The following idealized problem is intended to illustrate some basic thermodynamic concepts involved in kinetic friction. A block of mass m is sliding on top of a frictional, flat-topped table of mass M. The table is magnetically levitated, so that it can move without thermal contact and friction across a horizontal floor. The table is initially stationary, while the block has initial speed v[subscript i] and slides to rest relative to the table. The block and table are inside a large vacuum tank, so there is no air resistance, buoyancy, nor thermal losses to the atmosphere. Furthermore the inner surface of the vacuum tank is a perfect mirror so that the tank does not radiatively exchange heat with the block and table. The block and table are homogeneous, both initially have temperature T[subscript i], and they each have large thermal conductivities so that they rapidly attain a common final temperature T[subscript f] after the block has come to rest. The specific heat capacity of the block is c[subscript b] and that of the table is c[subscript t], and these heat capacities are assumed to be temperature independent over the range of temperatures that arises in this problem. (a) Find the common final speed v[subscript f] and temperature T[subscript f] of the block and table. (b) Find the changes in the bulk kinetic energies K (in the center-of-mass frame of the isolated block-table system), the internal energies U, and the entropies S of the block and table. (c) Discuss the first and second laws of thermodynamics in connection with these results.