Question

A bullet of mass m fired from a gun leaves the barrel with a speed v. Length of the barrel is L. Assuming the bullet accelerates uniformly from rest in the barrel. Find average power delivered to the bullet by the gases produced due to the burning of the gunpowder in the barrel.

Answer 1

Let the bullet accelerate with acceleration =a

Time taken to leave the barrel=t

$v-0=at$ and $v^2-0=2aL$

$t=\frac{v}{a}$ and $a=\frac{v^2}{2L}$

Force acting on the bullet $F=ma$

Work done on the bullet $=F.L=ma.L$

Average power delivered to bullet $=\frac{maL}{t}$

$\frac{maL}{\frac{v}{a}}=\frac{m{a}^{2}L}{v}$

$=\frac{m\left(\frac{v^4}{4L^2}\right)L}{v}=\frac{m{v}^3}{4L}$