Question

The rubber cord of a catapult has a cross-sectional area of 1.0 mm^2 and a total upstretched length 10.0 cm. It is stretched to a 120 cm and then released to project a missile of mass 50 g. From energy consideration or otherwise, calculate the velocity of projection, taking Young’s modulus for the rubber as 50 x 108 Nm^-2. State the assumptions made in your calculation.

Answer 1

Since the potential tensile energy is $E_p=\frac {k\times (\Delta l) ^ 2} {2}$ , where $k$ is the coefficient of elasticity ,$\Delta l$ is the change in body length. $k =\frac {E\times S} {l}$ , where $l$ length, $E$ is Young's modulus, $S$ is the cross-sectional area of the body.

According to the law of conservation of energy $E_p=E_c$ , where $E_c$ is the kinetic energy of the body, therefore

$\ frac {\frac {E\times S} {l }\times (\Delta l) ^ 2} {2} =\frac {m\times v ^ 2} {2}$ , where $m$ body weight, $v$ body speed

$v= \sqrt{\frac{\frac{E\times S}{l}\times (\Delta l)^2}{m}} =\sqrt{\frac{\frac{50\times 10^8\times 10^{-6}}{0.1}\times 1.1^2}{0.05}}=1100$ m/s.