A question came up on another list about the work done by air on a
massless piston. The piston is supported by a linear (Hookean) spring.
There is no friction between the piston and the walls of the cylinder.
The region behind the piston is evacuated, and then the piston is
released, allowing the air on the other side of the piston to compress
the spring. The force that the air exerts on the piston equals the
force that the spring exerts on the piston, because the piston is
massless. Initially, this force is less than atmospheric pressure times
the area of the piston. I argued that the force is less because the
piston is accelerating away from the air. This situation is analogous
to punching a sheet of paper that is falling through the air. The
maximum force that you can exert on the paper is limited, because the
paper accelerates away from your hand.
I further argued that even if the piston wasn't massless, the force that
the air exerts on the piston while it accelerates away from the air
would be less than atmospheric pressure times the area of the piston;
however, I can't figure out how to calculate the force acting on the
piston during its acceleration. For a sufficiently massive piston, the
reduction in force should be negligible, because the acceleration would
be too slow to make a significant difference.
Is this line of reasoning correct? Or is the nonphysical massless
piston just an anomolous case? Does anyone know how to calculate the
reduction in force as a function of the mass of the piston?
Thanks in advance.
Daniel Crowe
Loudoun Academy of Science
dcrowe@loudoun.k12.va.us