A simple model of orbital motion under a central force can be constructed by considering t...

A simple model of orbital motion under a central force can be constructed by considering the motion of a disk D sliding with no friction over a horizontal surface while connected to a fixed point O by a linear elastic cord of constant k and unstretched length L0. Let the mass of D be m = 0.45 kg and L0 = 1 m. Suppose that when D is at its maximum distance from O, this distance is r0 = 1.75 m and the corresponding speed of D is υ0 = 4 m/s. Determine the elastic cord constant k such that the minimum distance between D and O is equal to the unstretched length L0.

Figure P5.89