Question

In a simple firing testing, 1.03 g of an explosive material, which has a power index of 211.71

and can produce a gas product up to 9.2 dm3 per gram, was packed in a handgun ammunition

cartridge and triggered to detonate to propel a projectile weighed 2 g out of the barrel. The

efficiency of the energy transferred from the explosion to the projectile is 13 %. Calculate the

propelled bullet velocity in m/s if the heat evolved and gas volume produced in a detonation of

per gram picric acid is 3150 J/g and 0.831 dm3

.

Answer 1

Energy produced per gram of picric acid, $Q_{picric}=3150\space J/g$

Volume of picric acid, $V_{picric}=0.831\space dm^3$

Power Index $=211.71$

Let energy produced per gram of explosive material be $Q$

Volume of explosive material per gram $=9.2\space dm^3/g$

Volume of explosive material, $(V)$ for 1.03 g $=9.2\times1.03=9.476\space dm^3$

Power Index $=\dfrac{QV}{Q_{picric}V_{picric}}$

$Q=\dfrac{211.71\times3150\times0.831}{9.476}$

$Q=58482.765\space J/g$

Energy of Explosion $=58482.765\times1.03=60237.247\space J$

Efficiency of energy transferred from the explosion to the projectile $=13\%$

Energy of projectile $=0.13\times60237.247=7830.84\space J$

Mass of projectile, $m=2\space g=2\times10^{-3}\space kg$

Let velocity of projectile be $v$

$\dfrac{1}{2}mv^2=7830.84$

$v=\sqrt{\dfrac{2\times7830.84}{2\times10^{-3}}}$

$v=2798.36\space m/s$