Turn over 23 Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 10 marks) 24 7. θ O P u 2 5 a Figure 5 A package P of mass m is attached to one end of a string of length  2 5 a . The other end of the string is attached to a fixed point O. The package hangs at rest vertically below O with the string taut and is then projected horizontally with speed u, as shown in Figure 5. When OP has turned through an angle θ and the string is still taut, the tension in the string is T The package is modelled as a particle and the string as being light and inextensible. (a) Show that  T = 3mg cos θ – 2mg + 5 2 2 mu a (6) Given that P moves in a complete vertical circle with centre O (b) find, in terms of a and g, the minimum possible value of u (2) Given that  u = 2 ag (c) find, in terms of g, the magnitude of the acceleration of P at the instant when OP is horizontal. (3) (d) Apart from including air resistance, suggest one way in which the model could be refined to make it more realistic. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________