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Re: [Phys-l] Independent Variables



I suggest taking the broad view of the course requirement; intorduce the students to problem solving in the context of investigating a physical relationship. For example, and it is only an example, consider a block sliding down a very smooth plane, and consider investigating the relationship between distance slid and elapsed sliding time.
I would define the "dependent variable" to be the name of the quantity plotted on the y-axis, "independent variable" along the x-axis.
Plot the results two ways, letting each quantity, distance slid and elapsed time, in turn being the x-variable (this emphasizes the arbitrariness of the distinction), and doing various fits (depending upon the mathematical maturity of the class) to determine the rlationship. Since the relationship is monotonic, either variable may serve as proxy for the other.
The experiments can be repeated for different angles of inclination. Again, the teacher has lots of discretion as to how to treat the different results. At one level, the different relationships emphasize the necessity of controlling "extraneous variables" in comparing distance slid vs elapsed time. At another level the different relationships teach us how to correct for possible uncertainties in the inclination angle when comparing elapsed times for different lengths slids (systmatic uncertainties).
My point is, that one can take a very simple measurement like this and use it as a model for all the complexities that can arise in doing very sophisticated measurements. At the same time, the teacher can trivialize the importance of verbal distinction that might, as seems the case here, assume unjustified importance in the teaching curriculum.
Regards,
Jack














On Tue, 31 Oct 2006, Bob LaMontagne wrote:

I agree with Ludwik - I would simply avoid use of the words dependent and
independent. Yesterday, I did a conservation of energy lab with the Intro
Physics students. We drop a ball into a bucket of sand and create craters.
If a fixed percentage of the potential energy of the ball becomes potential
energy of the lifted sand, the fourth power of the crater diameter should be
proportional to the height through which the ball fell. The students prepare
a graph of the height versus the 4th power of the diameter of the crater and
it turns out to be surprisingly linear - and in a log-log plot the slope is
4. However, both the height of the ball and the diameter of the crater are
measured values. It really isn't appropriate to consider one as dependent
and the other as independent. They just are what they are - measured
quantities.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Ludwik Kowalski
Sent: Monday, October 30, 2006 9:39 PM
To: thecraftyphantom@australia.edu; Forum for Physics Educators
Subject: Re: [Phys-l] Independent Variables

On Oct 30, 2006, at 8:47 PM, thecraftyphantom@australia.edu wrote:

I was discussing independent and dependent variables with my physics
students in a recent class. No matter how I approached the subject a
number of them asked questions that showed they were having difficulty
with
identifying the independent and dependent variable in a number of
cases.

Have others struck this difficulty? If so, what approaches have you
used
to clarify this issue for students?

1) In physics, unlike in mathematics, the issue becomes important when
laboratory data are plotted. Why do you need adjectives, such as
"dependent" or "independent?" Our variables already have names, such
as time, distance, voltage, etc.

2) At a deeper level it might become the cause-and-effect issue. Why do
you really want to deal with this issue?

Ludwik Kowalski
Let the perfect not be the enemy of the good.
_______________________________________________
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


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