Re: [Phys-l] Force on an accelerating piston

["Josh Gates-fac" <Josh_Gates-fac@nobles.edu>]

Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
writes:


> Let me rephrase the question to make my intention clearer:
>
> If a rigid piston has mass, is the force that the gas exerts on the
> piston while the piston is accelerating away from the gas less than the
> force that the gas would exert on the piston if the piston was at rest?
>
> Daniel Crowe

 First, I'm assuming that, when you say "at rest," you mean "not
accelerating," ie: a static equilibrium.  Otherwise, the question doesn't
make a lot of sense, as there could be any amount of acceleration on a
resting piston, therefore any force(s) could be acting on it.

   It's not necessarily less than the steady-state gas force, but the
force exerted by the spring at this moment is less than the gas force at
this moment (the accelerated moment).  Now, assuming that the system is
closed, compare this gas force (at the accelerating moment, assuming that
it's at a low compression of the spring) to a couple of spring forces:
  - it is more than the gas force necessary to maintain equilibrium _at
the same level of compression_ (this amount of force is equal to the
spring force at this spring length)
  - it is less than the gas force necessary to maintain equilibrium _at a
higher level of compression_, where k and delta x are sufficiently high. 
Such a level of compression may be (that is, will be for certain values of
delta x and k, but not for others) beyond where the piston stroke would
ordinarily go, though: as the gas expands, the force that it exerts
decreases, so the gas will never exert this amount of force.
 
  JD's already discussed interpreting "accelerating" as "moving away."

jg


Josh Gates
Stoneleigh-Burnham School
Greenfield MA