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On 02/01/2011 07:18 AM, ludwik kowalski wrote in part:
axioms (self-evident truth)
Axioms are not truth, let alone self-evident truth.
Axioms are essentially hypotheses, put forth *without regard* to
whether
they are "true" or not. The Euclidean geometry book is one long
"if...then"
statement. For instance, it says *if* the Euclidean axioms apply
*then*
the sum of the interior angles in a triangle is 180 degrees.
You can perfectly well hypothesize Euclidean geometry on one side of
the
page and hypothesize non-Euclidean geometry on the other side. You
can
do that with hypotheses ... but you cannot do that with truth.
Truth is
not so flexible.
The theorems of geometry are not "true" in any absolute sense,
either. I
suppose you could say that they are conditionally true, conditioned
on the
axioms.
2) In mathematics (not only in Euclidean geometry), I used to tell
students, everything is derived. Mathematical claims are validated by
logical derivations.
No, not "everything".
You could say that everything you have derived is derived ... but
that is not particularly informative.
In contrast, *not* everything that is a valid consequence of the
axioms
is derivable. G?del proved this. Indeed he gave a _constructive_
proof, exhibiting a statement that must be true (given almost any
reasonable set of axioms) but is not derivable.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
A quick paste below/snip/
From website:<http://scienceblogs.com/dotphysics/2010/04/where_is_the_accelerometer_in.php>
-----------------------------
Measurement methods
You will not believe how many different ways I tried to rotate this iPod.
After making the video, I used Tracker Video Analysis to determine the angular velocity of the iPod. Note - autotracking feature on Tracker is the awesome.Super pointer! Thanks
-----------------------------
Paul Lulai
/snip//snip/
Since all methods of information transmission via E&M waves involves some encoding/decoding process, I would suggest that compensation for a Doppler-shifted carrier should be part of the decoding process.
Michael D. Edmiston, PhD.
A source for interesting / fun problems that aren't necessarily
physics problems. Car Talk Puzzlers.
A source for interesting / fun problems that aren't necessarily physics problems.The answer to a puzzle they asked two weeks ago would be helpful to
Car Talk Puzzlers. I haven't found a great way to implement them into my class, but they are fun. I am starting to post these questions and the TPT Physics Question of the month for my students as extra credit options. I don't yet feel comfortable requiring a certain number of these problems to be solved in the course of a quarter. I might move in that direction once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
A source for interesting / fun problems that aren't necessarily physicsThe answer to a puzzle they asked two weeks ago would be helpful to
problems.
Car Talk Puzzlers. I haven't found a great way to implement them into my
class, but they are fun. I am starting to post these questions and the
TPT Physics Question of the month for my students as extra credit options.
I don't yet feel comfortable requiring a certain number of these problems
to be solved in the course of a quarter. I might move in that direction
once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
?WRONG!
The center of mass point is NOT the same as the point which divides the mass
in two.
-----Original Message-----
From: brian whatcott
Sent: Tuesday, February 01, 2011 3:24 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] real-world problem
On 2/1/2011 1:08 PM, Paul Lulai wrote:
A source for interesting / fun problems that aren't necessarily physicsThe answer to a puzzle they asked two weeks ago would be helpful to
problems.
Car Talk Puzzlers. I haven't found a great way to implement them into my
class, but they are fun. I am starting to post these questions and the
TPT Physics Question of the month for my students as extra credit options.
I don't yet feel comfortable requiring a certain number of these problems
to be solved in the course of a quarter. I might move in that direction
once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
pre-calculus students.
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
[scroll down for spoiler.....]
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
Brian W
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
?WRONG!
The center of mass point is NOT the same as the point which divides the
mass
in two.
-----Original Message-----
From: brian whatcott
Sent: Tuesday, February 01, 2011 3:24 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] real-world problem
On 2/1/2011 1:08 PM, Paul Lulai wrote:
A source for interesting / fun problems that aren't necessarily physicsThe answer to a puzzle they asked two weeks ago would be helpful to
problems.
Car Talk Puzzlers. I haven't found a great way to implement them into
my
class, but they are fun. I am starting to post these questions and the
TPT Physics Question of the month for my students as extra credit
options.
I don't yet feel comfortable requiring a certain number of these
problems
to be solved in the course of a quarter. I might move in that direction
once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
pre-calculus students.
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
[scroll down for spoiler.....]
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
Brian W
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
?They can be very close, or very far apart.
It depends on the particular mass distribution.
-----Original Message-----
From: chuck britton
Sent: Tuesday, February 01, 2011 4:38 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] real-world problem
hmm, how far apart are these two points??
At 4:23 PM -0500 2/1/11, Bob Sciamanda wrote:
?WRONG!
The center of mass point is NOT the same as the point which divides the
mass
in two.
-----Original Message-----
From: brian whatcott
Sent: Tuesday, February 01, 2011 3:24 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] real-world problem
On 2/1/2011 1:08 PM, Paul Lulai wrote:
A source for interesting / fun problems that aren't necessarily physicsThe answer to a puzzle they asked two weeks ago would be helpful to
problems.
Car Talk Puzzlers. I haven't found a great way to implement them into
my
class, but they are fun. I am starting to post these questions and the
TPT Physics Question of the month for my students as extra credit
options.
I don't yet feel comfortable requiring a certain number of these
problems
to be solved in the course of a quarter. I might move in that direction
once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
pre-calculus students.
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
[scroll down for spoiler.....]
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
Brian W
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
?WRONG!
The center of mass point is NOT the same as the point which divides the mass
in two.
?They can be very close, or very far apart.
It depends on the particular mass distribution.
-----Original Message-----
From: chuck britton
Sent: Tuesday, February 01, 2011 4:38 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] real-world problem
hmm, how far apart are these two points??
At 4:23 PM -0500 2/1/11, Bob Sciamanda wrote:
?WRONG!
The center of mass point is NOT the same as the point which divides the
mass
in two.
-----Original Message-----
From: brian whatcott
Sent: Tuesday, February 01, 2011 3:24 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] real-world problem
On 2/1/2011 1:08 PM, Paul Lulai wrote:
A source for interesting / fun problems that aren't necessarilyThe answer to a puzzle they asked two weeks ago would be helpful to
physics
problems.
Car Talk Puzzlers. I haven't found a great way to implement them into
my
class, but they are fun. I am starting to post these questions and
the
TPT Physics Question of the month for my students as extra credit
options.
I don't yet feel comfortable requiring a certain number of these
problems
to be solved in the course of a quarter. I might move in that
direction
once I have a better feeling for how my students do with them.
< http://www.cartalk.com/content/puzzler/>
Paul Lulai
pre-calculus students.
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
[scroll down for spoiler.....]
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
Brian W
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________
No infections found in this incoming message
Scanned by iolo System Shield?
http://www.iolo.com
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________
No infections found in this outgoing message
Scanned by iolo System Shield?
http://www.iolo.com
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
On Feb 1, 2011, at 3:23 PM, Bob Sciamanda wrote:
?WRONG!
The center of mass point is NOT the same as the point which divides the mass
in two.
Howdy,
Simple example: 2M------------M (point masses) and the CM is 1/3 of
the way between them measured from 2M. Clearly not the same amount
of mass on the two sides.
Good Luck,
Herb Schulz
(herbs at wideopenwest dot com)
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
And a VERY strange way for the fuel to arrange itself in the tank!!!!
At 3:54 PM -0600 2/1/11, Herbert Schulz wrote:
On Feb 1, 2011, at 3:23 PM, Bob Sciamanda wrote:
?WRONG!
The center of mass point is NOT the same as the point which divides the mass
in two.
Howdy,
Simple example: 2M------------M (point masses) and the CM is 1/3 of
the way between them measured from 2M. Clearly not the same amount
of mass on the two sides.
Good Luck,
Herb Schulz
(herbs at wideopenwest dot com)
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
OTOH--Scientist and Engineers use equations all the time. Sometimes we have
not derived these, but rather understand them at some level (well the
scientists do) and trust that they have been thoroughly tested. I fit all
the equations needed for my first semester, Calculus level class on one side
of a standard piece of paper--and didn't use particularly small fonts. That
same sheet includes some math stuff, like basic Trig and the quadratic
formula (although they all have that function on their calculators these
days.) Many of the formulae were derived--kinematics from the definition of
acceleration, KE and grav PE from Work--but the work formula given through
the definition. Newtonian gravitation given--not derived, but then used to
derive Kepler's Third Law. While the derivation of centripetal acceleration
is given in all the books--I usually just use it. Likewise, we need the
velocity of a wave on a string formula in order to setup standing waves, and
it can be derived, but it is not worth the time and effort (IMO)--happy to
give and use the formula and reference the book derivation.
So--I would suggest a reasonable mix of derived and given equations is not
too bad. It is the way we all (well almost all, I suspect some do derive
everything from first principles) operate. I used statistics equations for
some time before sitting down and figuring out where they came from and I
fitted a lot of my thesis data (eons ago) using Distorted Wave Born
Approximations which I only vaguely understood--but had a program that would
do the calculations (yes on punch cards!)
;-)
Rick
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
*******************************************
Free Physics Instructional Software
www.saintmarys.edu/~rtarara/software.html
New 'Hi-Def' versions being posted as completed.
********************************************
----- Original Message -----
From: "Paul Lulai" <plulai@stanthony.k12.mn.us>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, January 31, 2011 2:35 PM
Subject: Re: [Phys-l] Any teaching tips
"an equation should be acceptable if the student can derive it."
High school freshman are not very good at deriving. The rearranging of a
single equation with 3 variables is a challenge for 1/2 of them (seemingly
insurmountable for 1/10 of them).
I plan to try the graphical analysis approach and find the relationships in
that manner this semester (don't often teach freshman). I suppose this
would count as deriving. I don't know how much success (or time would be
required) to derive a relationship from multiple other relationships.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
As Bob Sciamanda points out, the balance point is not the same as
the half (or quarter) mass point. I find that the balance point is
at .424413 R and the half mass point is at .403973 R. About 52.37%
of the semicircle mass lies closer to the diameter than the balance
point.
John Mallinckrodt
Cal Poly Pomona
On Feb 1, 2011, at 12:24 PM, brian whatcott wrote:
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
As Bob Sciamanda points out, the balance point is not the same as the half (or quarter) mass point. I find that the balance point is at .424413 R and the half mass point is at .403973 R. About 52.37% of the semicircle mass lies closer to the diameter than the balance point.
John Mallinckrodt
Cal Poly Pomona
On Feb 1, 2011, at 12:24 PM, brian whatcott wrote:
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
Those naughty entertainers describing a 40% radial mark when it is actually 40.4% ... :-)
Imagine!
Those naughty entertainers describing a 40% radial mark when it is actually
40.4% Disgraceful! As it happens, those fellows also mentioned
other strategies,
such as taking an empty beer can and filling it full; then weighing or
taking volumes (in a sight glass?) to establish quarters. :-)
Brian W
On 2/1/2011 4:16 PM, John Mallinckrodt wrote:
As Bob Sciamanda points out, the balance point is not the same as
the half (or quarter) mass point. I find that the balance point is
at .424413 R and the half mass point is at .403973 R. About 52.37%
of the semicircle mass lies closer to the diameter than the balance
point.
John Mallinckrodt
Cal Poly Pomona
On Feb 1, 2011, at 12:24 PM, brian whatcott wrote:
The question:
How can I find the quarter full mark using a dipstick in a [horizontal
axis] cylindrical fuel tank as fitted to a truck?
The answer:
Cut a circle from card.
Draw a diameter, and a perpendicular radius.
Cut a semicircle out on the diameter line.
Balance the semicircle on the radius line with a pencil tip for the pivot.
This is the centroid of the shape, and represents the center of mass of
a similar cylinder - this is about 40% of the radial distance from the
center.
A stick marked with three lines scaled to the diameter of the fuel tank
in question
therefore fits the purpose. A mark at 70% of the diametrical length,
one at 50% of the diameter, and one at 30% of the diameter.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
brian whatcott wrote:
Those naughty entertainers describing a 40% radial mark when it is actually 40.4% ... :-)Fair enough as far as that goes, but, of course, the difference Bob pointed to was one of principle and that difference isn't between 40.4 and 40; it is between 40.4 and 42.4.
John Mallinckrodt