Hooke's law and elastic energyAQA A-Level Further Maths: Mind map

Exam questions on Hooke's law and elastic energy

1. A light elastic string has natural length 1.2 m and modulus of elasticity 36 N. One end is fixed to a point $A$ on a smooth horizontal table and a particle $P$ of mass 0.5 kg is attached to the other end. $P$ is held on the table with the string stretched to a total length of 1.5 m.
   $P$ is released from rest. Find the speed of $P$ when the string reaches its natural length.2 marks
2. A particle of mass 2 kg hangs in equilibrium at the end of a light elastic string. The other end of the string is fixed to a point $O$. The natural length of the string is 0.5 m and its extension in equilibrium is 0.25 m. Take $g=9.8\text{ m s}^{-2}$.
   The particle is pulled down until the extension of the string is 0.6 m and is then released from rest. Find the speed of the particle at the instant the string becomes slack.2 marks
3. A toy truck of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N. The other end of the string is fixed to a point $B$ on a smooth horizontal floor. The truck is pulled along the floor until it is 1.0 m from $B$, with the string straight, and is then released from rest.
   Find the tension in the string and the initial acceleration of the truck.3 marks