A paper coffee filter in the shape of a truncated cone falls in a stable way and quickly reaches terminal speed because it has
a large area (big air resistance) but low mass (small gravitational force). Use a stopwatch to time the drop of coffee filters
from as high a starting position as you can conveniently manage. If a stairwell is available, drop the coffee filters there to
time a longer fall. This experiment is easier to do with a partner.
(a) By stacking coffee filters you can change the mass of a falling object without changing the shape. With this scheme
you can explore how the terminal speed depends on the mass. Time the fall for different numbers of stacked filters,
taking some care that the shape of the bottom filter is always the same (the filters tend to flatten out when removed
from a stack). Start the measurement after the filters have fallen somewhat, to allow them to reach terminal speed.
Average the results of several repeated measurements of time and height. Can you think of a simple experiment you
can do to verify that the coffee filters do in fact reach terminal speed before you start timing?
(b) We want to know quantitatively how air resistance depends on speed. Plot your data for the air resistance force vs.
the terminal speed. (The air resistance force is equal to the gravitational force when terminal speed has been reached,
so it is proportional to the number of filters in a stack). How does the air resistance force depend on v?
(c) There is an important constraint on the graph of speed dependence: Should the curve of the air resistance force vs.
terminal speed go through the origin (force and terminal speed both very small), or not?
(d) Analysis hint: If you suspect that the force is proportional to v3, you might plot force vs. v3 and see whether a
straight line fits the data.