A light inextensible string AB has the end A fixed to a vertical wall. The ends B is attached to a small elastic object which is drawn a side, from the wall, until the string makes an angle of 60° with the wall. The particle is then released from rest. Find the angle which the string makes with the wall when the particle next comes to instantaneous rest if the value of e is .
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This problem involves conservation of energy for an elastic object on a string. The object is released from rest at an initial angle of 60° and we must find the next angle at which it comes to rest. The coefficient of restitution, e, is 3/4, indicating an inelastic collision with the wall.
The initial potential energy is converted to kinetic energy and then, after an inelastic impact, to a new maximum potential energy. The relationship is given by the energy loss on impact: the square of the coefficient of restitution relates the heights before and after collision. The maximum height after impact is times the height before impact.
Using trigonometry, the height is proportional to (1 - cosθ). Setting the initial height at 60° equal to the final height gives the equation: . Substituting e=3/4 and cos60°=0.5, we solve for the final angle θf.
Final Answer: 97.2°