Abstract
A small ball rolls down from a quarter-circle to a frictionless plane. What will be themagnitude of the normal force when the ball arrives at the tangent point of the circle andthe plane? According to the centripetal force formula, the normal force will be3mg when the curvature radius of the circle is considered, but will bemg instead when the curvature radius of the plane is considered. Which one is the correctanswer? The difficulty is that Newton’s second law requires the second time derivative ofdisplacement 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.
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