Question

A shell of mass $100kg$ is fired from a cannon with a mass of $5\times {10}^{3}kg$. The kinetic energy of the shell at the end of the barrel is $7.5\times {10}^{6}J$. What is the kinetic energy imparted to the cannon by the recoil? Find the ratio of forces experienced by the shell and the cannon.

Answer 1

The conservation of momentum yields
$p_{shell}=p_{cannon}$
$\Rightarrow K{E}_{cannon}=\frac{p_{can}^2}{2M_{can}};{KE}_{shell}=\frac{p_{sh}^2}{2M_{sh}}$
$\Rightarrow K{E}_{cannon}=\frac{M_{sh}}{M_{canon}}{KE}_{sh}=\frac{100}{5\times {10}^3}\times 7.5\times {10}^6=1.5\times {10}^{5}J$
Further $\frac{F_1}{F_2}=1$. $F_1$ and $F_2$ are action reaction pair