6 Two identical light elastic strings, each of length \(l\) and modulus of elasticity \(\lambda m g\) are attached to a particle \(P\) of mass \(m\). The other end of the first string is attached to a fixed point A , and the other end of the second string is attached to a fixed point B . The points A and B are such that A is above and to the right of B and both strings are taut. The string attached to A makes an angle of \(30 ^ { \circ }\) with the vertical, and the string attached to B makes an angle of \(\theta ^ { \circ }\) with the horizontal, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{feb9a438-26b0-41d3-b044-6acd6efccde0-6_546_533_699_242} The system is in equilibrium in a vertical plane. The extension of the string attached to A is 0.9 l and the extension of the string attached to B is \(0.5 l\).

1. Explain how you know that APB is not a straight line.
2. Show that the elastic potential energy stored in string AP is \(k m g l\), where the value of \(k\) is to be determined correct to \(\mathbf { 3 }\) significant figures.