3 A light elastic string has natural length 1.2 m and stiffness \(637 \mathrm { Nm } ^ { - 1 }\).
- The string is stretched to a length of 1.3 m . Find the tension in the string and the elastic energy stored in the string.
One end of this string is attached to a fixed point \(A\). The other end is attached to a heavy ring \(R\) which is free to move along a smooth vertical wire. The shortest distance from A to the wire is 1.2 m (see Fig. 3).
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\caption{Fig. 3}
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The ring is in equilibrium when the length of the string \(A R\) is 1.3 m . - Show that the mass of the ring is 2.5 kg .
The ring is given an initial speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) vertically downwards from its equilibrium position. It first comes to rest, instantaneously, in the position where the length of AR is 1.5 m .
- Find \(u\).
- Determine whether the ring will rise above the level of A .