Running head: The Continental Drift Theory
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The Continental Drift Theory
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The Continental Drift Theory
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The Continental Drift Theory
Three ways in which Wegeners continental drift hypothesis has helped to shape modern
Proofs of Two Equations from Sec. 15.5 of Cutnell & JohnsonC.E. Mungan, Fall 1998
First we derive a useful mathematical relation. Recall from College Algebra that there exists
one special function which has the property that the value of the function at a
Summary of Formulae for Collision ProblemsC.E. Mungan, Fall 2000
We assume that we have an isolated system of two objects and that we are given m1, m2, 1i, and
2i and are trying to solve for 1f and 2f. (If instead you are given some or all of the informat
Multiple Strings and PulleysC.E. Mungan, Fall 2000
The solution to Serway P4.33 begins by arguing that mass m1 moves twice as far as mass m2
in equal time intervals and hence has double the acceleration. Some folks may have trouble
seeing why this is so.
Small-Angle Oscillations of an Arc about its MidpointC.E. Mungan, Summer 2000
Prove that for small angular displacements, a uniform circular arc of radius R balanced on a
knife edge executes simple harmonic motion of period
T = 2
2R
g
(1)
regardless of th
Mass on a Vertical SpringC.E. Mungan, Fall 1999
The following is not particularly profound, but is a subtle point often glossed over in
introductory textbooks. I remember it caused me some confusion as an undergraduate.
Introductory treatments of simple h
Infinite Square Lattice of ResistorsC.E. Mungan, Fall 1999
Problem: Find the equivalent resistance RAB between two adjacent junctions in an infinite square
lattice of 1- resistors.
A
B
C
Solution: Thanks to Robert Blumenthal for the following idea. Assume
Kinetic Energy of a Rigid BodyC.E. Mungan, Fall 2000
Introductory textbooks such as Serway are not very clear about whether the kinetic energy of
a rigid body is to be calculated by summing together translational and rotational terms or by
using the trans
Density of Air down a Bore Hole C.E. Mungan, Summer 2000
Multiple Choice: (A) A deep shaft is drilled into the earth starting at sea level and room
temperature. Neglecting both the geothermal gradient and the weakening of the gravitational
force with dept
Adiabatic Expansion of Soda PopC.E. Mungan, Summer 2000
Demo 15-04 in the Video Encyclopedia of Physics Demonstrations presents a plot of the
temperature of the air in a bottle as it is pressurized to the point that it blows its top. The
temperature just
Quick Reference to Elementary Methods for Solving Differential Equations
C.E. Mungan, Spring 1998
First-Order Linear
y + P( x ) y = Q( x )
The homogeneous equation is separable, giving y = Ae I where I Pdx ye I = constant .
d
Now observe in the inhomogene
Integral Representation of the Riemann Zeta FunctionC.E. Mungan, Fall 2001
Prove that
( s)
k
s
k =1
1
x s1
=
dx
( s) e x 1
0
(1)
where s > 1.
Tim Royappa communicated to me the following wonderfully compact solution. The trick is to use
the Laplace tran
Examples of Functions expressed in terms of Hypergeometric Series
C.E. Mungan, Spring 1998
F( a, b, c; x )
F(1,1,1; x ) =
1
1 x
( a )n (b )n x n
n!
n = 0 (c )n
geometric series
3
x F( 1 ,1, 2 ; x 2 ) = tan 1 ( x )
2
inverse trignometric functions
x F(1,1
Physics Cinema Classics VideosC.E. Mungan, Spring 2003
This is a 3-disc series published by AAPT.
Use audio channel 1 to ask questions of the students and
channel 2 for an explanation of the phenomena.
Disc 1 Side A
Chap. 76A person standing on a scale in
given a homogeneous second-order
differential equation
y + py + qy = 0
is the origin an
ordinary point?
yes
standard power series
method will give both
solutions
no
is the origin a
regular
singularity?
no
STOPLaurent series not treated
in this course
yes
Irrationality of Square RootsC.E. Mungan, Fall 1999
Prove that
square.
p / q (where p and q are relatively prime*) is irrational if p or q is not a perfect
*Definitions: counting numbers are positive integers cfw_1, 2, 3, .; some counting number y is
said
Talking like Donald DuckC.E. Mungan, Fall 1999
It is a commonly known fact that if you fill your lungs with helium, your voice will sound
unusually high pitched. Why? This is a nice question to discuss with introductory students
because it ties in well to
Solving Newtons Second Law in One Variable in the Absence of Dissipation
C.E. Mungan, Spring 1998
The goal of the problem considered here is to find the time required for a particle moving
along a specified curve (possibly a straight line or a circle, but
Completely Inelastic CollisionsC.E. Mungan, Fall 1998
Problem: Prove that a maximum amount of kinetic energy is lost in a completely inelastic
collision between two point masses, as claimed on page 201 of Cutnell & Johnson for instance.
This problem can b
Glossary of Thermodynamic TermsC.E. Mungan, Fall 1998
Temperature: Macroscopic definitionThe property of an object which determines how much
heat it will exchange with another object when brought into thermal contact with it. Microscopic
definitionA measu
Fresnel Boundary ConditionsC.E. Mungan, Fall 1998
Problem: Given that
A1eik1 x + A2 eik2 x = A3eik3 x
for all x, prove that A1 + A2 = A3 and that k1 = k2 = k3 .
Solution: Substitute x = 0 into Eq. (1) to find
A1 + A2 = A3 .
Next differentiate Eq. (1) and
Formal Derivation of Centripetal AccelerationC.E. Mungan, Fall 2001
Consider a particle executing uniform circular motion
(UCM). Place the origin at the center of the circular
trajectory of radius r. The fact that the speed is constant
means that the angl
Derivation of Two Laboratory Capacitance FormulaeC.E. Mungan, Spring 2001
A Boonton capacitance meter can be used to measure the dielectric constant of a thin
insulator. However, the capacitor plates have small spacers which prevent them from closing all
Solution to Tipler P25.59C.E. Mungan, Spring 2002
Three capacitors ( C1 = 2 F , C2 = 4 F , and C3 = 6 F ) are each separately charged up to
200 V. They are then wired in series and the two end terminals of the set are shorted together, as
sketched below.
A Generator and a CapacitorC.E. Mungan, Fall 1999
A simple demo of the properties of capacitors and generators/motors was first shown to me
by T.J. Miller and is also described by Robert Ehrlich in his lovely book of demos, Why Toast
Lands Jelly-Side Down
Relationship between Displacement and Pressure AmplitudeC.E. Mungan, Fall 2000
Consider a monochromatic plane sound wave traveling down the length of a tube of gas of
ambient density 0 at a phase speed s. Find an expression for the relationship between th
The Van der Waals Equation of StateC.E. Mungan, Spring 2000
The ideal gas law is
p = RT
(1)
where V / n is the molar volume. To obtain the van der Waals equation, we need to modify
the pressure and volume. Long-range attractive forces between molecules te
Angle of Minimum Deviation through a PrismC.E. Mungan, Spring 2001
Prove the well-known fact that one gets minimum deviation for a symmetric beam geometry.
4
1
1
3
2
n
It is easy to see from the geometry of this sketch that the apex angle is related to th
Derivations of Stirlings ApproximationC.E. Mungan, Spring 1998
Method 1: By Taylor Series
Begin with
n x
n! = (n + 1) = x e dx = e n ln x x dx
0
0
and for convenience define f ( x ) = n ln x x . By graphing f(x), you can convince yourself that it
peaks at
Theory of Holonomic ConstraintsC.E. Mungan, Fall 2002
Suppose we have N particles in D dimensions with C constraints. Assume for simplicity that
there are no nonconservative forces other than the constraint forces. Choose the generalized
coordinates so th