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John, I think what you're missing here is that I've actually calculated
all this stuff.
3) It should be obvious from theoretical considerations that a purely
normal force would be highly unsatisfactory. A purely normal force has no
lever arm about the center of the ball. That makes it kinda hard to exert
a torque.
Well, nature doesn't really care what's "satisfactory."
On a real pool
table, we observe that the collision is highly elastic, so the kinetic
friction forces are evidently fairly small,
... I assume static friction between the ball and
the tabletop, and kinetic friction between the ball and the cushion.
(They can't both be static friction forces, since then the ball couldn't
be moving!
Sliding friction is dissipative. I don't see how it could possiblyImpulse is defined as momentum transfer, not energy transfer.
cancel. You lose energy on the way in, and you lose energy on the way out.
The calculation is only about a page of algebra, and I'd encourage
anyone interested in discussing the topic to just go ahead and
do it before posting. You have six impulses:
impulse due to the tabletop's normal force
impulse due to the tabletop's static friction force
impulse due to the cushion's normal force before the ball stops
impulse due to the cushion's normal force after the ball stops
impulse due to the cushion's kinetic friction force before the ball stops
impulse due to the cushion's kinetic friction force after the ball stops
... you can easily verify numerically that it's not
possible to get a physically reasonable solution using the value
of b from an actual pool table.