For a)
Since no more information is given, I'll take this using the law of conservation of energy, where no energy is lost and all the dissipated energy is in the form of heat energy.
Energy (kinetic) at first is given by
Energy at the peak is given by

plus the kinectic energy.
The second total energy is less than the first one. The difference gives the heat energy dissipated.
b) Well, work done is Force times displacement in the direction of the force.
The work done on the box is equal in magnitude to its work done. You know the force, find the displacement, which in this case is equal to the distance AB.
