Where do Harmonic Series show up in nature What is the steepest angle that a sand dune can achieve 1100 1150 am in LRC 212 Katherine MeyerCanales Saddleback College Physics ID: 387343
Download Presentation The PPT/PDF document "www.saddleback.edu/faculty/pquigley/cmc3" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
www.saddleback.edu/faculty/pquigley/cmc3
Where do Harmonic Series show up in nature?
What is the steepest angle that a sand dune can achieve?
11:00 - 11:50 am in
LRC
212
Katherine Meyer-Canales, Saddleback College Physics Patrick Quigley, Saddleback College Math
Math Concepts Represented in the Physical World
Is math presented differently in some physics courses?
www.saddleback.edu/faculty/pquigley/cmc3Slide2
What is the steepest angle that a sand dune can achieve? Slide3
What does angle of repose change with?
density , surface area, shapes
of the particles, and
the coefficient of friction of the
material . . . and maybe gravitySlide4
Let Angle of Repose =
Is it easily calculated analytically?
How is it determined empirically (2 ways)?
“. . . calculation
of the
macroscopic angle of repose from the microscopic properties
of the grains has eluded solution.”Slide5
s
max
n
Find
q a
nalytically:
Empirically?
What does angle of repose depend on for a block on the verge of slipping on an incline?
GUESSES. . .Slide6Slide7
Where do Harmonic Series show up in nature?Slide8
Possible Instructional Objectives for Stacked Meter Sticks:
By trial and error, determine how to stack the sticks lengthwise, one on top of the other, out over the edge of the table such that end of the top stick is at a maximum distance D from the edge of the table. Once stacked, take measurements of the displacement of each stick, relative to the stick immediately below it and determine a
sequence, for these measured displacements.Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D.
Investigate the series graphically and see if series diverges using integral test.Use the sequence to predict the location of the center of mass of the stacked sticks.Slide9
Possible Instructional Objectives for Stacked Meter Sticks:
By trial and error, determine how to stack the sticks lengthwise, one on top of the other, out over the edge of the table such that end of the top stick is at a maximum distance D from the edge of the table. Slide10Slide11Slide12Slide13Slide14Slide15
Any guesses what the sequence
might be?Slide16Slide17
Possible Instructional Objectives for Stacked Meter Sticks:
By trial and error, determine how to stack the sticks lengthwise, one on top of the other, out over the edge of the table such that end of the top stick is at a maximum distance D from the edge of the table. Once stacked, take measurements of the displacement of each stick, relative to the stick
immediately below it and determine a sequence, for these measured displacements.Slide18
Possible Instructional Objectives for Stacked Meter Sticks:
By trial and error, determine how to stack the sticks lengthwise, one on top of the other, out over the edge of the table such that end of the top stick is at a maximum distance D from the edge of the table. Once stacked, take measurements of the displacement of each stick, relative to the stick immediately below it and determine a
sequence, for these measured displacements.Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D. Slide19
Possible Instructional Objectives for Stacked Meter Sticks:
By trial and error, determine how to stack the sticks lengthwise, one on top of the other, out over the edge of the table such that end of the top stick is at a maximum distance D from the edge of the table. Once stacked, take measurements of the displacement of each stick, relative to the stick immediately below it and determine a
sequence, for these measured displacements.Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D.
Investigate the series graphically and see if series diverges using integral test.Slide20
Integral Test for divergence:Slide21
Possible Instructional Objectives for Stacked Meter Sticks:
5) Use the
sequence to predict the location of the center of mass of the stacked sticks.
X=0Slide22Slide23Slide24Slide25Slide26Slide27Slide28Slide29
Where do Harmonic Series show up in nature?
www.Slide30
Is math presented differently in some physics courses?
Examples: coordinate systems, vectors, Maxwell’s equations
Denoting a vector
Magnitude of a
vector
Denoting a unit vectorSlide31Slide32Slide33Slide34Slide35
Thanks to Karla
Westphal
, Kaz Tarui, and Katherine Meyer-Canales for developing this handout. Some formulas taken from hyperphysics website.Slide36