AP Physics C - Mechanics
Round Lake High School
Mr. Steven M. Pichman
This syllabus has been audited and approved by the College Board.
2014-2015
I.
II.
III.
IV.
Overview: Students must be concurrently enrolled in AP Calculus. Students must have
passed the prerequisite AP Physics B course.
Textbook: We use Physics for Scientists and Engineers by Raymond Serway, and Jewett,
Ninth Edition. It is a traditional Calculus-level textbook with a wealth of sample problems to
solve.
Implimentation:
The course will be a 45 minute class, 5 days per week. Extended labs will require students
to utilize study hall time, and/or before school or after school to complete. On average, we
will spend one period per week on labs, if not two. Quizzes will be weekly, and tests will be
monthly. Students will keep all work in a 3 ring binder that will involve dated notes, dated
homework, and chronologically ordered and dated lab notebooks and reports.
Course Design, Objectives, and Strategies.
Our goal in AP C Physics is to provide an experience that is identical to the college
experience that engineers and scientists have had towards their careers in the sciences. We
will be utilizing conceptual tests developed by the American Association of Physics Teachers,
and published AP C exams from the past.
Although the homework will have a traditional problem-solving flavor, our class periods will
be using Modelling techniques including Whiteboarding, Peer Review, and a host of hands
on/minds on labs, where students will present their findings just like scientists do when they
make discoveries. Some of the labs will be traditional proof labs, but most will be open
ended discovery with prompts toward discovering the law of physics experimentally. A
student centered approach will be utilized, as the guided inquiry approach has proven to be
valuable.
We will also be working in close collaboration with our AP Calculus teachers to make sure
that the two courses complement each other.
V.
Sequence
a. Kinematics
b.
c.
d.
e.
Newtonian Mechanics starts with Galilean Kinematic Instruction. Beichner’s Testing of
Understanding of Graphing in Kinematics will be the conceptual instrument (from
American Journal of Physics, volume 62, No.8, August 1994, p. 750-762.) We will also
introduce Vectors during this unit. The major representation utilized during this unit will
be position vs time graphs, velocity vs. time graphs, and acceleration vs. time graphs.
The classic ball shot into the cup lab will be the guided inquiry lab for this unit. We also
have Pasco projectile launchers for a host of student led labs.
Dynamics
Newtonian Mechanics will get a deeper instruction during Newton’s Laws of Motion.
Swackhammer’s Force Concept Inventory, and Mechanic’s Baseline Test (from The
Physics Teacher, March 1992, re written by Arizona State Modelling group in 2000) will
be instruments of conceptual assessment. The major representation of Dynamics will
be the Free-Body Diagrams. Homework will be heavy on Gravitational field calculations,
and Gravitational force calculations. We will hint on Gauss’s law applied to Gravitational
fields, but not truly cover it in depth until the very end of Classical Mechanics
Differentiation and Integration. The algebraic equations of Newtonian Mechanics will
serve as the guide to understanding of taking slopes of functions, and finding areas
under curves of functions. We will closely work with the pace and sequence of our AP
Calculus Teacher to introduce limits, derivatives, and integrals at the pedagogically
correct time. We will also use the Kinematics Graphs as templates for further
investigation. During the momentum and force units we will discover the area under the
curve of a Force vs. Time graph to calculate the change in momentum. We will also look
at as many derivatives of functions as we can graph experimentally. A lab that has been
developed at Round Lake involves relating the Volume of liquid in an Erlenmeyer Flask
(a cone) to the depth of the liquid. The changing cross sectional area can be calculated.
Then the students will measure the height of the Erlenmeyer flask vs the diameter of
the flask at the different heights. Calculations will yield the similar changing cross
sectional area from before, with the error being contributed as the thickness of the
glass. These cone calculations are an integral part of the AP Calculus course here at
Round Lake.
Work . Work will be the first topic that will use both Integration, and the Vector Dot
Product during calculations. We will use Calculus to derive equations for Kinetic Energy
and Potential Energy. The conceptual instrument we will employ will be the EMC test
from Singh and Rosengrant, American Journal of Physics, p 607-617, June 2003.
Energy. Our Instruction in Energy will follow from the derivations of Kinetic Energy and
Potential Energy, and the Labs we will employ to create both Classical Cartesian
Coordinate Graphs, as well as Energy Bar Charts, and Energy Flow Diagrams. Multiple
representations of the Law of Conservation of Energy will be the cornerstone of this
unit. Air track labs will take center stage, as we will also investigate the error involved
with assuming there is no friction, and the assumption that no heat is lost. The
inevitable inequality in starting mechanical energy to final mechanical energy will point
towards the heat that is not part of the AP C curriculum. The classic coffee filter lab will
be the guided inquiry lab in this unit, as it will help us introduce the calculation of air
resistance as a force that results in heating. Elastic “Happy Balls” and Inelastic “Sad
Balls” will also be a quick hands on lab to review all previous concepts in a multiple
representation method that pays homage to Arizona State’s Modeling method of
instruction.
f. Momentum. Collisions in the air tracks from the previous energy unit will be first
explored on the linear air track, then we will start to expand the vectors to both two and
three space opening up calculation of Center of Mass, and other related topics. We will
hint towards Elementary Particle Physics that we will work on after taking the AP Test in
May, as those topics are not in the Classical framework of AP C. The concepts of system
of particles will be introduced here from a collision standpoint. Also, the falling chain
lab will be the guided inquiry lab in this unit. Students will get a choice of sensors in this
investigation, and we will determine which sensor works best….photogates, smart
pulley, force sensors, motion sensors, or any of the other Vernier probes we can use.
(thermometers may be outside the realm of AP Mechanics, but Joule’s classic
experiment is always a good one).
g. Power…Energy Changing form per unit time will be the graphical starting point in this
unit, where the concept of Power will be developed and utilized to further investigate
dimensional analysis that can be shown through derivations and integrations. Although
the labs will also utilize electricity, and thermo concepts as well, most of the homework
problems will be in Classical Mechanics in gravitational fields.
h. Circular Motion. Several Hands On labs will be employed in this unit to discover the
application of Centripetal accelerations and Centripetal Forces to create more equations
in coordination with the Free Body Diagrams from the Dynamics Unit. Two body
problems in gravitation will be explored. Bowling balls rolled in circles with a broom will
be a model that we start with, and we will also “orbit” bowling balls around a large drain
tile in the parking lot to model the centripetal acceleration of gravity. The mathematical
analysis of this will center on the vector diagrams. The displacement vector, the
tangential velocity vector, and the centripetal acceleration vectors will be shown as
being locked in a 90 degree angle dance. Their horizontal and vertical components will
be graphed to discover and prove the derivatives and integrals of sine and cosine
functions.
i. Harmonic Motion. This will be the capstone unit for Linear Newtonian Dynamics. The
Lab investigation will be a mass bobbing on a spring. We will use this lab to review
every single interpretation of physical reality up to now. The students will consider
distance vs. time graphs, velocity vs. time graphs, and acceleration vs. time graphs and
discover the calculus of the trig functions experimentally. A parallel to uniform circular
motion will likely be discovered as well, as the students find mathematical solutions to
the second order differential equation that defines a mass on a spring. Energy
perspectives will be utilized to find Spring Potential Energy , and the related area under
the Hooke’s Law, Force vs. Stretch length graph. Momentum and Kinetic energy
perspectives at the Force equilibrium positions will explore the differences between
inertial mass and gravitational mass that may give rise to new explanations of
Gravitational Field Theory. In preparation for Electric and Magnetic Fields, we will look
into Divergence, Gradient, and Curl shown in 3 D graphs of Gravitational potential of
Warped Space time graphs that are Non-Classical in Nature. During the time after the AP
Test, this will serve as our launching point for Modern Physics topics of Wave / Particle
Duality. If we have extra time, we will also revisit the pendulum lab from the Physics B
course they all took last year. This year, though, it will be the Conical Pendulum.
j. Systems of particles – We will start with the traditional calculations of gravitational
forces due to multiple bodies in the solar system. We will then continue with
calculations of more and more bodies, until the concept of integration seams to make
much more sense. Linear densities, surface area densities, and volumetric densities will
be introduced as changes to the limits of integration start to require more investigation
into calculus skills. The ruler drop lab involves hinging a ruler on the lab table and
placing pennies from one end to the other. This system of particles will be investigated,
but we won’t do the full-blown calculations until we discuss torque and moment of
inertia.
k. Rotational Dynamics – The rotational Dynamics unit will be a heavy dose of Vector
Calculus. At Round Lake, our AP Calculus program works towards the AB test, so these
mathematical skills will have to be developed in Physics. Vector Cross Products will be
employed to calculate torques, and Angular momentum. Once again we will draw a
synthesis with linear velocity to angular velocity, linear acceleration to angular
acceleration, and linear distance to rotational angle. Beichner’s test will serve as a
template for the graphical analysis of these three ideas that seam to simply substitute
Greek letters for the English letters!! Due to the multi-dimensional nature of this
subject, we will be spending much class time in learning the fundamental math ideas
involved. Every effort will be made to use this topic as the stepping stone to Electricity
and Magnetism, as the Vector Calculus is essential for student success. Labs will include
Gyroscope labs, spinning 3 D boards, spinning/rotating tubes, Australian Bullroarers,
and a host of other hands on experiences that are very fun to experiment with. The
Gyroscope Lab, in particular will be a guided inquiry lab where a mass falling off the
table tied to a string will be the source of energy, power, and angular acceleration for
our toy gyroscope. The precession will be explained.
Calculations of the various Moments of Inertia will also be done on paper, then we will
experiment with their implication through labs that roll and rotate various geometric
shapes to prove the theory. The classical linear equations will all be reinvestigated as
we replace the “m” of mass with the “I” of moment of inertia.
A simple balance lab will be imployed to investigate the effects of torque, and torque
equilibrium. An open ended student created lab will be the capstone activity of this
unit. We will then revisit the Ruler lab from system of particles unit.
l.
The Law of Conservation of Angular Momentum will be heavily explored as we review
Gravitiational Physics. We will investigate all the areas where this law is crucial such as
planetary motion, Kepler’s laws, and the quantum mechanical laws that shape the atom
and give structure to the periodic table of the elements. We will employ derivatives and
integrals , as well as Vector Cross products using 3x3 matrix calculations in Cartesian
coordinates, spherical coordinate systems, and cylindrical coordinate systems. Last, but
not least, we will look to the Conic Sections for more mathematical understanding.
m. The Mechanical Universe series will be used as a backdrop to solidify the concepts of
Gravitation, as we review all the concepts in Newtonian Physics. Our Vector calculus
education will also continue with Divergence, Gradiants, and Curls applied to
Gravitational Field Theory. Line integrals and closed surface integrals will also be
investigated mathematically. Gauss’ Law applied to gravitational fields will be our final
topic and stepping stone to Electric Fields, and Gravitational fields for the E&M half of
the class.
n. Review and Practice for the Exam