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I'm uncomfortable with the "momentum transfer but no
energy transfer" model described in earlier posts.
Consider a similar situation, the hypothetical
perfectly elastic collision between a fall ing ball
and the floor. Model the floor as an ideal spring.
During the first half of the interaction, as the
"floor spring" is being compressed, the floor does
"negative work" on the ball, thereby reducing both its
KE and momentum to zero (in the floor ref frame).
During the second half of the interaction, as the
"floor spring" is recovering it is doing "positive
work" on the ball, increasing both its KE and momentum
to their original absolute values.