Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Computational Physics



What follows is an 'in-house' description of a third semester course we
teach here. The prerequisites are a 2-semester, 'algebra' physics course=

and calculus. The overall intent is to 'spiral' the curriculum up a notc=
h
by looking at a number of topics drawn from the general course that requi=
re
more advanced math techniques. The 'lab', homework, and special project
descriptions might provide some ideas for a computational physics course.=

This particular course meets 3 periods a week with a 2 hour 'lab'. For
Leigh's benefit, note that most of the labs involve some hands on
experimental activities along with the computational/computer components.=



Topics
1. Instantaneous quantities as derivatives
=

2. Integral and differential forms of the kinematics equations.
a) solve for x, v, and a given any one of these quantities.

3. Integral and differential forms of Newton's second law.
a) Variable force problems=97e.g. air resistance
b) Variable mass problems=97e.g. the rocket problem.

4. Work in its integral form. =

a) Calculating work from non constant forces=97e.g. gravitational PE=97W=
ORK

5. Gravitation
a) Spherically symmetric, inverse square force=97proving that uniformly
distributed mass can be taken to act as though concentrated at the COM.
b) Gravitational Field and Potential
c) Work various problems=97e.g. 'g' at bottom of a pit.

6. Harmonic motion.
a) Differential solutions to damped and forced harmonic motion.

7. Wave Motion
a) Trigonometric functional representation=97traveling waves, standing
waves, beats.

8. Thermo
a) Carnot Cycle=97show that efficiency =3D (Thot - Tcold)/Thot
b) Specific heats of gases=97degrees of freedom

9. E&M
a) Electric Force and Electric Field from continuous charge distribution=
s.
b) Gauss' Law
c) Electric potential=97differential and integral relationships to Field=

d) Capacitance=97effect of dielectrics. Differential equations of charg=
ing
and discharging.
e) Kirchoff's laws via matrix techniques.
f) Magnetic Fields=97force on charge, field from current, force between
currents, induction=97vector calculus.

LABS

1. Ballistic Motion=97full analysis of the Cenco Ballistic gun. A
theoretical equation is derived using the FULL geometry of the gun and
using the spring constant. The equation relates the initial position of
the ball relative to the floor, the angle, and the spring compression to
predict the range. Measurements are made to determine the spring constan=
t
(firing the ball vertically upwards), then the guns are fired to collect
range data. The analysis is done on an instructor prepared spreadsheet. =

Students develop their own graphical analysis.

2. Learning the spreadsheet. Students must design their own spreadsheet=

to analyze a ball dropped from a height equal to the radius of the earth.=
=

They must account for the change in the acceleration of gravity with
height.

3. Air resistance. This is a two week lab. In the first week a procedu=
re
is developed and data taken on a very light foam ball. Electronic timing=
s
are made over short distances, and the library is utilized to obtain hand=

timings of very large distances. The second week requires that a
spreadsheet be developed to analyze the data and to determine the
functional form of the air resistance force.

4. Damped harmonic motion. First students use an instructor prepared
spreadsheet where by adjusting Amplitude, frequency, wavelength, phase, a=
nd
damping factor they need to match an experimental damping curve with a
standard. They must then analyze how these quantities effect the curve a=
nd
what are the internal interrelationships. Then they go into lab and mus=
t
develop a procedure to measure the damping factor for different spring/ma=
ss
combinations.

5. Electric Field Mapping II. Building off their 218 experience with
mapping electric fields, the students must now collect numerical Potentia=
l
data and through graphical differentiation, determine the electric fields=

for three different charge distributions.

6. Electrical measurement instruments. Students study how ammeters and
voltmeters can be constructed from a simple galvanometer.

7. Kirchoff's laws. Computer techniques for solving matrix forms of
Kirchoff's equations are studied using 4, 5, and 6 unknown problems. The=

theoretical solutions are determined and then the actual circuits are bui=
lt
and the currents measured.

8. Logic circuits=97applications of boolean algebra. AND, OR, NAND, and=
NOR
logic circuits are discussed and then modeled using light bulbs and
switches. Then these circuits are combined to design a complex burglar
alarm circuit. =


9. Basics of computer programming. One lab period is used to provide
hands-on (at the computers) experience in simple True Basic programming. =

This is part of a class project=97see below.

10. Oscilloscopes, oscillators, etc. A hands on exploration of the use =
of
oscilloscopes.

HOMEWORK

One or two problems assigned for each class. Students presented solution=
s
in class. Graded on participation and general quality (integrated over t=
he
semester) of their solutions.

Special homework assignment involved calculating the work that God had to=

do to assemble our solar system.

SPECIAL PROJECT

Working in teams of two or three, students have to prepare a computer
program that animates the interaction between three charged masses
constrained to move in two dimensions. The mass, charge, and initial
positions of the charges must be adjustable. The Programming Lab provide=
s
the necessary programming information. The bulk of the project is to bre=
ak
the task down into finding the components of the forces, the components o=
f
the accelerations, the components of the velocities, and finally the x,y
position of each object. Students must also decide how to deal with
boundary conditions such as if the separation of two objects gets VERY
small.


FWIW

Rick

*****************************************************
Richard W. Tarara =

Department of Chemistry & Physics =

Saint Mary's College =

Notre Dame, IN 46556 =

219-284-4664 =

rtarara@saintmarys.edu =

=

FREE PHYSICS INSTRUCTIONAL SOFTWARE AVAILABLE AT =

http://estel.uindy.edu/aapt/rickt/software
http://www-hpcc.astro.washington.edu/mirrors/tarara/ =

---updates are posted often---
******************************************************* =