6. A particle of mass 5 kg is attached to a string \(A B\) and a rod \(B C\) at the point \(B\). The string \(A B\) is light and elastic with modulus \(\lambda \mathrm { N }\) and natural length 2 m . The rod \(B C\) is light and of length 2 m . The end \(A\) of the string is attached to a fixed point and the end \(C\) of the rod is attached to another fixed point such that \(A\) is vertically above \(C\) with \(A C = 2 \mathrm {~m}\). When the particle rests in equilibrium, \(A B\) makes an angle of \(50 ^ { \circ }\) with the downward vertical.

1. Determine, in terms of \(\lambda\), the tension in the string \(A B\).
2. Calculate, in terms of \(\lambda\), the energy stored in the string \(A B\).
3. Find, in terms of \(\lambda\), the thrust in the rod \(B C\).