The formula for kinetic energy is given as:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

For head-on collisions:

$\overline{){{\mathbf{v}}}_{\mathbf{1}\mathbf{f}}{\mathbf{=}}\frac{\mathbf{(}{\mathbf{m}}_{\mathbf{1}}\mathbf{-}{\mathbf{m}}_{\mathbf{2}}\mathbf{)}}{\mathbf{(}{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{)}}{{\mathbf{v}}}_{{\mathbf{10}}}}$

and

$\overline{){{\mathbf{v}}}_{\mathbf{2}\mathbf{f}}{\mathbf{=}}\frac{\mathbf{2}{\mathit{m}}_{\mathbf{1}}}{\mathbf{(}{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{)}}{{\mathbf{v}}}_{{\mathbf{10}}}}$

The collision between a hammer and a nail can be considered to be approximately elastic. Calculate the kinetic energy acquired by a 13-g nail when it is struck by a 560-g hammer moving with an initial speed of 4.6m/s .

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