Limits & Conclusion
After all
of that work, the roller coaster differs by 5.9 meters per
second, roughly 20% less than would be predicted without
drag being accounted for, and the difference only gets
larger the higher the roller coaster starts from. And this
is actually a little low, considering that this still
reverted to an assumption of a straight drop, rather than
a slope. There are also other assumptions that were made,
such as frictionless wheels & axles and constant drag.
The coefficient of drag may have been too high, but
without an actual way to test it, we're left just looking
for a value that seems like it would be close. However, this is why drag is not introduced at the same time as conservation of energy. The purpose of roller coaster problems is not to accurately predict the final velocity of a falling object, but to illustrate that energy is always conserved, even if it is more complicated than simply moving from potential energy and back again. Also, in case it was not apparent before, the physics of drag are far more complicated than the physics of conservation of energy.