generating a current.

Electricity and magnetism have a more fundamental relationship, a topic to be explored in later courses.

By the end of this unit, students will be familiar with the following vocabulary words

Magnet, magnetic field, compass, magnetic monopole, magnetic dipole, ferromagnetism, diamagnetism, paramagnetism, magnetic flux, magnetic induction, electromotive force (emf), solar wind, aurora, electromagnetic wave, right-hand rule

By the end of this unit, students will be familiar with the following sign conventions

Right hand rule #1: shows direction of looped magnetic field lines around a straight-line current

Right hand rule #2a: shows direction of magnetic force on a charged particle moving through a magnetic field

Right hand rule #2b: shows direction of magnetic force on a current-carrying wire moving through a magnetic field

Right hand rule #3: shows direction of magnetic field pointing out of the center of a circular current loop

By the end of this unit, students will be familiar with the important equations describing magnetism and electromagnetism as detailed in the course textbook

Performance Tasks

Students will use a compass and/or iron filings to sketch the magnetic field around magnets and current-carrying wires of various geometries. Students will determine the attraction/repulsion characteristics of magnets on their own.

Students will build speakers using a coil of wire, a battery, and a magnet.

Students will build a working telegraph machine and communicate a message with it using readily available supplies.

Students will build an electromotor using a coil of wire, a battery, and a magnet.

Students will build an electric generator using a coil of wire, a battery, and a magnet.

IX. Electric Circuits

Topics

Electric circuits are practical applications of the theory of electricity and magnetism developed in the previous two units. A source of electric potential generates a current through objects that depends on their electrical resistance.

DC circuits can be analyzed by breaking them into idealized components: voltage sources, current sources, resistors and capacitors. AC circuits display different behavior.

The power dissipated in a resistive light bulb is related to its brightness, thus one can learn about simple circuits by studying bulb-and-switch circuits.

Questions

How is electricity generated, transferred, and employed to do useful work?

Under what circumstances am I safe from electric shock? How do I determine how dangerous a circuit is? What is a safe way to experiment with live circuits?

What principles should I use to analyze complex circuits? If I find myself faced with an electric circuit, how can I reduce its complexity?

Knowledge and skills

By the end of this unit, students will be able to

Starting with a drawn or wired circuit, draw an accurate schematic using the standard symbols. Topics here include voltage supplies, ammeters, voltmeters, resistors, and switches.

Starting with a schematic, build an accurate wired circuit.

Calculate the voltage drop required to drive a specified current through a resistor. Perform all the algebraic manipulations required to solve for V, I, or R using Ohm’s law.

Describe and calculate the differences in current and voltage drop that occur in circuits involving resistors in parallel and series.

Calculate the equivalent resistance of resistors in series and parallel.

Calculate the power dissipated in resistors in complex parallel and series circuits.

Qualitatively and quantitatively describe the flow of current through a branching circuit; qualitatively and quantitatively analyze the voltage drops across various resistors in a branching circuit.

Qualitatively describe the flow of current through a resistor and into a capacitor for storage.

Calculate the RC time constant for a given circuit

By the end of this unit, students will understand that

Calculating the equivalent resistance of a circuit allows you to determine the current drawn from a voltage supply.

The voltage drop across a conducting wire is essentially zero; in other words, they have zero resistance.

Kirchhoff’s Laws allow you to solve for all currents and voltage drops in all resistor/voltage supply circuits. The first law says that the voltage drop around a complete circuit is zero. The second says that current into a junction equals current out of the junction.

Power (and brightness, for lamps) is related to the product of current and voltage. Thus energy delivery depends on both of these quantities, not just one or the other.

Certain power dissipations can burn you or start fires; a modest current passing through your heart (say by entering and exiting at your two hands) can kill you.

Light bulbs are inefficient; light-emitting diodes stay cool by emitting most of their dissipated energy as light.

Circuit elements are the “alphabet” – there are many more “letters” to be learned at a different time: transistors, diodes, inductors, op-amps, digital circuits, etc.

By the end of this unit, students will be familiar with the following vocabulary words

power supply, voltage supply, cell, resistor, wire, power, voltage drop, ammeter, voltmeter, multimeter, two-prong switch, three-prong switch

By the end of this unit, students will be familiar with the important equations for analyzing circuits as detailed in the course textbook

Performance Tasks

Students will build an “upstairs-downstairs” circuit using a light bulb, two three-prong switches, and a battery.

Students will predict current flow and voltage drops in complex circuits then measure them directly.

Students will predict and measure the temperature dependence of the resistance of a light bulb.

All Units

Instructional methodology

Instructors will use a variety of methods in order to achieve the highest and broadest possible understanding among the students. The methods can include, but are not limited to: standard lecture, problem set assignments, standard quizzes and exams, discovery and formal laboratory exercises, long and short-term projects, multimedia presentations, computer simulation, demonstrations, one-on-one instruction, peer instruction, “studio”-based instruction, and “Modeling” of the sort David Hestenes has promoted at Arizona State University.

It is understood that physics needs to be fun, approachable, and interesting. Instructors will, from time to time, share new discoveries, old ideas, and stories that capture the history, mood, and excitement we associate with natural science.

Instructors will deal head-on with student’s alternative conceptions of physics. As Randy Knight points out in his excellent book Five Easy Lessons,

“Students enter our classroom not as ‘blank slates,’ tabula rasa, but filled with many prior concepts…. Student’s concepts are rather muddled, not well differentiated, and contain unrecognized inconsistencies. By the standards of physics, their concepts are mostly wrong.” “Students’ prior concepts are remarkably resistant to change. Conventional instruction – lecture classes, homework, and exams that are predominately or exclusively quantitative – makes almost no change in a student’s conceptual beliefs.”

Knight’s solution is to follow the Five Easy Lessons: (paraphrased here)

Keep students actively engaged and provide rapid feedback. A short list of active engagement methods includes interactive lecture demonstrations, nearest neighbor discussion activities, collaborative group activities, computer-based laboratories or other guided-discovery laboratories, and take-home experiments.

Focus on phenomena rather than abstractions. Use experiential labs. Work inductively, from the concrete to the abstract. Ask the questions “How do we know …?” and “Why do we believe … ?”.

Deal explicitly with students’ alternative conceptions. Students have to recognize and accept that there really is a conflict between their wrong predictions and reality. Left to themselves, many students will brush the conflict aside as of no relevance.

Teach and use explicit problem-solving skills and strategies. These include interpretation, pictorial, graphical, and reasoning skills. Make explicit the assumptions, decisions, and reasoning that are part of an expert’s problem-solving strategy but which usually go unsaid.

Write homework and exam problems that go beyond symbol manipulation to engage students in the qualitative and conceptual analysis of physical phenomena. Balance qualitative and quantitative reasoning. Emphasize reasoning, de-emphasize formulas and equations. Deal directly with phenomena and observations. Derivations have little efficacy for students at this level.

Common methodologies between physics honors sections

Instructors within physics honors will agree to make a good faith attempt towards standard usage (for names, variables, quantities, and sign conventions) and codify this usage within this curriculum document.

Instructors will demonstrate the importance of unit analysis, unit definitions, and unit cancellation throughout the course.

Instructors will provide examples of excellent work by past or current students so that it is clear what is expected.

Instructors within physics honors will make a good faith attempt towards common exam outcomes with content that is varied between periods. One strategy is a system in which a common test bank will be agreed upon at the start of the unit and exam problems will be selected from this bank at random at the end of the unit.

Instructors will conduct yearly blind studies of student progress through internal assessments as well as external assessments designed in the physics education research community, and make adjustments to the curriculum and instructional methodology based on the results of these assessments.

In their Understanding by Design Handbook, Wiggins and McTighe describe quizzes and tests as “simple, content-focused questions that assess for factual information, concepts, and discrete skills.” Academic prompts are “open-ended questions or problems that require students to think critically, not just recall knowledge, and to prepare a response, product, or performance … under school exam conditions.”

Quizzes, Tests, and Prompts

Students will be provided with a sheet that lists the important equations. This serves to emphasize to the student that knowledge of equations is not sufficient for understanding physics. For practicing scientists, memorization of equations happens naturally through use.

Students will be given weekly or biweekly quizzes based on homework-type problems.

Weekly quizzes and unit and midterm exams will include a variety of question cues in the vein of Bloom’s Taxonomy:

Knowledge: list, define, tell, describe, identify, show, label, collect, examine, tabulate, quote, name, who, when, where, etc.

Comprehension: summarize, describe, interpret, contrast, predict, associate, distinguish, estimate, differentiate, discuss, extend

Application: apply, demonstrate, calculate, complete, illustrate, show, solve, examine, modify, relate, change, classify, experiment, discover

Analysis: analyze, separate, order, explain, connect, classify, arrange, divide, compare, select, explain, infer

Synthesis: combine, integrate, modify, rearrange, substitute, plan, create, design, invent, what if?, compose, formulate, prepare, generalize, rewrite

Evaluation: assess, decide, rank, grade, test, measure, recommend, convince, select, judge, explain, discriminate, support, conclude, compare, summarize

Homework problems, weekly quizzes, and unit and midterm exams will include a mix of pictorial and written representations of problems; multiple choice, short answer, and free response problems; written answers involving no equations and complex equation-based solutions; and laboratory-based questions involving error analysis

Students will be asked to make predictions, hypotheses, measurements, and analyses in the laboratory. Some laboratories will be informal (or ‘guided discovery’-based). At least one laboratory exercise in each quarter will emphasize error estimation and written report skills.

Homework assignments may or may not be collected and/or graded. Students will be provided with examples of excellent work.

At least part of each test will require mathematical sophistication appropriate to the physics honors math prerequisites. Examples include using right-triangles or SOH-CAH-TOA to break a vector into x and y components; solving systems of two equations and two unknowns; using exponential, logarithmic, or trigonometric functions; converting units with multiple steps; solving a problem purely symbolically, with no reference to numerical values; sketching curves, drawing best-fit curves, and properly labeling x and y axes; and/or using scaling relationships and functional forms to predict ratios (i.e., using the inverse-square law to predict that at three times the distance, the force is nine times smaller.)

Bibliography

The Understanding by Design Handbook, by Grant Wiggins and Jay McTighe, published by the Association for Supervision and Curriculum Development (1999)

Five Easy Lessons: Strategies for Successful Physics Teaching, by Randall Knight, published by Addison Wesley (2004).

Particle Data Group website: http://www.particleadventure.org