Elastic strings and springs

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   A particle $P$ of mass $0.4\,\text{kg}$ is attached to one end of a light elastic string of natural length $1\,\text{m}$ and modulus of elasticity $19.6\,\text{N}$. The other end is attached to a fixed point $O$. $P$ is held at $O$ and released from rest, and falls vertically.

   Find the greatest extension of the string in the subsequent motion.

   Mark scheme

   • M1 Energy method from release to lowest point, with $P$ at rest at both positions (1)
   • B1 Loss of GPE $= 0.4 \times 9.8 \times (1 + x)$ (1)
   • B1 Gain in EPE $={\displaystyle \frac{19.6x^{}}{}}$ (1)