A bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system
A bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system
Momentum is $\frac{{mvM}}{{M + m}}$
Kinetic energy is $\frac{{m{v^2}}}{2}$
Momentum is $\frac{{mv(M + m)}}{M}$
Kinetic energy is $\frac{{{m^2}{v^2}}}{{2(M + m)}}$
A bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system
Initial momentum = $mv$
Final momentum = $(m + M)V$
By conservation of momentum $mv = (m + M)V$
Velocity of (bag + bullet) system$V = \frac{{mv}}{{M + m}}$
Kinetic energy = $\frac{1}{2}(m + M)\;{V^2}$
=$\frac{1}{2}(m + M){\left( {\frac{{mv}}{{M + m}}} \right)^2}$$ = \frac{1}{2}\frac{{{m^2}{v^2}}}{{M + m}}$
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