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\includegraphics[max width=\textwidth, alt={}, center]{7a67db39-4934-4808-a56b-c6841950d324-3_591_668_776_737}
Each of two identical strings has natural length 1.5 m and modulus of elasticity 18 N . One end of one of the strings is attached to \(A\) and one end of the other string is attached to \(B\), where \(A\) and \(B\) are fixed points which are 3 m apart and at the same horizontal level. \(M\) is the mid-point of \(A B\). A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to the other end of each of the strings. \(P\) is held at rest at the point 0.8 m vertically above \(M\), and then released. The lowest point reached by \(P\) in the subsequent motion is 2 m below \(M\) (see diagram).
- Find the maximum tension in each of the strings during \(P\) 's motion.
- By considering energy,
(a) show that the value of \(m\) is 0.42 , correct to 2 significant figures,
(b) find the speed of \(P\) at \(M\).