Data Analysis and
Conclusion
Initial observations would suggest a
fair approximation of the surface of the water by both the set of calculations
with and without surface tension. All
three curves in each graph comparing the two sets of calculations and the
experimental data follow the same parabolic-like path for all nine trials. There are, however, some trends that deserve
closer attention.
First, the percent error is less around
the axis of rotation than the sides.
This suggests that perhaps the experimental data is not as accurate
toward the outer edges of the water. The
rotational velocity was relatively constant but still had a standard deviation
of about 50 degrees per second, which is significant. The
disc may have exhibited a tendency to change in velocity after adjustment of
the sticks on one side, so the data may be biased to that side. Also, using
pickup sticks and eyeballing where it touches the water means that the
measurements may not be accurate to more than an eighth of an inch. This phenomenon may also have arisen becuase the estimate for the surface tension is done
with a six degree
Second, there are obvious
discrepancies between the theoretical values calculated using the derived
formulae with and without surface tension.
This may be because the surface tension values are approximated and
involve the data collected at the lowest point of the curve. The experimental
data were used to derive the initial conditions, and since the data may or may
not be accurate, the predicted values differ.
Furthermore, since the surface tension formula is approximated using a
power series, it will not yield the same values that the original formula
would, so there is some approximation error.
In conclusion, although the
calculations derived to model the shape of the spinning water provide a rough
approximation of the actual shape, there exist both mathematical and
experimental discrepancies that upset the precision of these calculations.