Elastic energy and the work-energy principleEdexcel A-Level Further Maths: Mind map

Exam questions on Elastic energy and the work-energy principle

1. A light elastic string has natural length $0.8$ m and modulus of elasticity $40$ N. It is stretched so that its extension is $0.2$ m.
   The string is stretched further until its extension is $0.4$ m. Calculate the additional work done in stretching it.2 marks
2. A particle of mass $2$ kg is attached to one end of a light elastic string of natural length $1.5$ m and modulus of elasticity $147$ N. The other end of the string is fixed to a point $O$. Take $g=9.8$ m s$^{-2}$.
   The particle is now held at rest with the string just taut, and then released. Find the speed of the particle when it passes through the equilibrium position.2 marks
3. A particle $P$ of mass $0.4$ kg lies on a horizontal table. It 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 $A$ on the table. $P$ is pulled to a point $1$ m from $A$, with the string stretched, and released from rest. Take $g=9.8$ m s$^{-2}$.
   The table is smooth. Find the speed of $P$ when the string becomes slack.3 marks