Answer 1:
Twisting the rubber band does work on the
band and stores
potential energy in it, meaning the capacity
for the band to do work has increased.
When the rubber band is allowed to unwind, the
band does work and that potential energy is
converted to
kinetic energy, which is energy of an
object in motion.
High speed means having a lot of
kinetic energy, and reaching large distance means
the kinetic energy has caused the plane to travel
very far. Thus, for both speed and distance,
having more potential energy means being able to
reach a higher value. A twisted rubber band is
essentially a torsion spring, for which the
stored
energy U can be calculated with
U=1/2*k*T^{2}, where
k is the torsional spring constant, and
T is the angle of twist.
From this one can see that
increasing the number of twists (increasing T)
will always increase the stored energy. This
means that there is not a limit to the number
of twists to increase either speed or distance:
more twists increases the potential energy and
enables greater speeds and distances (until the
rubber band is twisted so many times that it
breaks of course).
BUT, here is another aspect to consider (a twist,
if you will): for a given amount of energy (i.e.,
for a given number of twists), reaching the
highest speed prevents having the largest
distance. High speeds require high thrust,
which is obtained by having the propeller rotate
very quickly. Objects moving through fluids
experience
drag though, which is essentially
friction due to moving through the fluid.
Drag converts the
kinetic energy of the propeller and plane into
other forms, such as heat and sound, in which
case that energy is not pushing the airplane
forward.
Because drag
increases with velocity, moving fast reduces
efficiency (more potential energy is ultimately
lost to drag instead of being used to push the
aircraft forward). So to reach a large distance
it is generally better to fly slower for a longer
period of time (like
this one).
