Question

A catapult consists of two parallel rubber strings, each of lengths 10 cm and cross-sectional area 10 $m{m}^2.$ When stretched by 5 cm, it can throw a stone of mass 100 gm to a vertical height of 25 m. Determine Young's modulus of elasticity of rubber.

Answer 1

A stretched catapult has elastic potential energy stored in it (Strain energy stored in both the rubber strings) $U=\left(\frac{1}{2}\frac{YA{L}^2}{L}\right)\times 2$ This energy, when imparted to the stone, it flies off a height 20 m. Energy possessed by the Stone = mgh. Now, $U=mgh\Rightarrow \frac{YA{l}^2}{L}=mgh$ Y = $\frac{mghL}{A{l}^2}=\frac{1\times {10}^{-1}\times 10\times 25\times {10}^{-1}}{10\times {10}^{-6}\times (5\times 10{}^{-2}{)}^2}$ Y = $10\times {10}^{8}N/m^2$