24 7. A spring of natural length a has one end attached to a fixed point A. The other end of the spring is attached to a package P of mass m. The package P is held at rest at the point B, which is vertically below A such that AB = 3a. After being released from rest at B, the package P first comes to instantaneous rest at A. Air resistance is modelled as being negligible. By modelling the spring as being light and modelling P as a particle, (a) show that the modulus of elasticity of the spring is 2mg (5) (b) (i) Show that P attains its maximum speed when the extension of the spring is 1 2 a (ii) Use the principle of conservation of mechanical energy to find the maximum speed, giving your answer in terms of a and g. (6) In reality, the spring is not light. (c) State one way in which this would affect your energy equation in part (b). (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________