1 A light elastic string has one end fixed to a vertical pole at A . The string passes round a smooth horizontal peg, P , at a distance \(a\) from the pole and has a smooth ring of mass \(m\) attached at its other end B . The ring is threaded onto the pole below A . The ring is at a distance \(y\) below the horizontal level of the peg. This situation is shown in Fig. 1.
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\caption{Fig. 1}
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The string has stiffness \(k\) and natural length equal to the distance AP .
- Express the extension of the string in terms of \(y\) and \(a\). Hence find the potential energy of the system relative to the level of P .
- Use the potential energy to find the equilibrium position of the system, and show that it is stable.
- Calculate the normal reaction exerted by the pole on the ring in the equilibrium position.