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Re: Kinematics - a vs. t graphs



You're exactly right that the noise is a propagation of error issue.
However, note that the software allows you to find accelerations using a
variety of weightings of points, so that for most cases you can get
acceptably quiet acceleration values.

What I'm writing should be true of most data collection software, so I
hope this post is not taken as commercial.

You can alter the number of points used in finding derivatives (the
location of that setting depends on your particular software). This is a
little-known setting, but it is really important if you are teaching
with velocity and acceleration graphs. The optimal setting depends on
several things:

1. the data rate and the degree of smearing of features you can accept
2. the reflecting quality of the target
3. the actual acceleration of the object (is it uniform or not?)

Note that the velocity and acceleration are NOT calculated by
delta-position/delta-time, etc. Such calculations would be wildly noisy.
The actual calculation involves finding the slope of a set of points.
For example, over five points, which would include two points before the
current time, the current time, and two points after.

Using more points will result in quieter velocity and acceleration
graphs, but you will lose temporal resolution. That might or might not
be important to you.

If you're looking at an object that is moving smoothly, e.g., a cart or
glider, then you can use few points for derivatives and get very good
data. If you're looking at a student walking, you'll want to use lots of
points (7? 15 even?) to even things out. The student's acceleration IS
varying a lot. After all , it is not the details in the acceleration
graph you want, it is the broader features.

There can be other sources of noise unrelated to a sub-optimal choice
of number of derivative points:

Data rates above 30 Hz tend to not give the best results regardless of
the target, especially if you are in a room with hard walls.
Targets with poor reflectivity of ultrasound will give erratic
results.
Some computer monitors emit interference that will confuse the motion
detector. Move the MD well away from the monitor.

JEG




--
John Gastineau
Staff Scientist
Vernier Software & Technology
13979 SW Millikan Way
Beaverton OR 97005
(503) 277-2299 voice (503) 277-2440 fax
(888) 837-6437 toll-free
jgastineau@vernier.com www.vernier.com

Hemmig@D-E.ORG 09/17/03 12:32PM >>>
"You cannot reliably infer the acceleration from samples
of the x and t coordinates, not without some nontrivial
regularization assumptions."

We are using old Vernier software and motion detectors for Workshop
Physics labs in which we generate d, v, and a vs. t graphs. The a vs
t
graphs are always noisy, and generally look like the edge of a
carpenter's saw. I'm not familiar with the latest software and
equipment, and wonder if cleaner graphs are now possible.

Despite the difficulties mentioned in the thread above, I expect that
the main issue here is coming from the propagation of error. If the
motion detector takes say 30 readings per second, then I assume that
it
calculates 30 average velocities per second, and uses Ludwik's method
to
find 30 average accelerations per second. I find that the noise
varies
from one machine to another in my room despite similar setups and
conditions.

Gary Hemminger
The Dwight-Englewood School
Engelwood, NJ
hemmig@d-e.org