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. . . During the Pasco cart collision, momentum is
transferred during the entire time of contact (during
which forces act) but the motions of the CMs of the
cars (ie, the velocities) are only changed during a
portion of the contact time. That is, the integral of
Fdx occurs over a different (ie, shorter) time than
that during which there is momentum transfer. During
the "rest" of the time energy is "dissipated"
internally producing an increased internal energy
which does not contribute to CM motion.
. . .