Elastic potential energyEdexcel International A Level Further Maths: Mind map

Exam questions on Elastic potential energy

1. A light elastic string has natural length $0.6$ m and modulus of elasticity $30$ N. The string is stretched to a length of $0.9$ m.
   The string is now stretched slowly from a length of $0.9$ m to a length of $1.1$ m. Find the work done against the tension of the string.2 marks
2. A particle $P$ of mass $0.5$ kg is attached to one end of a light elastic spring of natural length $0.4$ m and modulus of elasticity $20$ N. The other end of the spring is fixed to a point $O$ on a smooth horizontal table. $P$ is held on the table at a distance $0.6$ m from $O$ and released from rest.
   Find the speed of $P$ when it is $0.5$ m from $O$.2 marks
3. A particle $P$ of mass $2$ kg is attached to one end of a light elastic string of natural length $1.5$ m and modulus of elasticity $60$ N. The other end of the string is fixed to a point $A$ on a ceiling. $P$ is released from rest at $A$ and falls vertically. Take $g=9.8$ m s$^{-2}$ and ignore air resistance.
   Show that, when $P$ first comes to instantaneous rest, the extension $x$ metres of the string satisfies $20x^2-19.6x-29.4=0$.3 marks