Georgetown Day School
Ed Eckel and Deb Maresh
PreCalculus and Honors Physics - High School Level
Syllabus

Goal: Structuring understanding

Note: These courses are separate but coordinated; different student population will be found in each. Of the 60 students served, approximately 10 will be in both classes.

Course Descriptions:

PreCalculus: The students entering PreCalculus have already studied a considerable amount of trigonometry. Very few topics in trigonometry will be new to them. The students will review trigonometry and quickly move on to modeling data, statistics, probability, conics, graphs of functions, and the definition of a limit. The order that the topics will be covered is not set in stone as I teach only two of the four PreCalculus classes, and students changing their schedule could become a big issue. Some coordination must be done with the other PreCalculus teacher.

Honors Physics: The students in Honors Physics span grades 10-12. Some will be in Pre-Calculus and others in the Algebra 2/Triginometry offering. The course will cover Classical Mechanics, Thermodynamics, Electricity and Magnetism and select from Optics, Fluids, and Modern Physics depending on time available and interest. An essential feature will be the use of experiment to inform conceptual understanding and conceptual understanding to dictate the mathematical description of phenomena studied.

PreCalculus

Trigonometry (incorporate programming on the calculator)

Periodic functions/the six trig functions (review)

**begin review with calculator lab and parametric equations

** x=cost, y=sint

**journal question - when is a function periodic?

Graphs/modeling (review)

Properties/Identities/Combos (half review)

**section on composition of ordinates and harmonic analysis

Rotary motion/inverses/applications (half review)

Triangles/vectors (review)

**journal question - In the ASS triangle, why can there be two possible triangles?

Graphs of functions(polynomials and rational)/Limits/Derivatives

Quick recap of the graphs and properties of specific functions

**journal question - for logarithmic functions, why is the base greater than zero and not one?

Graphs

**synthetic division/substitution

**zeros

**asymptotic behavior

Notion of limits

**journal question - How would you define/describe a limit to a 5th grader? An 8th grader?

**journal question - Draw a function whose limit from the right of 3 is not the same as the left of 3.

Definition of a derivative

**journal question - Draw several different functions on separate graphs. For each, draw lines to indicate you understand the definition of a derivative. How would you explain a derivative to a person who just completed an Algebra I course?

Fitting Functions to Data

Finding patterns in data

**"nice" vs "not so nice" data

**Coffee filter idea, then revisit coffee filter idea when combining different functions

Scattered data

**analyze appropriateness of model

Lends itself well to a labs

"Hook up" with Ed’s 3rd period class

Statistics/Probability

Discuss statistics found in magazines.

**journal entry - How honest are they?

One variable

Combinations/permutations/random variable

Possible labs (? that aren’t trivial ?)

**journal entry - Discuss the "Let’s Make a Deal" problem. Is it better to switch?

Conics

Graphs

Focus/directrix/center/etc

Rotation of axes

(?)Construct a paraboloid - find project from NCTM Conference

Visit www.cpo.com/weblabs/projecta.htm#Parabola

Polar Coordinates/Parametric Equations

Lab with position/distance and time

**Use CBL’s and calculator

Complex Numbers/Series

Ball bouncing idea from class 6/21

Motion detector/CBL’s

Honors Physics

1. Newton and Aristotle: What Is Change
The purpose of this unit is to explore the Aristotelian and Newtonian worldviews. We will observe and graphically represent several motions yielding various functional forms and thus different shapes on position time graphs. This unit will be used to introduce the CBL and MBL acquisition systems. Both position-position and position-time graphs will be used.

Topics:
Ball falling
Coffee filters falling
Ball bouncing
Simple Harmonic Motion (pendulum and spring)

2. Modeling
This unit will teach/review unit circle trig. We will start with the SHM from Unit 1 and explicitly relate it to circular motion, describe the unit circle and define the trig functions sine, cosine, and tangent in the mathematical way. Coordinate systems will be introduced. The use of right triangle trig to move between coordinate representations will be introduced. The essential feature is the position of an object does not change during a coordinate transform, only the description of the position. Finally, we will look at the relative value of a position-position plot (snapshot of space frozen in time) and the position-time plot. We will introduce parameterization as a means of creating a "movie" of the motion. We will restrict the "movie" to one dimension as ‘an artifact’ of making 2-D drawings with one axis devoted to time. Care must be used to avoid the impression that a graph is ‘a picture’ of the motion.

Finally, we will explore using the spreadsheet to generate functions that yield graphs matching the data collected. We will link closely with math in the analysis of the features of the functions generated.

Topics:
Periodicity and the Unit Circle
Describing where something is
Trig functions and unit circle
Trig functions and similarity
Coordinate systems
Rectangular
Cylindrical
Spherical
Parameterization
Using an equation to represent the data
Use of Spreadsheet

3. Kinematics in 1-D: mass doesn’t matter!
Galileo’s Experiment will be repeated using ramps at different slopes, measuring distance traveled and time to travel. Graphical representations created by all lab groups will be used to search for patterns in the data. We will work with the math class in developing functions that represent the rate of change in the data. We analyze the functions and then repeat the process until we find something which does not change. We ask: is a general pattern evident and how might we describe it? What assumptions are buried in the abstracted patterns (standard kinematics formulas, definitions of speed and acceleration and, in particular, the mass of the object is not accounted for).

Topics:
Galileo’s Experiment
Patterns in the data
Data Mining: Modeling, Slopes, and Re-representation.
Patterns in the Representations

4. Vectors: Fully Representing Pertinent Information
We consider the Galileo experiment and ask if the ramps had a part to play. We find that the pattern of constant acceleration is robust from small to vertical slopes. We note the slope of the ramp contributes a magnitude effect. We consider the generality of the abstracted patterns. We ask about motions with superficially different character: the tossed ball. We consider direction in addition to magnitude of motion. We investigate the relation between horizontal velocity and vertical acceleration. We work with the math class to test our understanding on stomp rocket flights (predict, test, evaluate.)

Topics:
Magnitude and Direction
Projectile Motion
Hypothesis: cause and effect between vertical acceleration and horizontal velocity
How Far I go depends on how far I fall!
Stomp Rockets

5. Newtonian View and Newton’s Laws: yes, mass matters!
The stomp rockets reveal some problems: flights are neither as far nor as straight as expected. We ask about the cause and effect nature of acceleration. What causes acceleration and what influences its effect?

Topics:
First Law
Inertia is NOT a force
Second Law
Meaning of multiplication
‘Sum’ means all: FBD
‘Net’ means a single effect: acceleration
Cause and effect: knowability
Third Law
The difference between walking on water and walking in space

Interregnum (essay and reflection)
Time, Change, and the Ability to Understand: Forces and Nature

An Interregnum is an ancient Latin term for a pause. For me, it carries the connotation of reflection. Thus, we pause to reflect on what we have discovered, to gather to ourselves the critical elements of our investigations. This is a critical part of the course. We will spend time discussing the implications of Newton’s Laws on the worldview of the Physicist. We will examine a quote from Wittgenstein about the ability of a proof to change and indeed organize the way we perceive the world. We challenge the view from the concern of ideological rigidity. We find we must continue the journey, by looking at the implications of the definition of force.

6. Forces through time and displacement
As we study forces and the effect of the application of a force on a mass, we see that a particular force is not required to produce a particular effect. In fact, it is the time over which the force acts that seems to control things. That is, small force acting for a long time may produce the same effect as a large force acting for a short time. We study this through experimental observation, consideration of what the meaning of various mathematical combinations of force and time. We examine the robustness of our conclusions by looking for effects associated with the vector nature of force. Finally, we arrive at a conservation law.

We proceed to consider the idea that forces acting for a finite and non-vanishing period of time also must act on the body after movement has been induced. That is, the point of application of the force moves while the force continues to be applied. We begin with simple observations about the application of a known force over different distances, move to a theoretical discussion, and then revisit the idea of conservation.

Topics:
Momentum
Impulse
Collisions
Decay (1 and 2-d)
Conservation
Energy
Kinetic Energy
Potential Energy
Work-Energy Theorem
Weak Form of Conservation of Energy
Non-Conservation under the weak form: friction and temperature increase

Interregnum: A Mental Map
Students produce a map explicitly revealing assumptions and constraints in linear dynamics. A paper detailing the differences and advantages of Newtonian and Aristotelian view is produced and shared. Each student makes written comments on the writing of the others.

7. Project: Extending to Angular Dynamics
This is a group project in which the students are called on to use their maps to build a kinematics and dynamics for rotational motion. This is expected to be hard. Worksheets and seeds of lab ideas will be provided but student suggestions for investigations will be avidly sought.

Topics:
Review of Angular variables
Angular kinematics
Moment of inertia (oops, the distribution of matter does matter, a lot!)
Torque (Where the cause happens is nice to know)
Angular momentum
Rotational KE
Conservation of Energy (weak) made Stronger
Hoop and disk races

8. Are all forces contact forces: Gravitation and Electrostatic
This begins a fundamentally different section of the course. We look for ways of understanding the motion of the moon about the earth. We look for confirmation of the Keplerian reduction of Brahe’s data. We look for evidence of other phenomena that behave as a non-contact agent of change. We look at abstractions associated with the study of electro-magnetism but equally well applied to any causal agent.

Topics:
Newton’s Law of Gravitation
Kepler’s Laws as Empirical Construction
Kepler’s Laws as Theoretical Construct
Coulomb’s Law
Gauss’s Law
Work and energy
Potential and field

9. Kinetics: discovering complexity through theoretical consistency

Topics:
Model of matter
Phases of matter
Appearance of energy (temperature and heat flow)
Interactions (Pressure, volume)

10. Thermodynamics

Topics:
State variables
Intrinsic and extrinsic variables
First Law of Thermodynamics: absolute conservation of energy
Carnot Engines
Second Law of Thermodynamics: Modeling the Reality of Absoluteness
Entropy and the Reality of Puritan Ethics

11. Circuits

Topics:
Elements (batteries, wires, and extraction devices)
Relate to Carnot’s thoughts
Potential and current
Kirchhoff’s Laws
Capacitors

12. Magnetism

Topics:
The changing electric field due to a moving point source
The detailed atomic structure of naturally magnetic materials
Catalogue ways to make a magnet display the effect of external force on it
Ampere’s Law
Changing Magnetic Fields
Faraday’s Law
Magnetism and work
Solenoid

If we have time and possibly as small group study projects:
Optics
Fluids
Modern (as done by Zollman at UNL)

7/30/99