1978M1. An amusement park ride consists of a ring of radius A from which hang ropes of length éwith seats for the riders as shown in Figure I. When the ring is rotating at a constant angular velocity o each rope forms a constant angle 0 with the vertical as shown in Figure II. Let the mass of cach rider be m and neglect friction, air resistance, and the mass of the ring, ropes, and seats. In the space below, draw and label all the forces acting on rider X (represented by the point below) under the constant rotating condition of Figure II. Clearly define any symbols you introduce. a. b. Derive an expression for o in terms of A, 4 0 and the acceleration of gravity g. Determine the minimum work that the motor that powers the ride would have to perform to bring the system c. from rest to the constant rotating condition of Figure II. Express your answer in terms of m, g, 4 0, and the speed v of each rider.

1978M1. An amusement park ride consists of a ring of radius A from which hang ropes of length éwith seats for the riders as shown in Figure I. When the ring is rotating at a constant angular velocity o each rope forms a constant angle 0 with the vertical as shown in Figure II. Let the mass of cach rider be m and neglect friction, air resistance, and the mass of the ring, ropes, and seats. In the space below, draw and label all the forces acting on rider X (represented by the point below) under the constant rotating condition of Figure II. Clearly define any symbols you introduce. a. b. Derive an expression for o in terms of A, 4 0 and the acceleration of gravity g. Determine the minimum work that the motor that powers the ride would have to perform to bring the system c. from rest to the constant rotating condition of Figure II. Express your answer in terms of m, g, 4 0, and the speed v of each rider.