Question

A 1 kg hammer moving with a velocity of 50 m/s strikes a 200 gm nail in a block of wood. If half the energy of hammer goes into heating the nail, what will be the rise in temperature of nail? Take specific ht capacity of ironn nail as 452 j/kg c

Answer 1

$$\begin{gathered} \mathrm{Kinetic}\mathrm{energy}\mathrm{of}\mathrm{hammer}: \\ \mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2 \\ =\frac{1}{2}\times 1\times {50}^2 \\ =1250\mathrm{J} \\ \mathrm{Heat}\mathrm{energy}\mathrm{to}\mathrm{the}\mathrm{nail}: \\ \mathrm{H}=\frac{\mathrm{K}}{2} \\ =\frac{1250}{2} \\ =625\mathrm{J} \\ \mathrm{Temperature}\mathrm{rise}\mathrm{of}\mathrm{the}\mathrm{nail}: \\ △\mathrm{t}=\frac{\mathrm{H}}{\mathrm{mc}} \\ =\frac{625}{0.2\times 452} \\ =6.9^{\mathrm{o}}\mathrm{C} \end{gathered}$$