One of the exercises in my textbook (Giancoli) deals with a car going up the slope of a hill and then decending into a valley. Curvature/radius is $R$ in both situation, and I'm supposed to answer the question at which point (top of hill/lowest point in valley) the normal force is smallest and largest respectively. Intuitively I'm ok answering the question, in that I feel lightest at the top of the hill (lowest normal force), and heavier at the bottom of the valley (largest normal force), but I'm having a hard time figuring out the equations. In the answers section it says, at the crest of the hill the centripal force is directed downwards, so the normal force must be less than the weight. But force implies acceleration in the same direction, does it not? But if there was acceleration in the y direction, at that very instant, would the car not "sink" into the ground?
edit: I'm sorry this is most certainly not a homework assignment, I'm 45 and I'm pursuing physics out of interest in astronomy.