Problem 15.140 ! A particle of mass m is attached to a light string that runs through a smooth hole in a circularly shaped bowl that lies in the vertical plane. A force P is applied to the other end of the string so that the mass can rotate in a horizontal circle with constant speed 1. Use sin 30 = 1/2 and cos 30 = 3/2 in your calculations. (a) If the tension in the string is P = mg when the mass is in 1 determine its speed " as a function of g and R. (b) If the force is increased to P2 so that the mass moves to the new circular path shown in 2 determine the new speed of the mass "2. (c) Determine, as a function of m and g, the required tension in the string P in 2 Use sin 15 = 3-1 22 and cos 15 = 3+1 22. 30 R 30 P