7
\includegraphics[max width=\textwidth, alt={}, center]{7f8646df-a7d8-4ca1-a6ee-3ceab6bb83af-4_232_905_762_621} A light elastic string has natural length 10 m and modulus of elasticity 130 N . The ends of the string are attached to fixed points \(A\) and \(B\), which are at the same horizontal level. A small stone is attached to the mid-point of the string and hangs in equilibrium at a point 2.5 m below \(A B\), as shown in the diagram. With the stone in this position the length of the string is 13 m .

1. Find the tension in the string.
2. Show that the mass of the stone is 3 kg . The stone is now held at rest at a point 8 m vertically below the mid-point of \(A B\).
3. Find the elastic potential energy of the string in this position.
4. The stone is now released. Find the speed with which it passes through the mid-point of \(A B\).