A pendulum consists of a 3.4 kg stone swinging on a 3.7 m string of negligible mass. The stone has a speed of 8.2 m/s when it passes its lowest point. (a) What is the speed when the string is at 57 ° to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system?