Mathematica examples from
the LC undergraduate
physics curriculum
John Eric Goff
Lynchburg College
Lynchburg, VA 24501
CS-AAPT Fall 2007 – Radford University
Radford, VA 24142
November 3, 2007
LC Physics
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•
•
•
Small number of physics faculty (2 or 3).
We need a niche!
We have a computational emphasis.
Computational Physics joins theory and
experiment to form the new triumvirate in
physics.
• Some form of computation permeates all
our courses.
What do we do?
• Intro: Excel (Euler method in second lab),
some Mathematica, simulations (Kinetic
Books and Physlets)
• Intermediate: Mathematica (especially
Classical Mechanics in 4th semester)
• Advanced: Mathematica and Full
Programming (Computational Physics
Course)
Intro Example (1st Semester)
• “Curtain of Death” problem (HRW 4-68)
What is typically done?
Curtain of Death (HRW 4-68)
6
5
y (km)
4
3
2
1
0
0
5
10
x (km)
Excel Plot
15
20
Use Mathematica!
Intro Lab – Kirchhoff’s Rules
PASCO
Six equations in six unknowns (currents)!
How do students compare with theory without
spending most of “lab” doing algebra???
Use Mathematica!
• Make sure students write down the six equations
in six unknowns. Do not skip the physics!
Students evaluate “sol” with their own V and R values.
Classical Mechanics
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•
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Taken by sophomores in spring semester.
Mathematica is used throughout course.
One week of class devoted to Mathematica.
Homework and exam questions require
numerical solutions.
Velocity-Dependent Forces
• Thornton and Marion 2-18 (worked fully in class)
• Softball problem uses quadratic air drag.
• Problem cannot be solved analytically!
Phase Plots
• Thornton and Marion 3-15
• Underdamped Oscillator
Noninertial Reference Frames
• Thornton and Marion Example 10.2
• Hockey Puck on a Merry-Go-Round
Electromagnetism
• Griffith’s 3-25
• Cylinder (radius R) with charge density
σ() = k sin(5)
• Answer:
5
ks
V ( s,  ) 
sin( 5 ) , s  R
4
10 0 R
6
kR
V ( s,  ) 
sin( 5 ) , s  R
5
10 0 s
Visualize with Mathematica!
Quantum Mechanics
• Griffiths 2.17 (1st ed.)
• Time evolution of particle in even mixture
of ground- and first-excited states of
harmonic oscillator potential.
Animate with Mathematica!
Quantum Mechanics - Project
See Stuart Farrell’s Spring 2005 CS-AAPT talk.
Optics
Fringe patterns on a holographic plate.
Optics – Final Exam Question
Diffraction intensity for a rectangular aperture.
Computational Physics
• Giordano and Nakanishi “Cream in the
Coffee” Problem
• Animation is a must!
Cream in the Coffee
Show the entropy’s progression toward a constant value.
Fluid Mechanics Project
Velocity field of fluid moving around rectangular obstruction.
Fluid Mechanics Project
Stream function of fluid moving around rectangular obstruction.
Fluid Mechanics Project
Vorticity of fluid moving around rectangular obstruction.