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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/cmc3
What is the steepest angle that a sand dune can achieve?
What does angle of repose change with?
density , surface area, shapes of the particles, and the coefficient of friction of the material . . . and maybe gravity
Let Angle of Repose =
Is it easily calculated analytically?
How is it determined empirically (2 ways)?
“. . . calculation of themacroscopic angle of repose from the microscopic propertiesof the grains has eluded solution.”
smax
nFind q analytically:
Empirically?
What does angle of repose depend on for a block on the verge of slipping on an incline?
GUESSES. . .
Where do Harmonic Series show up in nature?
Possible Instructional Objectives for Stacked Meter Sticks:
1) 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.
2) 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.
3) Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D.
4) Investigate the series graphically and see if series diverges using integral test.
5) Use the sequence to predict the location of the center of mass of the stacked sticks.
Possible Instructional Objectives for Stacked Meter Sticks:
1) 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.
Any guesses what the sequence might be?
Possible Instructional Objectives for Stacked Meter Sticks:
1) 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.
2) 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.
Possible Instructional Objectives for Stacked Meter Sticks:
1) 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.
2) 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.
3) Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D.
Possible Instructional Objectives for Stacked Meter Sticks:
1) 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.
2) 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.
3) Sum the sequence found above to find a series which can be used to predict the theoretical value of the distance D.
4) Investigate the series graphically and see if series diverges using integral test.
Integral Test for divergence:
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=0
Where do Harmonic Series show up in nature?
www.
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 vector
Thanks to Karla Westphal, Kaz Tarui, and Katherine Meyer-Canales for developing this handout. Some formulas taken from hyperphysics website.
