Question

A bomb of mass $3.0kg$ explodes in air into two pieces of masses $2.0kg$ and $1.0kg$. The smaller mass goes at a speed of $80m/s$. The total energy (in $kj$ ) imparted to the two fragments is

Answer 1

Find speed of the larger mass.
Given, mass of the bomb, $M=3kg$
Mass of the two pieces, $=2kg$ and $1kg$
Speed of the smaller fragment, $80m/s$
And initially the bomb is at rest. So initial momentum, $p_i=0$

As there is no external force act on the shell, so momentum will be conserved,

$0=1\times 80+2\times v$

$v=-40m/s$

$-ve$ sign indicates the opposite direction of the motion.

Find the total energy imparted to the two fragments.
Formula used: $K.E=\frac{1}{2}m{v}^2$

Total energy imparted to the two fragments,
$K.E=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2$

$=\frac{1}{2}\times 1\times (80{)}^2+\frac{1}{2}\times 2\times (40{)}^2$

$=4800j=4.8kj$