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As I understand it, work is not done by the kinetic energy. Rather themassive)
force of friction, acting in the block, does work, the effect of whichis to reduce the kinetic energy of the block - essentially to 0, if the
plate is massive enough. The work done by the reaction force, acting
on the plate, has the effect of increasing the internal energy of the
system, to the extent that the kinetic energy imparted to the (very
block is negligible. Under those circumstances, dU = K (almost).
Al Clark goes on the say:
PS. I believe the "internal energy" is normally used to refer only to
the energy of atomic motion with a material, not to the macroscopically
measurable energies. One could use it to refer to the total energy of
a system, if you wished, in which case the discussion would be
different.