10 A light, elastic string has natural length 0.5 m and modulus of elasticity 49 N. The end A is attached to a point on a ceiling. A small object of mass of 3 kg is attached to the end B of the string and hangs in equilibrium.
(1) Calculate the length AB.
A second string, identical to the first one, is now attached to the object at B and to a point C on the floor, 2.5 m vertically below the point A. The system is in equilibrium with B a distance xm below A, as shown in the diagram below.
xm
BO
2.5 m
(ii) Find the tension in each of the strings in terms of x and hence show that x = 1.4.
(iii) Calculate the total elastic potential energy in the strings when the object hangs in equilibrium.
The object is now pulled down 0.1 m from its equilibrium position and released from rest.
(iv) Calculate the speed of the object when it passes through the equilibrium position. Any resistances to motion may be neglected.
Help will be most appreciated especially (iv) .