- A light inextensible string of length \(a\) has one end attached to a fixed point \(O\). The other end of the string is attached to a small stone of mass \(m\). The stone is held with the string taut and horizontal. The stone is then projected vertically upwards with speed \(U\).
The stone is modelled as a particle and air resistance is modelled as being negligible.
Assuming that the string does not break, use the model to
- find the least value of \(U\) so that the stone will move in complete vertical circles.
The string will break if the tension in it is equal to \(\frac { 11 m g } { 2 }\)
Given that \(U = 2 \sqrt { a g }\), use the model to - find the total angle that the string has turned through, from when the stone is projected vertically upwards, to when the string breaks,
- find the magnitude of the acceleration of the stone at the instant just before the string breaks.