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... here's the
terminology (fairly standard, I think?) I've been using:
static friction = friction in which the surfaces are not
slipping over each other; there can be motion, but
not relative motion at the point of contact; the
surface has no memory
kinetic friction = friction without memory, excluding static
friction
rolling friction: cannot be understood if the surface has no
memory -- neither static nor kinetic friction can
slow down a ball that's initially rolling without
slipping, since both are zero
Static friction is zero for a ball that's rolling without
slipping.
I [jsd] wrote:
Sliding friction is dissipative. I don't see how it could possibly
cancel. You lose energy on the way in, and you lose energy on the way out.
the momentum transfer to the ball is always in the same direction,
which is why the ball's momentum reverses its sign.
... didn't say that the situation was exactly symmetric, only approximately
so. ...
I [jsd] wrote:
The way I do it, I find that for a cushion 1/5th of a radius above the
midline, it suffices to have a force inclined upwards at 11.5
degrees. This does not strike me as impossible.
It's impossible based on the assumptions given in the pdf
file I posted on my site (http://www.lightandmatter.com/pool/pool.pdf).
.... Of course at
least one of my assumptions has to be wrong, since the result
disagrees with reality.
The angle you give could, for example,
occur if the usual textbook model of friction was incorrect.
(Actually it's not even possible for the angle to stay constant
throughout the collision, if there's an abrupt reversal of the
direction of the kinetic friction force at the cushion.)
it's possible that the center of mass deviates /invisibly/
from horizontal motion. It's then possible that the ball rolls
without slipping on the /cushion/: either it can make a tiny,
invisible upward hop, or it can slide against the table top
and push down into the table. There could also be multiple
microscopic bounces.