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The Canterbury Episcopal School
Scope and Sequence
Honors Physics I
Text: Physics, Serway, Raymond A. & Faughn, Jerry S., Holt, Rinehart, & Winston, Austin, 2009.
Physics is introduced as the most mathematical of the sciences so that students understand:
● how physics compares with the other major areas of science
● that physics research shows the so-called “scientific method” as an organic, human activity as opposed to some
mechanical “recipe”
● that a scientific theory is so much more than an “educated guess”
● that the scientific enterprise is a combination of unbridled imagination and of merciless skepticism
● the relations and distinctions among science, engineering, and technology
Students are aware of the mathematical skills and background for which they are responsible:
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algebraic skills of isolating variables making up an equation
simplification skills of adding and subtracting fractions and of simplifying rational algebraic expressions
knowledge of how to solve a quadratic equation
how to solve a two-equation, two-unknown system of equations using substitution
how to utilize a scientific calculator to do the arithmetic of numbers expressed in scientific notation
how to obtain trigonometric function values and inverse trig function values for the calculator
basic trig identities
basic properties of right triangles
Pythagorean Theorem, Law of Sines, & Law of Cosines
To the above are added the following, which students must also demonstrated their ability to utilize:
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the “uddu method” of simplifying complex fractions
the replacement of variables in equations with a number and its unit
the arithmetic, manipulation, and transformation of units
the power method of transforming units of area and volume
the MKS system of units, emphasizing the usage of prefixes in the process of transformation
the three basic units of mechanics – length, mass, and time
Students must demonstrate their ability to solve physics stated problems, wherein they must be able to:
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write down appropriate given algebraic variables with their values and their units
write down the appropriate variable to be found
sketch an appropriate simplified schematic of the situation described by the problem
find by elimination the only equation containing the unique set of given variables and variables to be found
rearrange the equation to isolate the unknown variable either on the left or on the right
“naively” substitute for every given variable its value and its units
let the calculator “crunch” the numbers and carry through each step the units
let the units play out instead of assuming the correct units at the end
where applicable, see if the value and the units of the answer are expected and reasonable
Students start applying the problem solving method outlined above on the simple equations for
distance, velocity, acceleration, and density, showing they are acutely aware that:
● every equation can be rearranged into as many equations for variables as there are variables in the equation
● units are the “key” from going from step to step, for knowing if transformations are required, and for knowing
whether or not the answer is correct
● the method works on the simple and the complex
● the method serves the student for a life time
The Kinematical Equations (equations for constant acceleration) are derived for the students, who, in
turn, demonstrate they know how to solve problems using:
● Eqn. [1] (containing no acceleration ‘a’)
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● Eqn. [2] (containing no distance ‘x’)
● Eqn [3] (containing no final velocity ‘vf‘)
● Eqn [4] (containing no time ‘t’)
Students demonstrate their ability to use the equations for free fall, which are Kinematical Equations
[1] through [4] with the earth’s acceleration for gravity, ‘g’, substituted in them for generic
acceleration ‘a.’ They do so understanding:
● they must furnish the value and sign for ‘g’
● frictional effects are neglected
Students apply their knowledge of kinematics by recording data of a steel ball rolling down an inclined
ramp toward submitting a beginning lab report by:
● graphing the distance down the ramp as a function of time
● “stacking” graphs of velocity vs time and acceleration vs time beneath distance vs time using slopes found with
straight edges and calculators (a 3-tiered stack of graphs)
● reading the final velocity of the ball at the bottom of the ramp from the graph -- a vexp (an experimental v)
● using kinematics, calculating what the velocity of the ball at the bottom should be – a vstd (a standard v)
● calculating a percent difference between vexp and vstd
● understanding their “write up” is a prototype of the college-like laboratory report required in higher education
labs
Differences between scalar quantities and vector quantities are introduced and students show they are
capable of adding (or subtracting) two or more vectors (finding their resultant R) by utilizing their
ability to:
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express any vector with both its magnitude and its direction
denote vectors with sketched arrows and express vectors in i and j notation (2-D vectors)
represent vectors in the four quadrants of the coordinate plane
resolve any vector into two components at right angles to each other (x and y components) using the sine and
cosine of reference angles measured from the x axis
follow the sign behavior of components quadrant to quadrant
add together all x components and all y components to get the numbers R x and Ry, respectively
from Rx and Ry calculate the magnitude of R, R, and the direction of R, θ, a reference angle on the coordinate
plane
add two actual vectors with a force table, comparing the table results with the calculated prediction
Students understand that two-dimensional kinematics is based upon the principle that motion can be
studied independently along two axes at right angles to each other (e.g. horizontal and vertical axes)
and upon the derived equations of motion in two dimensions. Students utilize the equations to find for
projectiles:
● parametric equations for x and y in time, x(t) and y(t), and in terms of the angle of elevation θ
● parametric equations for vx and vy in terms of the initial velocity vi and θ
● given a θ and a vi:
> time of flight
> time to maximum height ymax
> ymax
> quadratic equation y(x) with time ‘t’ eliminated
> the projectile’s range xmax
Dynamics is introduced as kinematics considering the cause of motion, force. After understanding a
force as a push or pull, students go on to work dynamics problems, utilizing the kinematical equations
as necessary tools along the way, by:
● demonstrating the ability to sketch force diagrams or free-body diagrams
● understanding the concept of mass and inertia
● understanding Newton’s 3 Laws of Motion:
> 1st Law → Law of Inertia (1 mass, m)
> 2nd Law → Law of Acceleration (1 mass), F = ma
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> 3rd Law → Law of Action-Reaction (2 masses)
solving dynamics problems on horizontal surfaces
solving dynamics problems on inclined planes of angle θ
solving problems involving the definition of weight (F g = mg), knowing weight and mass are not the same
utilizing the concept of frictional force upon the moving object on a horizontal or on an incline
applying the concepts of coefficients of friction and normal forces to calculate the frictional force F f
knowing the difference between µs and µk
solving dynamics problems involving friction on horizontal surfaces and inclined planes
Students are capable of solving work problems, demonstrating they understand:
● the directional relationship between the force and the displacement, two vector quantities that give the scalar
quantity of work
● the dot product definition of work
> the magnitude equation of work involving the angle θ between F and d
> the i, j, k vector component equation of work when F and d are given in terms of i, j, k
● work is given in units of joules, (J = Nm)
Energy is defined for the students (unit is J, like work), as well as various equations for both kinetic
energy (KE) and potential energy (PE). Students, using these concepts and equations go on to solve
problems:
● calculating KE
● calculating PE
> gravitational PE, PEg
> elastic PE, PEel
● utilizing the work-KE theorem\
● applying the conservation of mechanical energy (ME), where ME = KE + PE
● utilizing the definition of power, P (in units of watts, W = J/sec) in displacement/time form and in velocity form
Momentum is defined for the students as another conserved quantity, and upon this basis the students
can solve problems:
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calculating momentum p = mv
involving p as the rate of change of force
utilizing the impulse-change in momentum equation
applying conservation of p in one direction
applying conservation of p in two direction (two-equation, two-unknowns system of equations)
A mass moving in a circle at constant speed is used as a model for the students to understand the
concept of centripetal acceleration and centripetal force, whose equations are used by the students to
solve:
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centripetal force problems
problems involving objects moving in “loops”
simple problems of circular orbits
the problem of how accurately the centripetal force equation predicts the measured motion of masses twirled
in horizontal circles
Movement in a circle or radius r at constant v is used to derive the basic concepts of circular or rotary
motion, which are direct analogies to linear motion. Students will generate a “table of analogies”
showing analogous concepts of both linear and rotary motion, saving the derivation of a new set of
formulas. Using this table, students will be able to:
● understand that moment of inertia, I, is analogous to mass (issued an “I” chart)
● call up all kinematical equations, dynamical equations, energy and work equations, and momentum equations
in rotary form
● solve all forms of rotary motion problems
● understand why the results of the ramp lab were not good because the rotation of the ball was ignored
● adjust the results of the ramp lab using the proper rotary motion expression for a smaller percent difference
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The concepts of center of mass (center of gravity) and the expanded version of equilibrium to include
rotary as well as linear motion are combined for the students to solve:
● non-vectored torque problems
● total (forces & torque) equilibrium problems
● vectored torque problems where torque is introduced as a vector cross product calculated using the determinant
method and the vectors i, j, k
● conservation of angular momentum problems
● problems using angular momentum as a vector cross product
● the mystery of the “floating bicycle wheel”
● torque problems using predicted calculations and experimental measurements from weights hung from a meter
stick lever
Newton’s Universal Law of Gravitation is introduced to the students as a specific application of
Newton’s 2nd Law of Dynamics. Combining with Kepler’s Law of Planetary Motion, it is utilized by
students to calculate:
● forces between two masses
● gravitational field intensities
● verification that g at the surface of the earth is indeed 9.81 m/sec 2, as was originally given near the course’s
beginning
● Kepler’s constant
● periods of natural and artificial satellites
● orbital speeds of natural and artificial satellites
Students are given a review of the six simple machines and their formulas for mechanical advantage
(MA) and efficiency, so that students may calculate MA for the lever, wheel and axle, wedge, pulley,
screw, and inclined plane.
The Physics of Fluids or Fluid Dynamics is given to the students as three principles using the
definition of fluid density, ρ, each principle with its own set of equations. Applying the three
principles one at a time, students are able to solve problems:
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calculating buoyant force, using Archimedes’s Principle
measuring buoyant force using an Archimedes’s Principle laboratory kit
relating pressure with the depth of the fluid
calculating related values of pressure and area using Pascal’s Principle, the basis of hydraulics
calculating related values of pressure and fluid velocity, using Bernoulli’s Principle, the basis of aerodynamics
that use the Continuity Equation
suggested by using a Venturi Tube
Students are introduced to the new basic unit of measurement, temperature, T, with emphasis that it is
a statistical measurement associated with the average KE of molecules. Heat is introduced as another
form of energy in the unit J, though long-held other units are listed for conversion purposes. Students
demonstrate their ability to:
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convert from one temperature scale to any of the others
calculate heat contained in a mass using specific heats
calculate change of state problems using specific heats, latent heats of fusion, and latent heats of vaporization
measure the heat of fusion of ice using a calorimeter
solve thermal expansion problems using coefficients of linear expansion, 1α, coefficients of area expansion,
β = 2α, and coefficients of volume expansion, γ = 3α
● compare calculated and experimental results of heating small rods of various metals
Students can work problems applying the Laws of Thermodynamics, including problems that:
● calculate work done by an expanding gas
● employ the definitions of iso-volumetric, isothermal, and adiabatic processes
● apply the First Law of Thermodynamics (conservation of energy)
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explain how devices such as a heat engine and a refrigerator follow the First Law
calculate heat energy efficiency as well as the amount of entropy in a heat exchange
apply the Second Law of Thermodynamics
avoid misconceptions about the Second Law
introduce the statistical form of entropy in terms of molecular states
review the Ideal Gas Law as a combination of Charles’, Boyles’, and Gay-Lussac’s Laws
> work with 1 situation or 2 situations
> utilize with equal ease the chemists’ version (PV = NRT) and/or the physicists’ version (PV = nkT)
Simple Harmonic Motion (SHM) of a mass-on-spring and a simple pendulum is modeled
mathematically for the students as a repeating circular motion pattern, applying rotary motion and
trigonometric functions of time to the mechanics of SHM. (The variable T for temperature is now
considered TK – K for Kelvin scale – from now on so that is the period for SHM.) Students
demonstrate the ability to calculate:
Mass-on-spring
Pendulum of length L
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displacement as a periodic function of time x(t)
velocity as a periodic function of time v(t)
acceleration as periodic function of time a(t)
period T and frequency f as functions of m and k
KE as a function of mass m, T, t, & amplitude A
PE as a function of spring constant k, A, & t
displacement as a periodic function of time θ(t)
angular velocity as a periodic function of time ω(t)
angular acceleration as a periodic function of time α(t)
period T and frequency f as functions of L and g
KE as a function of m, L, t, and θ
PE as a function of m, L, t, and θ
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the spring constant of a spring as measured from of graph of Hooke’s Law data collected in the lab
how accurate predicted mass-on-spring periods are to periods measured in the lab
how accurate predicted periods of pendulums of various lengths are to periods measured in the lab
the verification of conservation of mechanical energy (KE + PE) for a mass-on-spring whose parameters
are measured in the lab
The properties of waves are reviewed by the students, for both mechanical waves (represented by
sound) and electromagnetic waves (represented by light). This combined approach enables the
students to:
● solve problems using the wave equation for sound (v = fλ) and for light (c = fλ)
● calculate the speed of sound for all temperatures
● measure the speed of sound using resonance tubes in the lab (using standing wave patterns) and compare with
value predicted by the temperature equation
● calculate f or λ for any part of the electromagnetic spectrum (especially radio and signals, as well as color)
● demonstrate the properties of mirrors using the Law of Reflection and a laser in the lab
● solve applications of the Law of Refraction using Snell’s Law of Refraction and the concept of indices of
refraction
● apply Snell’s Law to light entering and exiting glass prisms in the lab with the help of a laser
● demonstrate diffraction and interference of light by using the slits of their fingers
● measure interference patterns using lab-safe microwave generators in the lab
● solve problems using the concept of total internal reflection to find critical angles of light transmitting media
● measure in the lab parameters of reflection, refraction, diffraction, and interference using a ripple tank
The principles necessary to introduce the Doppler Effect for sound and light waves are introduced to
the students, so that they will be able to:
● solve problems utilizing the General Doppler Effect for all values of the speed of the detector (v D) and the
speed of the source of sound (vs)
● solve problems of the Doppler Effect for light
> switch to equations altering λ instead of f
> recognize the difference between and solve both “redshift” and “blueshift” problems
● apply Doppler and superposition to understand shock waves
> describe the phenomena of aircraft breaking the “sound barrier”
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> describe the phenomena of sub-atomic particles breaking the “light barrier” within media with indices of
refraction > 1
> describe Cerenkov radiation
Using the definition of sound and light intensity, students will solve problems calculating:
● the decibel level of sound intensity in units of dB
● light intensity in Watts/square meter, or W/m2