Consider this setup to study conservation of energy:
It is usually taught that the potential energy at any point on this roller coaster is given by:
Where $h$ is the height above the ground.
But the gravity is not the only force here. There is friction due to the the surface of the roller coaster, then there is air resistance, and finally the normal force to the surface of the roller coaster (the one that keeps it from falling down).
We can neglect friction and air resistance to make the problem simpler but how can we neglect the normal force? I am clearly missing something, can someone help?