We actually discussed this before. In was in May 2005 and is in the
archives. The topic of the thread started out as Human Error and then
evolved into reaction time. Anyway, I thought we we some agreement that
the best place to start/stop the watch is in the middle (highest
velocity).
In addition to my post copied below, you might also want to read a post
from John Denker about starting the watch once, recording the "split
times" for each swing, then graphing these and getting the
linear-regression line. Of course there is no time to record those for
a fast pendulum, but for a long pendulum you might be able to record the
split times, particularly if one person records while a different person
runs the stop-watch buttons. If the pendulum is too fast, you could
record the split times every fifth swing or every tenth swing. That
would probably require three students.
Here is most of a long post I made at that time...
*** Reaction time ***
I agree with an earlier post of John M. in which he said (I am
summarizing his words, accurately I hope) that reaction time is the time
it takes one to respond when surprised.
I would hope reaction time is not common in timing experiments because
we ought not be surprised by the start and stop of the event we are
hoping to time. That does not mean students always pay attention. I
have seen students start a watch, settle back to count 50 pendulum
swings, set the watch down, then scramble to pick up the watch and find
the stop button when they suddenly realize they are at count 49.
I am also aware there is the possibility of wanting to time an event
that is going to surprise us. That is, I am aware of cases in which we
have no immediate prior indication that an event is about to start or
end. However, if we are timing motion, we see the object approach the
starting point and we see the object approach the stopping point.
That's a whole lot different from being surprised.
*** Uncertainty of Anticipated Start/Stop Timing ***
As stated above, if we are able to observe an event progressing toward
the start and finish, we are not dealing with reaction time. Rather, we
are dealing with how well a person can anticipate and synchronize with
the event. This has much less uncertainty than reaction time. Better
yet, if the start and stop are similar things (such as starting and
stopping a watch as a pendulum passes the marked center of its swing) we
don't need synchronization as much as we need consistency. It's fine to
actuate the timer 50 ms early if we also stop the timer 50 ms early. A
person who consistently anticipates 50 ms early can be a better timer
for anticipated events than one who is randomly off by 20 ms.
BTW, I'm with Bernard concerning starting and stopping as the pendulum
passes (a marked) center point. Rick says the pendulum spends more time
at the ends of the swings and that makes it easier. I say that makes it
harder.
*** Timing Long Times ***
George said "I suggest to my students that claiming the instrumental
limit as the uncertainty of their measurement is unreasonable,
especially for a single trial." I would say that depends entirely on
the nature of the experiment.
If a clock with a stated accuracy of +-10 ppm, is used to time an event
that lasts about 10,000 s (roughly 3 hours) the clock would contribute
+- 0.1 s to the overall uncertainty. The person starting and stopping
the clock might contribute uncertainty less than that if the event being
timed has anticipatable start and stop times. Of course the overall
uncertainly is the proper combination of both of these uncertainties.
Rick concurs with my feelings about timing pendulums. We don't want to
time many periods by starting and stopping for each measurement. We
want to start and stop just once, with many periods occurring between
the start and stop. Of course, we assume the pendulum is swinging with
small and therefore fairly constant amplitude. Timing many individual
periods would be a good way to determine the uncertainty of starting and
stopping the clock, if that were the goal. If measuring the pendulum
period is the goal, then start once, count many periods, stop once. I
have found that when doing this, the greatest student error is a
miscount.
*** Human Error ***
As I stated before, I don't generally consider these start/stop issues
as human error. It's just inherent in the design of the
human/instrument interface. Since it's "designed in" it's just as much
an instrument error as a human error.
Of course, miscounting the number of periods between the start and stop
would be a human error. This often happens right at the beginning. The
student thinks or says "one" when starting the timer rather than saying
"zero" when starting the timer.
Another interesting human error can happen when the student isn't paying
attention and misses the desired start/stop point. I say interesting
because it doesn't have to be an error in many cases.
I saw a student start timing a pendulum with the intent of stopping the
timer after 50 periods. By not paying attention, he missed the stop
point, but stopped the timer anyway, perhaps one second late (for a long
5-second pendulum). I said, "Although you should have been paying
attention, you didn't really goof until you stopped the watch. After
missing 50, you should have stopped at 51, or 55, or 60. There is
nothing magic about 50 periods. Now you don't know exactly how many
periods you timed, and you have to start over."
Similarly, a student was measuring the half-life of 137m-Ba and was
starting a one-minute GM-counter at two-minute intervals. He wasn't
paying attention and missed starting the timer at t = 8 minutes. Perhaps
15 to 20 seconds late, he started the counter. I said, "You had better
write down the time you actually started your 8-minute count. He
responded, "I didn't notice. I already missed it, so what difference
does it make." I said, "Why don't you think about it for a while, then
tell me what difference it makes, then you can start over." Of course,
had he written down the time he actually started the count, the data
would have been fine. There is nothing magic about starting on precise
two-minute intervals.
Alas... there are plenty of opportunities for actual human error... but
in my labs those opportunities are also accompanied by the opportunity
to start over.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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