Turn over 19 Question 5 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 10 marks) 20 6. α Y X l Figure 2 A light elastic spring has natural length 3l and modulus of elasticity 3mg. One end of the spring is attached to a fixed point X on a rough inclined plane. The other end of the spring is attached to a package P of mass m. The plane is inclined to the horizontal at an angle α where tan α = 3 4 The package is initially held at the point Y on the plane, where XY = l . The point Y is higher than X and XY is a line of greatest slope of the plane, as shown in Figure 2. The package is released from rest at Y and moves up the plane. The coefficient of friction between P and the plane is 1 3 By modelling P as a particle, (a) show that the acceleration of P at the instant when P is released from rest is 17 15 g (5) (b) find, in terms of g and l , the speed of P at the instant when the spring first reaches its natural length of 3l . (6) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________