Question

The rubber cord of a catapult has a cross sectional area 1.0mm^2 and a total unstretched length 10.0cm. It I stretched to 12.0cm and then released to project a missile of mass 5.0g. From energy considerations, or otherwise, calculate the velocity of projection, taking the young modulus for the rubber as 5.0x10^8 Pa. State the assumptions made in your calcukation

Answer 1

Potentional energy of the stretched cord

$E_p=\frac{E\times S\times\delta l^2}{2l}$

where E - young modulus, S - cross sectional area, l - unstretched length, $\delta l$ - difference in length.

$E_p=\frac{5\times 10^8 \times 10^{-6} \times2\times 0.02^2}{2\times0.1}=2J$

Kinetic energy of the missile:

$E_k=\frac{mV^2}{2}$

Velocity:

$V=\sqrt\frac{2E_k}{m}=\sqrt\frac{2\times2}{5}=0.9m/s$

Assumption is cord's cross sectional area doesnt change during stretching.