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Re: Air resistance



I do not know about you but I find reading and thinking about messages on
this thread more pleasent than grading. Assuming this is true for some
phys-L-ers let me poste a private message received this morning. I would
like to hear more about "reflections from turbulances"; perhaps an
experiment with a hair blower can be useful.

I will use the "rule of six" (or the rule of three if there is only one
contributor) to recognize when the thread is dead.
Ludwik Kowalski
...........................................................................
At 01:42 PM, you wrote:
I was thinking that the "processing of 15 distances" means finding the
average distance and assigning it to an appropriate time moment. After
that v is calculated from each pair of consecutive d and a is calculated
for each pair of consecutive v. What do you mean by the "least square
fit" in this context?

The 15 points, centered on a given time, are used in a straight line fit (a
least square calculation). the intercept information is discarded, and the
slope is used as the velocity value.

As such the velocity values at 2.2 s (to use your example) are influenced
by the constant position values at times before 2 s. Since the velocity is
changing most of the time, there's no need to discard the 8 points before
the drop started; just recognize that there is the same "smearing" of the
velocity over a fairly wide time interval.

What John M says is correct; the velocity and acceleration data are of
distinctly lower quality than the position data. Any analysis that you
really care about should be done with the position data. e.g., in a free
fall experiment, don't fit a line to the velocity data; fit a parabola to
the distance data.

Unfortunately for the air resistance problem, you have to do much more
complicated analysis to make use of the distance data.

... The word "averaging" is not used very appropriately in MacMotion.

I do know what the least square fit means in general, I do not see how
it is used to construct a table. Perhaps you are referring to graphs
rather than tables. Please explain.

Again, it's just fitting a straight line to a set of n (15, in this example)
distance time pairs, and finding the slope of the line fit to those data. If
you like you can think of it graphically; drag MacMotion's tangent line
along the distance graph, and write down the slope at each time increment.
You just generated a table. That's how MM does the velocity column of the
data table. At least, that's how I have been told that it works by the
Vernier people.

P.S. How did you learn about reflections from air turbulances?

From talking to many users of sonic rangers. That's just an application of
rangers that is prone to trouble. Sometimes it works, sometimes it doesn't.
This is private email to you; feel free to post it to phys-l if you think
there is interest.