When the ice skater in Section 13-2 pushes herself away from the railing her internal energy E_int, decreases. What happens to her internal energy when she skates up to the railing and then pushes herself to a stop?

The potential energy will increase as the ice skater skates up. This is so since the potential energy is directly proportional to the height of the body. Increasing the potential energy will result the decrease of the internal energy of the ice skater but the kinetic energy of the ice skater should remain constant. If the kinetic energy of the ice skater is not constant, then the decrease of potential energy will appear in the form of increase of kinetic energy as the energy is just transform from one form to another. Therefore keeping kinetic energy as a constant quantity, the internal energy of the ice skater will increase as she skates up to the railing and then pushes herself to a stop.