6 A light elastic string has one end attached to a point \(A\) fixed on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. The other end of the string is attached to a particle of mass 6 kg . The elastic string has natural length 4 metres and modulus of elasticity 300 newtons. The particle is pulled down the plane in the direction of the line of greatest slope through \(A\). The particle is released from rest when it is 5.5 metres from \(A\).
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1. Calculate the elastic potential energy of the string when the particle is 5.5 metres from the point \(A\).
2. Show that the speed of the particle when the string becomes slack is \(3.66 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to three significant figures.
3. Show that the particle will not reach point \(A\) in the subsequent motion.