In my last post, I said that static friction can do no work - that was
intended to be applied to this case only and I still maintain that. The
site of the frictional force does not move, the frictional force is not
applied over any distance, it does no work.
Consider the cylinder (or wheel) rolling down a slope. There you must have
static friction, but it doesn't do any work. It can easily be shown that
the gain in K = loss in U(grav) when rotational kinetic energy is
included. Why is this any different? Just because there is an engine
applied?
The case of work only complicating things is somewhat valid. Certainly by
Newton's Laws and the extent of the FCI, the only force that can cause an
acceleration is the static friction. That is why, at first glance, answer
C was (the most) correct. Case closed. However, in our course, work comes
about 3 lectures after Newton's Laws and this is still very fresh in the
mind.
How can something start to move when there is no force capable of doing
work on it? The energy has to come from somewhere - where? Ok, ultimately
it comes from the fuel, which came from the sun, which is a result of
matter annihilation - but that is irrelevant. There has to be a force that
is the intermediary to transfer the energy (via work) into kinetic energy.
Maybe this is not static friction after all. At what point does the
enormous number of contact points moving zero distance (=zero work) change
to an enormous number of contact points moving an infinitesimal distance
(=finite work). Which is real? How does a unicycle work?