A small ball rolls down from a quarter-circle to a frictionless plane. What will be the magnitude of the normal force when the ball arrives at the tangent point of the circle and the plane? According to the centripetal force formula, the normal force will be 3 "mg" when the curvature radius of the circle is considered, but will be "mg" instead when the curvature radius of the plane is considered. Which one is the correct answer? The difficulty is that Newton's second law requires the second time derivative of displacement to be continuous; however, this condition is not fulfilled at the tangent point. In this paper we will discuss several possible solutions to this problem in detail. (Contains 3 figures.)