North Allegheny Science Department

North Allegheny School District

Science Curriculum
March 2003

Course Title: AP Physics C

Course Number: 4092

Grade: 11/12

Course Description: This course is designed to meet the objectives of the AP Physics C syllabus as published by the College Board. Students will be prepared to take both the Mechanics and Electricity/Magnetism AP Physics C exams. Mechanics is that part of physics dealing with motion and energy and studying the way objects behave when acted on by forces. The electricity and magnetism section of the course starts with electrostatics and the use of Gauss’s Law to determine electric fields, moves through electrodynamics and finishes with a complete description of electromagnetic induction (including LRC circuits). Completing both sections of the course can be quite demanding. Fewer topics are covered than in AP Physics B, but topics are treated in greater depth. Mathematics, including calculus, is used to model relationships among physical quantities and to solve problems. Since physics is approached in a limited scope, it is highly recommended, although not required, that students successfully complete another physics course before taking this one, with AP Physics B as the recommended prerequisite. This course will provide an outstanding preparation base for rigorous college science majors such as engineering, computer science, astrophysics, and pure sciences such as physics or chemistry.

I. K-12 Science Standards:

1. Scientific Investigation: Students will understand and use the processes of
scientific investigation including the elements of scientific inquiry and
technological design processes to solve problems.

2. Biological Science: Students will understand the processes and interactions of
organisms, and know the characteristics, structures, and functions of biological
systems. '

3. Physical Science: Students will know, understand, and apply relationships
between properties of matter and energy while identifying the various forms of
each.

4. Earth and Space: Students will know and understand the features, processes and
interactions of Earth's systems and the Earth's relationship to other objects in
space.

5. Science and Technology: Students will know and understand interrelationships
between scientific technology and society.

6. Environment and Ecology: Students will understand how human interactions
impact the sustainability of the natural and human-made environment and the
resources they provide.

II. Unit One: Kinematics

A. Benchmarks and Instructional Objectives

1. All students will understand the general relationships among position,
velocity, and acceleration for the motion of a particle along a straight
line, so that:

(a) Given a graph of one of the kinematic quantities, position, velocity, or acceleration, as a function of time, they can recognize in what
time intervals the other two are positive, negative, or zero, and can
identify or sketch a graph of each as a function of time.

(b) Given an expression for one of the kinematic quantities, position,
velocity, or acceleration, as a function of time, they can determine
the other two as a function of time, and find when these quantities
are zero or achieve their maximum and minimum values.

2. All students will understand the special case of motion with constant
acceleration so that they can:

(a) Write down expressions for velocity and position as functions of time, and identify or sketch graphs of these quantities.

(b) Use the equations v = v_o + at, x = x_o + vt + at²,and v² –v_o² = 2a(x-x_o) to solve problems involving one-dimensional motion with constant acceleration

3. All students will know how to deal with situations in which acceleration
is a specified function of velocity and time so they can write an
appropriate differential equation dv/dt =f(v)g(t) and solve it for v(t),
incorporating correctly a given initial value of v.

4. All students will know how to deal with displacement and velocity vectors so they can:

(a) Relate velocity, displacement, and time for motion with constant
velocity.

(b) Calculate the component of a vector along a specified axis, or
resolve a vector into components along two specified mutually
perpendicular axes.

(c) Add vectors in order to find the net displacement of a particle that
undergoes successive straight-line displacements.

(d) Subtract displacement vectors in order to find the location of one
particle relative to another, or calculate the average velocity of a
particle.

(e) Add or subtract velocity vectors in order to calculate the velocity
change or average acceleration of a particle, or the velocity of one
particle relative to another.

5. All students will understand the general motion of a particle in two
dimensions so that, given functions x(t) and y(t) which describe this
motion, they can determine the components, magnitude, and direction of
the particle's velocity and acceleration as functions of time.

6. All students will understand the motion of projectiles in a uniform
gravitational field so they can:

(a) Write down expressions for the horizontal and vertical components
of velocity and position as functions of time, and sketch or identify
graphs of these components.

(b) Use these expressions in analyzing the motion of a projectile that is
projected above level ground with a specified initial velocity.

7. All students will understand the uniform circular motion of a particle so
they can:

(a) Relate the radius of the circle and the speed or rate of revolution of
the particle to the magnitude of the centripetal acceleration.

(b) Describe the direction of the particle's velocity and acceleration at
any instant during the motion.

(c) Determine the components of the velocity and acceleration vectors
at any instant, and sketch or identify graphs of these quantities.

B. Content

1. Motion in one dimension

2. Motion in two dimensions

C. Suggested Activities

1. Use the PASCO cart/track systems to investigate kinematics relationships

2. Use the computerized motion sensor to develop motion graphs

3. Use the PASCO projectile launchers to investigate parabolic motion

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Two: Newton's Laws of Motion

A. Benchmarks and Instructional Objectives

1. All students will be able to analyze situations in which a particle remains at
rest, or moves with constant velocity, under the influence of several forces.

2. All students will understand the relation between the force that acts on a body and the resulting change in the body's velocity so they can:

(a) Calculate, for a body moving in one direction, the velocity change
that results when a constant force F acts over a specified time
interval.

(b) Calculate, For a body moving in one dimension, the velocity change that results when a force F(t) acts over a specified time interval.

(c) Determine, for a body moving in a plane whose velocity vector
undergoes a specified change over a specified time interval, the
average force that acted on the body.

3. All students will understand how Newton's Second Law, F = ma,
applies to a body subject to forces such as gravity, the pull of strings, or contact forces, so they can:

(a) Draw a well-labeled diagram showing all real forces that act on the
body.

(b) Write down the vector equation that results from applying Newton's
Second Law to the body, and take components of this equation along
appropriate axes.

4. All students will be able to analyze situations in which a body moves
with specified acceleration under the influence of one or more forces so they can determine the magnitude and direction of the net force, or of one of the forces that makes up the net force, in situations such as the following:

(a) Motion up or down with constant acceleration (in an elevator, for
example).

(b) Motion in a horizontal circle (e.g., mass on a rotating merry-go-
round, or car rounding a banked curve).

(c) Motion in a vertical circle (e.g., mass swinging on the end of a
string, cart rolling down a curved track, rider on a Ferris wheel).

5. All students will understand the significance of the coefficient of friction so they can:

(a) Write down the relationship between the normal and frictional forces
on a surface.

(b) Analyze situations in which a body slides down a rough inclined
plane or is pulled or pushed across a rough surface.

(c) Analyze static situations involving friction to determine under what
circumstances a body will start to slip, or to calculate the magnitude
of the force of static friction.

6. All students will understand the effect of fluid friction on the motion of a body so they can:

(a) Find the terminal velocity of a body moving vertically through a
fluid that exerts a retarding force proportional to velocity.

(b) Describe qualitatively, with the aid of graphs, the acceleration,

velocity, and displacement of such a particle when it is released from
rest or is projected vertically with specified initial velocity.

7. All students will understand Newton's Third Law so that, for a given
force, they can identify the body on which the reaction force acts and
state the magnitude and direction of this reaction.

8. All students will be able to apply Newton's Third Law in analyzing the
force of contact between two bodies that accelerate together along a
horizontal or vertical line, or between two surfaces that slide across one
another.

9. All students will know that the tension is constant in a light string that
passes over a massless pulley and should be able to use this fact in
analyzing the motion of a system of two bodies joined by a string.

10. All students will be able to solve problems in which application of
Newton's Laws leads to two or three simultaneous linear equations
involving unknown forces or accelerations.

B. Content

1. Static Equilibrium (First Law)

2. Dynamics of a Single Body (Second Law)

3. Systems of Two or More Bodies (Third Law)

C. Suggested Activities

1. Use the PASCO cart/track systems to investigate force relationships.

2. Use the centripetal force apparatus to investigate circular motion.

3. Use the Pasco timing kits to investigate fluid friction for an object falling in fluid.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Three: Work, Energy and Power

A. Benchmarks and Instructional Objectives

1. All students will understand the definition of work so they can:

(a) Calculate the work done by a specified constant force on a body that
undergoes a specified displacement.

(b) Relate the work done by a force to the area under a graph of force as
a function of position, and calculate this work in the case where the
force is a linear function of position.

(c) Use integration to calculate the work performed by a force F(x) on
a body that undergoes a specified displacement in one dimension.

(d) Use the scalar product operation to calculate the work performed by
a specified constant force F on a body that undergoes a
displacement in a plane.

2. All students will understand the work-energy theorem so they can:

(a) State the theorem precisely, and prove it for the case of motion in
one dimension.

(b) Calculate the change in kinetic energy or speed that results from
performing a specified amount of work on a body.

(c) Calculate the work performed by the net force, or by each of the
forces that makes up the net force, on a body that undergoes a
specified change in speed or kinetic energy.

(d) Apply the theorem to determine the change in a body's kinetic
energy and speed that result from the application of specified
forces, or to determine the force that is required in order to bring a
body to rest in a specified distance.

3. All students will understand the concept of a conservative force so they
can:

(a) State two alternative definitions of "conservative force," and explain
why these definitions are equivalent.

(b) Describe two examples each of conservative forces and
nonconservative forces.

4. All students will understand the concept of potential energy so they can:

(a) State the general relation between force and potential energy, and
explain why potential energy can be associated only with
conservative forces.

(b) Calculate a potential energy function associated with a specified one-
dimensional force F(x).

(c) Given the potential energy function U(x} for a one-dimensional
force, calculate the magnitude and direction of the force.

(d) Write an expression for the force exerted by an ideal spring and for
the potential energy stored in a stretched or compressed spring.

(e) Calculate the potential energy of a single body in a uniform
gravitational field.

(f) Calculate the potential energy of a system of bodies in a uniform
gravitational field.

(g) State the generalized work-energy theorem and use it to relate the
work done by nonconservative forces on a body to the changes in
kinetic and potential energy of the body.

5. All students will understand the concepts of mechanical energy and of
total energy so they can:

(a) State, prove, and apply the relation between the work performed on
a body by nonconservative forces and the change in a body's
mechanical energy.

(b) Describe and identify situations in which mechanical energy is
converted to other forms of energy.

(c) Analyze situations in which a body's mechanical energy is changed
by friction or by a specified externally applied force.

6. All students will understand conservation of energy so they can:

(a) Identify situations in which mechanical energy is or is not conserved.

(b) Apply conservation of energy in analyzing the motion of bodies that
are moving in a gravitational field and are subject to constraints
imposed by strings or surfaces.

(d) Apply conservation of energy in analyzing the motion of bodies that
move under the influence of other specified one-dimensional forces.

7. All students will be able to recognize and solve problems that call for
application both of conservation of energy and Newton's Laws.

8. All students will understand the definition of power so they can:

(a) Calculate the power required to maintain the motion of a body with
constant acceleration (e.g., to move a body along a level surface, to
raise a body at a constant rate, or to overcome friction for a body
that is moving at a constant speed).

(b) Calculate the work performed by a force that supplies constant
power, or the average power supplied by a force that performs a
specified amount of work.

(c) Prove that the relation P = F • v follows from the definition of
work, and apply this relation in analyzing particle motion.

B. Content

1. Work and the Work-Energy Theorem

2. Conservative Forces and Potential Energy

3. Conservation of Energy

4. Power

C. Suggested Activities

1. Use the PASCO cart/track systems to investigate energy relationships.

2. Use a pendulum to establish relationship between kinetic and potential energy.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Four: Systems of Particles and Linear Momentum

A. Benchmarks and Instructional Objectives

1. All students will understand the technique for finding center of mass so
they can:

(a) Identify by inspection the center of mass of a body that has a point
of symmetry.

(b) Locate the center of mass of a system consisting of two such bodies.

(c) Use integration to find the center of mass of a thin rod of nonuniform density, of a plane lamina of uniform density, or of a solid of revolution of uniform density.

2. All students will be able to state, prove, and apply the relation between center-of-mass velocity and linear momentum, and between center-of-mass acceleration and net external force for a system of particles.

3. All students will be able to define center of gravity and to use this concept to express the gravitational potential energy of a rigid body in terms of the position of its center of mass.

4. All students will understand impulse and linear momentum so they can:

(a) Relate mass, velocity, and linear momentum for a moving body, and calculate the total linear momentum of a system of bodies.

(b) Relate impulse to the change in linear momentum and the average force acting on a body.

c) State and apply the relations between linear momentum and center-of-mass motion for a system of particles.

(d) Define impulse, and prove and apply the relation between impulse and momentum.

5. All students will understand linear momentum conservation so they can:

(a) Explain how linear momentum conservation follows as a
consequence of Newton's Third Law for an isolated system.

(b) Identify situations in which linear momentum, or a component of the
linear momentum vector, is conserved.

(c) Apply linear momentum conservation to determine the final velocity
when two bodies that are moving along the same line, or at right
angles, collide and stick together, and calculate how much kinetic
energy is lost in such a situation.

(d) Analyze collisions of particles in one or two dimensions to
determine unknown masses or velocities, and calculate how
kinetic energy is lost in a collision.

(e) Analyze situations in which two bodies are pushed apart by a spring or other agency, and calculate how much energy is released in such a process.

6. All students will understand frames of reference so they can:

(a) Analyze the uniform motion of a particle relative to a moving medium such as a flowing stream.

(b) Transform the description of a collision or decay process to or from a frame of reference in which the center of mass of the system is at rest.

(c) Analyze the motion of particles relative to a frame of reference that is accelerating horizontally or vertically at a uniform rate.

B. Content

1. Center of Mass

2. Impulse and Momentum

3. Conservation of Linear Momentum

4. Collisions

C. Suggested Activities

1. Use air tracks to study conservation of momentum and energy during collisions.

2. Use marble tracks to study the conservation of momentum during collisions.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Five: Rotation

A. Benchmarks and Instructional Objectives

1. All students will understand the concept of torque so they can:

(a) Calculate the magnitude and sense of the torque associated with a given force.

(b) Calculate the torque on a rigid body due to gravity.

2. All students will be able to analyze problems in statics so they can:

(a) State the conditions for translational and rotational equilibrium of a rigid body.

(b) Apply these conditions in analyzing the equilibrium of a rigid body under the combined influence of a number of coplanar forces applied at different locations.

3. All students will understand the analogy between translational and rotational kinematics so they can write and apply relations among the angular acceleration, angular velocity, and angular displacement of a body that rotates about a fixed axis with constant angular acceleration.

4. All students will be able to use the right-hand rule to associate an angular velocity vector with a rotating body.

5. All students will develop a qualitative understanding of rotational inertia so they can:

(a) Determine by inspection which of a set of symmetric bodies of equal mass has the greatest rotational inertia.

(b) Determine by what factor a body's rotational inertia changes if all its dimensions are increased by the same factor.

6. All students will develop skill in computing rotational inertia so they can find the rotational inertia of:

(a) A collection of point masses lying in a plane about an axis perpendicular to the plane.

(b) A thin rod of uniform density, about an arbitrary axis perpendicular to the rod.

(d) A solid sphere of uniform density about an axis through its center.

7. All students will be able to state and apply the parallel-axis theorem.

8. All students will understand the dynamics of fixed-axis rotation so they can:

(a) Describe in detail the analogy between fixed-axis rotation and straight-line translation.

(b) Determine the angular acceleration with which a rigid body is accelerated about a fixed axis when subjected to a specified external torque or force.

(d) Analyze problems involving strings and massive pulleys.

9. All students will understand the motion of a rigid body along a surface so they can:

(a) Write down, justify, and apply the relation between linear and angular velocity, or between linear and angular acceleration, for a body of circular cross-section that rolls without slipping along a fixed plane, and determine the velocity and acceleration of an arbitrary point on such a body.

(b) Apply the equations of translational and rotational motion simultaneously in analyzing rolling with slipping.

(c) Calculate the total kinetic energy of a body that is undergoing both translational and rotational motion, and apply energy conservation in analyzing such motion.

10. All students will be able to use the vector product and the right-hand rule so they can:

(a) Calculate the torque of a specified force about an arbitrary origin.

(b) Calculate the angular momentum vector for a moving particle.

(c) Calculate the angular momentum vector for a rotating rigid body in simple cases where this vector lies parallel to the angular velocity vector.

11. All students will understand angular momentum conservation so they can:

(a) Recognize the conditions under which the law of conservation is applicable and relate this law to one- and two-particle systems such as satellite orbits or the Bohr atom.

(b) State the relation between net external torque and angular

momentum, and identify situations in which angular momentum is conserved.

(d) Analyze a collision between a moving particle and a rigid body that can rotate about a fixed axis or about its center of mass.

B. Content

1. Torque and Rotational Statics

2. Rotational Kinematics

3. Rotational Inertia

4. Rotational Dynamics

5. Angular Momentum and Its Conservation

C. Suggested Activities

1. Use steel and aluminum rods to investigate torque for various pivot locations

2. Use Pasco rotational motion apparatus with computer interface to study rotational inertia for various mass distributions.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Six: Oscillations

A. Benchmarks and Instructional Objectives

1. All students will understand the kinematics of simple harmonic motion so
they can:

(a) Sketch or identify a graph of displacement as a function of time, and
determine from such a graph the amplitude, period, and frequency of the
motion.

(b) Write down an appropriate expression for displacement of the form
A sin wt or A cos wt to describe the motion.

(d) Find an expression for velocity as a function of time.
(e) State qualitatively the relation between acceleration and displacement.

(f) Identify points in the motion where the acceleration is zero or achieves
its greatest positive or negative value.

(g) State and prove the relation between acceleration and displacement.
(h) State and apply the relation between frequency and period.

(i) Recognize that a system that obeys a differential equation of the form
d²x/dt² = -kx must execute simple harmonic motion, and determine the
frequency and period of such motion.

(j) State how the total energy of an oscillating system depends on the

amplitude of the motion, sketch or identify a graph of kinetic or potential
energy as a function of time, and identify points in the motion where this
energy is all potential or all kinetic.

(k) Calculate the kinetic and potential energies of an oscillating system as

functions of time, sketch or identify graphs of these functions, and prove
that the sum of kinetic and potential energy is constant.

(1) Calculate the maximum displacement or velocity of a particle that moves in simple harmonic motion with specified initial position and velocity.

(m) Develop a qualitative understanding of resonance so they can identify
situations in which a system will resonate in response to a sinusoidal
external force.

2. All students will be able to apply their knowledge of simple harmonic motion to the case of a mass on a spring, so they can:

(a) Derive the expression for the period of oscillation of a mass on a spring.
(b) Apply the expression for the period of oscillation of a mass on a spring.

(d) Analyze problems in which a mass attached to a spring oscillates horizontally.

(e) Determine the period of oscillation for systems involving series or parallel combinations of identical springs, or springs of differing lengths.

3. All students will be able to apply their knowledge of simple harmonic motion to the case of a pendulum, so they can:

(a) Derive the expression for the period of a simple pendulum.

(b) Apply the expression for the period of a simple pendulum.

(d) Analyze the motion of a torsional pendulum or physical pendulum in
order to determine the period of small oscillations

B. Content

1. Simple harmonic motion

2. The study of pendula

C. Suggested Activities

1. Use the PASCO cart/track systems with springs to investigate SHM relationships.

2. Use various types of mass distributions to distinguish between types of pendula.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit Seven: Gravitation

A. Benchmarks and Instructional Objectives

1. All students will know Newton's Law of Universal Gravitation so they can:

(a) Determine the force that one spherically symmetrical mass exerts on
another.

(b) Determine the strength of the gravitational field at a specified point
outside a spherically symmetrical mass.

(c) Describe the gravitational force inside and outside a uniform sphere, and
calculate how the field at the surface depends on the radius and density
of the sphere.

2. All students will understand the motion of a body in orbit under the
influence of gravitational forces so they can:

(a) For a circular orbit:

(i) Recognize that the motion does not depend on the body's mass,
describe qualitatively how the velocity, period of revolution, and
centripetal acceleration depend upon the radius of the orbit, and
derive expressions for the velocity and period of revolution in such
an orbit.

(ii) Prove that Kepler's Third Law must hold for this special case.

(iii) Derive and apply the relations among kinetic energy, potential
energy, and total energy for such an orbit.

(b) For a general orbit:

(i) State Kepler's three laws of planetary motion and use them to

describe in qualitative terms the motion of a body in an elliptic orbit.

(ii) Apply conservation of angular momentum to determine the velocity
and radial distance at any point in the orbit.

(iii) Apply angular momentum conservation and energy conservation to relate the speeds of a body at the two extremes of an elliptic orbit.

(iv) Apply energy conservation in analyzing the motion of a body that is projected straight up from a planet's surface or that is projected directly toward the planet from far above the surface.

B. Content

1. Newton’s law of universal gravitation

2. Kepler’s laws of planetary motion

3. Orbits

C. Suggested Activities

1. Have students use planetary data to determine the eccentricity of an orbit.

D. Time

2 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 8: Electrostatics and Gauss’s Law

A. Benchmarks and Instructional Objectives

1. All students will understand the concept of electric field so they can:

(a) Define it in terms of the force on a test charge.

(b) Calculate the magnitude and direction of the force on a positive or
negative charge placed in a specified field.

(d) Given a diagram on which an electric field is represented by flux
lines, determine the direction of the field at a given point, identify
locations where the field is strong and where it is weak, and identify
where positive or negative charges must be present.

(e) Analyze the motion of a particle of specified charge and mass in a
uniform electric field.

2. All students will understand the concept of electric potential so they can:

(a) Calculate the electrical work done on a positive or negative charge
that moves through a specified potential difference.

(b) Given a sketch of equipotentials for a charge configuration,

determine the direction and approximate magnitude of the electric
field at various positions.

(c) Apply conservation of energy to determine the speed of a charged
particle that has been accelerated through a specified potential
difference.

(d) Calculate the potential difference between two points in a uniform
electric field, and state which is at the higher potential.

(e) Given electric field strength as a function of position along a line,
use integration to determine electric potential as a function of
position.

(f) State the general relationship between field and potential, and define
and apply the concept of a conservative electric field.

3. All students will understand Coulomb's Law and the principle of
superposition so they can:

(a) Determine the force that acts between specified point charges, and
describe the electric field of a single point charge.

(b) Use vector addition to determine the electric field produced by two
or more point charges.

4. All students will know the potential function for a point charge so they can:

(a) Determine the electric potential in the vicinity of one or more point
charges.

(b) Calculate how much work is required to move a test charge from one
location to another in the field of fixed point charges.

(c) Calculate the electrostatic potential energy of a system of two or
more point charges, and calculate how much work is required to
move a set of charges into a new configuration.

5. All students will be able to use the principle of superposition to calculate
by integration:

(a) The electric field of a straight, uniformly charged wire.

(b) The electric field and potential of a thin ring of charge on the axis of
the ring, or of a semicircle of charge at its center.

6. All students will know the fields of highly symmetric charge distributions
so they can:

(a) Identify situations in which the direction of the electric field

produced by a charge distribution can be deduced from symmetry
considerations.

(b) Describe the electric field of:

(i) Parallel charged plates.

(ii) A long uniformly charged wire or thin cylindrical shell.

(iii) A thin spherical shell.

(d) Derive expressions for electric potential as a function of position in
the above cases.

7. All students will understand the relationship between field and flux

so they can:

(a) Calculate the flux of a uniform electric field E through an arbitrary
surface.

(b) Calculate the flux of E through a curved surface when E is uniform
in magnitude and perpendicular to the surface.

(c) Calculate the flux of E through a rectangle when E is perpendicular
to the rectangle and a function of one coordinate only.

(d) State and apply the relationship between flux and lines of force.

8. All students will understand Gauss's Law so they can:

(a) State the law in integral form, and apply it qualitatively to relate flux
and electric charge for a specified surface.

(b) Apply the law, along with symmetry arguments, to determine the
electric field near a large uniformly charged plane, inside or outside
a uniformly charged long cylinder or cylindrical shell, and inside or
outside a uniformly charged sphere or spherical shell.

(c) Apply the law to determine the charge density or total charge on a
surface in terms of the electric field near the surface.

(d) Graph the electric field and potential function by the calculus
method of finding maxima and minima.

B. Content

1. Charge, field and potential

2. Coulomb’s law

3. Fields, potentials and charge distributions

4. Gauss’s law

C. Suggested Activities

1. Use various electrostatic demonstration tools such as the Van de Graff generator, the electrophorus device and Jacob’s ladder to show the fundamentals of electrostatics.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 9: Capacitors

A. Benchmarks and Instructional Objectives

1. All students will understand the nature of electric fields in and around
conductors so they can:

(a) Explain the mechanics responsible for the absence of electric field
inside a conductor, and why all excess charge must reside on the
surface of the conductor.

(b) Explain why a conductor must be an equipotential, and apply this
principle in analyzing what happens when conductors are joined by
wires.

(d) Prove that all excess charge on a conductor must reside on its
surface and that the field outside the conductor must be
perpendicular to the surface.

(e) Prove and apply the relationship between the surface charge density
on a conductor and the electric field strength near its surface.

2. All students will be able to describe and sketch a graph of the electric
field and potential inside and outside a charged conducting sphere.

3. All students will understand induced charge and electrostatic shielding so
they can:

(a) Describe qualitatively the process of charging by induction.

(b) Determine the direction of the force on a charged particle brought
near an uncharged or grounded conductor.

(c) Explain qualitatively why there can be no electric field in a charge-
free region completely surrounded by a single conductor, and
recognize consequences of this result.

(d) Explain qualitatively why the electric field outside a closed

conducting surface cannot depend on the precise location of charge
in the space enclosed by the conductor, and identify consequences of
this result.

4. All students will know the definition of capacitance so they can relate
stored charge and voltage for a capacitor.

5. All students will understand energy storage in capacitors so they can:

(a) Relate voltage, charge, and stored energy for a capacitor.

(b) Recognize situations in which energy stored in a capacitor is
converted to other forms.

6. All students will understand the physics of the parallel-plate capacitor so
they can:

(a) Describe the electric field inside the capacitor, and relate the strength
of this field to the potential difference between the plates and the
plate separation.

(b) Relate the electric field to the density of the charge on the plates.

(d) Determine how changes in dimension will affect the value of the
capacitance.

(e) Describe how the insertion of a dielectric between the plates of a
charged parallel-plate capacitor affects its capacitance and the field
strength and voltage between the plates.

(f) Analyze situations in which a conducting or dielectric slab is
inserted between the plates of a capacitor.

(g) Derive and apply expressions for the energy stored in a parallel-plate
capacitor and for the energy density in the field between the plates.

(h) Analyze situations in which capacitor plates are moved apart or
moved closer together, or in which a conducting slab is inserted
between capacitor plates, either with a battery connected between
the plates or with the charge on the plates held fixed.

7. All students will understand cylindrical and spherical capacitors so they can:

(a) Describe the electric field inside each.

(b) Derive an expression for the capacitance of each.

B. Content

1. Equipotential

2. Capacitors

3. Dielectrics

C. Suggested Activities

1. Demonstrate the use of various capacitors such as the parallel plate capacitor.

2. Have students charge and discharge capacitors on a circuit board.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 10: Current and Resistance

A. Benchmarks and Instructional Objectives

1. All students will understand the definition of electric current so they can
relate the magnitude and direction of the current in a wire or ionized
medium to the rate of flow of positive and negative charge.

2. All students will understand conductivity, resistivity, and resistance so
they can:

(a) Relate current and voltage for a resistor.

(b) Write the relationship between electric field strength and current
density in a conductor, and describe qualitatively, in terms of the
drift velocity of electrons, why such a relationship is plausible.

(d) Derive an expression for the resistance of a resistor of uniform
cross-section in terms of its dimensions and the conductivity of the
material from which it is constructed, and apply this result in
comparing current flow in resistors of different material or different
geometry.

(e) Derive expressions that relate the current, voltage, and resistance to
the rate at which heat is produced when current passes through a
resistor.

(f) Apply the relationships for the rate of heat production in a resistor.

3. All students will understand the behavior of series and parallel
combinations of resistors so they can:

(a) Identify on a circuit diagram resistors that are in series or in parallel.

(b) Determine the ratio of the voltages across resistors connected in
series or the ratio of the currents through resistors connected in
parallel.

connected in series or in parallel, or of a network of resistors that
can be broken down into series and parallel combinations.

(d) Calculate the voltage, current, and power dissipation for any resistor
in such a network of resistors connected to a single battery.

(e) Design a simple series-parallel circuit that produces a given current
and terminal voltage for one specified component, and draw a
diagram for the circuit using conventional symbols.

4. All students will understand the properties of ideal and real batteries so
they can:

(a) Calculate the terminal voltage of a battery of specified emf and
internal resistance from which a known current is flowing.

(b) Calculate the rate at which a battery is supplying energy to a circuit
or is being charged up by a circuit.

(c) State what external resistance draws maximum power from a battery
of specified internal resistance, and apply this result in solving
problems involving one or more resistors connected to a single
battery.

5. All students will be able to apply Ohm's Law and Kirchhoff's rules to
direct-current circuits in order to:

(a) Determine a single unknown current, voltage, or resistance.

(b) Set up and solve simultaneous equations to determine two unknown
currents.

6. All students will understand the properties of voltmeters and ammeters so
they can: |

(a) State whether the resistance of each is high or low.

(b) Identify or show correct methods of connecting meters into circuits
in order to measure voltage or current.

7. All students will understand the behavior of capacitors connected in
series or in parallel so they can:

(a) Calculate the equivalent capacitance of a series or parallel
combination.

(b) Describe how stored charge is divided between two capacitors
connected in parallel.

8. All students will understand energy storage in capacitors so they can:

(a) Relate voltage, charge, and stored energy for a capacitor.

(b) Recognize situations in which energy stored in a capacitor is
converted to other forms.

9. All students will be able to calculate the voltage or stored charge, under
steady-state conditions, for a capacitor connected to a circuit consisting
of a battery and resistors.

10. All students will understand the discharging or charging of a capacitor
through a resistor so they can:

(a) Calculate and interpret the time constant of the circuit.

(b) Sketch or identify graphs of stored charge or voltage for the

capacitor, or of current or voltage for the resistor, and indicate on the
graph the significance of the time constant.

(c) Write expressions to describe the time dependence of the stored
charge or voltage for the capacitor, or of the current or voltage for
the resistor.

11. All students will develop skill in analyzing the behavior of circuits
containing several capacitors and resistors so they can:

(a) Determine voltages and currents immediately after a switch has been
closed and also after steady-state conditions have been established.

(b) Identify graphs that correctly indicate how voltages and currents
vary with time.

B. Content

1. Current

2. Resistance

3. Power

4. Kirchoff’s Rules for DC circuit analysis

5. RC circuit analysis

C. Suggested Activities

1. Have students build and analyze basic circuits with resistors, batteries, and capacitors using circuit boards.

2. Use the “Multisim” computer application to conduct virtual circuit analysis.

D. Time

3 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 11: Magnetostatics

A. Benchmarks and Instructional Objectives

1. All students will understand the force experienced by a charged particle

in a magnetic field so they can:

(a) Calculate the magnitude and direction of the force in terms of
q, v, and, B, and explain why the magnetic force can perform
no work.

(b) Deduce the direction of a magnetic field from information about the
forces experienced by charged particles moving through that field.

(c) State and apply the formula for the radius of the circular path of a
charge that moves perpendicular to a uniform magnetic field, and
derive this formula from Newton's Second Law and the magnetic
force law.

(d) Describe the most general path possible for a charged particle
moving in a uniform magnetic field, and describe the motion of a
particle that enters a uniform magnetic field moving with specified
initial velocity.

(e) Describe quantitatively under what conditions particles will move
with constant velocity through crossed electric and magnetic fields.

2. All students will understand the force experienced by a current in a
magnetic field so they can:

(a) Calculate the magnitude and direction of the force on a straight
segment of current-carrying wire in a uniform magnetic field.

(b) Indicate the direction of magnetic forces on a current-carrying loop
of wire in a magnetic field, and determine how the loop will tend to
rotate as a consequence of these forces.

(c) Calculate the magnitude and direction of the torque experienced by a
rectangular loop of wire carrying a current in a magnetic field.

3. All students will understand the magnetic field produced by a long
straight current-carrying wire so they can:

(a) Calculate the magnitude and direction of the field at a point in the
vicinity of such a wire.

(b) Use superposition to determine the magnetic field produced by two
long wires.

4. All students will understand the Biot-Savart Law so they can:

(a) Deduce the magnitude and direction of the contribution to the magnetic
field made by a short straight segment of current-carrying wire.

(b) Derive and apply the expression for the magnitude of B on the axis
of a circular loop of current.

5. All students will understand the statement and application of Ampere's
Law in integral form so they can:

(a) State the law precisely.

(b) Use Ampere's law, plus symmetry arguments and the right-hand
rule, to relate magnetic field strength to current for a long straight
wire, or for a hollow or solid cylinder.

6. All students will develop skill in applying the superposition principle so
they can determine the magnetic field produced by combinations of the
configurations listed above.

B. Content

1. Forces on moving charges in B-fields

2. Forces on current carrying wires in B-fields

3. B-fields around current carrying wires

4. Biot-Savart law

5. Ampere’s law

C. Suggested Activities

1. Use strong magnets to demonstrate the basic rules of magnetism.

2. Use devices such as air-core solenoids to show magnetic effects of a curren-carrying conductor.

D. Time

2 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 12: Electromagnetic Induction

A. Benchmarks and Instructional Objectives

1. All students will understand the concept of magnetic flux so they can:

(a) Calculate the flux of a uniform magnetic field through a loop of
arbitrary orientation.

(b) Use integration to calculate the flux of a nonuniform magnetic field,
whose magnitude is a function of one coordinate, through a
rectangular loop perpendicular to the field.

2. All students will understand Faraday's Law and Lenz's Law so they can:

(a) Recognize situations in which changing flux through a loop will
cause an induced emf or current in the loop.

(b) Calculate the magnitude and direction of the induced emf and
current in:

(i) A square loop of wire pulled at a constant velocity into or out of
a uniform magnetic field.

(ii) General cases of a loop of wire that is being pulled into or out of a uniform magnetic field.

(iii) A loop of wire placed in a spatially uniform magnetic field
whose magnitude is changing at a constant rate,

(iv) A loop of wire placed in a spatially uniform magnetic field
whose magnitude is a specified function of time.

(v) A loop of wire that rotates at a constant rate about an axis
perpendicular to a uniform magnetic field.

(vi) A conducting bar moving perpendicular to a uniform magnetic
field.

3. All students will develop skill in analyzing the forces that act on induced
currents so they can solve simple problems involving the mechanical
consequences of electromagnetic induction.

4. All students will understand the concept of inductance so they can:

(a) Calculate the magnitude and sense of the emf in an inductor through
which a specified changing current is flowing.

(b) Derive and apply the expression for the self-inductance of a long
solenoid.

5. All students will develop skill in analyzing circuits containing inductors
and resistors so they can write and solve the differential equation that
relates current to time.

6. All students will be familiar with Maxwell's equations so they can associate
each equation with its implications.

B. Content

1. Electromagnetic induction

2. Inductance

3. Maxwell’s equations

C. Suggested Activities

1. Use the Lenz’s law apparatus and the Thompson apparatus to discuss the concept of magnetic flux.

2. Use the “Multisim” computer application to conduct virtual analysis of LRC circuits.

D. Time

2 weeks

E. Methods of Assessment

1. Quiz

2. Test

3. Internet Assignments

4. Lab Reports

Unit 13: AP Test Review

A. Benchmarks and Instructional Objectives

1. All students will participate in activities which will help focus their studies toward excelling on the AP Physics C examinations.

B. Content

1. Effective study habits

C. Suggested Activities

1. Overview of the year

2. Practice AP tests

D. Time

2 weeks

E. Methods of Assessment

1. Final comprehensive test

2. Internet Assignments