Question

A bullet of 50 g is fired from a revolver with a velocity of 100 $m{s}^{-1}$ into an ice block at $0^{\circ }C$. The bullet stops after it gets embedded into ice. Assuming that all the kinetic energy of the bullet is converted into heat energy which is absorbed by the melting ice, find the quantity of the ice that just melted.

Answer 1

Mass of the bullet, $M=50g=0.05kg$

Velocity of the bullet, $V=100m{s}^{-1}$

K.E. of the bullet, $T=\frac{1}{2}M{V}^2=\frac{1}{2}\times 0.05\times 100\times 100=5\times 50\times =250J$

K.E. of heat energy is transformed into heat energy fully.

$\therefore 250J$ of heat energy is used to melt a part of the ice.

$\therefore q=250J$

let the heat of fusion, $\Delta H_f=334J/g$

Let the mass of ice melted be $m$

$\therefore q=m\Delta H_f$

or, $m=\frac{q}{\Delta H_f}=\frac{250}{334}=0.748g$