YEARS 7–12 IDEAS
ARTICLES
FOR THE CLASSROOM
Using Real Data, and Analysing Errors (continued)
Figure 4: The effect of a curved track is consistent with our experimental observations.
The fall times from our mathematical model were interpreted as
uniform accelerations using the equation a = 2l/t 2 and plotted
in figure 4. The results calculated over a range similar to our
experiment closely match the experimental observations if the
track is 0.16 mm higher in the middle. This is plausible and
consistent with all our observations. The distance is so small that
it is beyond our ability to measure directly.
my absolute belief in the correctness of Newton’s description
of motion under most laboratory and real life conditions. The
curvature is small enough to be physically plausible. The track
is attached to the I-beam by five pairs of adjusting threads and
butterfly nuts spaced along the length of the track, but the distance
to move is a small fraction of the thread pitch. The curvature of
the track makes the assumption of uniform acceleration invalid,
particularly at very low angles.
The model also examined what happens when the curve bows
downwards, but the results will not be expanded upon here beyond
the term “long pendulum” to show a key idea in interpreting the
result. This is left as “an exercise for keen students”.
The method examined negative slopes, where the glider
accelerates in the other direction. This was intended to give a
longer baseline for calculating the gradient of the graph. In fact,
using both directions demonstrated problems with the track being
slightly curved, and possibly not uniformly. The acceleration in
the negative direction was slightly less.
Discussion
The longer fall times and much lower speeds of this experiment
gave a better value of g than using stopwatches to record balls
falling through 7.5 metres in an earlier experiment. The raw data
give g at about 10.0 to 10.1 m.s –2 , more precise but not accurate.
Analysis of the data and discussion with students revealed four
sources of error: leveling the track, curvature of the track, the
initial velocity of the glider, and both random and systematic
errors in the timing by students and teacher.
Leveling the track was a minor problem, easily corrected by
tweaking the data to adjust the angle by a plausibly small amount. Some students commented on greater variation in the fall times
at low angles. Tiny initial speeds would significantly affect the
timing. To minimise this, the glider was restrained until launch by
the tip of a biro. This was rapidly removed in the forward direction
to make the launch consistent, and avoiding contact with sticky
human hands. The glider carried several 50 g masses to
minimise the effect of any external forces other than gravity. The
increased mass does not measurably change the acceleration,
as expected.
Curvature of the track was examined by mathematical modeling,
which was highly consistent with the observations. This reinforces Collecting results from several students can be used to examine
the reliability of this method, (and possibly measure the unreliability
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SCIENCE EDUCATIONAL NEWS VOL 67 NO 3