A small bead of mass m is constrained to move along a frictionless track as shown. The track consists of a semicircular portion of radius R followed by a straight part. At the end of the straight portion there is a horizontal spring of spring constant k attached to a fixed support. At the top of the circular portion of the track, the bead is pushed with an unknown speed v_0 . The bead comes momentarily to rest after compressing the spring a distance d . The magnitude of the acceleration due to the gravitational force is g . What is the magnitude of the normal force exerted by the track on the bead at the point A, a height R above the base of the track? Express your answer in terms of m , k , R, D , and g but not in terms of V_0 .

Question

A small bead of mass m is constrained to move along a frictionless track as shown. The track consists of a semicircular portion of radius  R followed by a straight part. At the end of the straight portion there is a horizontal spring of spring constant k attached to a fixed support. At the top of the circular portion of the track, the bead is pushed with an unknown speed  v_0  . The bead comes momentarily to rest after compressing the spring a distance d . The magnitude of the acceleration due to the gravitational force is g . What is the magnitude of the normal force exerted by the track on the bead at the point A, a height R  above the base of the track? Express your answer in terms of m , k ,  R, D , and g  but not in terms of   V_0 .