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I would suppose that if the whole process is adiabatic (dQ = 0) and no
work is done on the surroundings of this apparatus (dW = 0); then the
change in internal energy for the system is zero (dU = 0). (It is OK if
one part of the apparatus does work on another.) My guess would be (3)
since the kinetic energy of the sliding mass is already part of the
internal energy of the system. So, I say dU = 0 -- no change in internal
energy.
An iron cube whose mass is m slides horizontally over a long iron
plate. The mass of the plate M is much larger than m. The plate is
at rest while the cube has an initial kinetic energy K. Friction
brings the cube to rest before its base reaches the plate's boundary.
Everything is in the vacuum and the internal energy, dU, added to
both pieces of iron is not radiated in any substantial amount.
[In principle, dU can be calculated from the observed change of
temperature but no thermometer is available.] Which of the following
is correct and why?
*********************************************************************1. The internal energy dU is equal to K.
2. Only part of K goes into dU, the rest is used to do work W=R*x,
where R is the force of kinetic friction and x is the distance
the cube slides before comming to rest.
3. Neither of the above is correct.