Imagine an initially stationary block is placed at some height on a frictionless ramp. The ramp has several hills and valleys in it. Assume the block never flies off the ramp, the hills have identical circular tops, and the hills are of progressively greater heights, all shorter than the height at which the block is first placed. Why is the normal force on the block different from hilltop to hilltop? I realize that the velocity and kinetic energy of the block varies from hilltop to hilltop as it is transferred to and from gravitational potential energy. I believe this means that the centripetal acceleration is greater on shorter hills, because the kinetic energy and thus the velocity is greater there - right? But how is this related to the normal force acting on the block?