18 5. A light inextensible string of length a has one end attached to a fixed point O. The other end of the string is attached to a small stone of mass m. The stone is held with the string taut and horizontal. The stone is then projected vertically upwards with speed U. The stone is modelled as a particle and air resistance is modelled as being negligible. Assuming that the string does not break, use the model to (a) find the least value of U so that the stone will move in complete vertical circles. (6) The string will break if the tension in it is equal to 11 2 mg Given that U = 2 ag , use the model to (b) find the total angle that the string has turned through, from when the stone is projected vertically upwards, to when the string breaks, (6) (c) find the magnitude of the acceleration of the stone at the instant just before the string breaks. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________