Question

A bullet moving with a uniform velocity stops suddenly after hitting target. Let whole mass melts be $m$ , specific heat be $S$ , initial temperature be ${25}^{o}C$ , melting point be ${475}^{o}C$ , and the latent heat be $L$ . Then $v$ is given by

Answer 1

From conservation of energy, the whole kinetic energy is changed in thermal energy.

$\frac{1}{2}m{v}^2=mS\Delta T+mL$

$\frac{1}{2}{v}^2=S\Delta T+L$

$\frac{1}{2}{v}^2=S\left(475-25\right)+L$

$v^2=2\left(450S+L\right)$

$v=\sqrt{2\left(450S+L\right)}$

$v=\sqrt{\left(900S+2L\right)}$

Thus velocity relation with specific heat and latent heat of fusion is determined.