How do the potential energy and the kinetic energy change as the skater moves from the top of the u-shaped ramp to the bottom?

In the general sense of energy, there are only two types: the potential energy and the kinetic energy. All other types of energy like heat, electricity, mechanical, chemical, etc, are all under these two classification.

The potential energy is characterized as the energy of the object at a certain height. Its equation is: PE = mgh, where m is mass, g is the gravity and h is the height. Kinetic energy is the energy of the object in motion. The equation is: KE = 1/2mv², where v is the velocity.

Therefore, at the top of the U-shaped ramp, KE=0 and PE is at its maximum. As it moves down the ramp, PE decreases and KE increases. When it reaches to a stop, KE=0 and PE=0.

Yes it would be a physical change.