Question Number 225700 by mr W last updated on 07/Nov/25
Commented by mr W last updated on 07/Nov/25
$${mass}\:{of}\:{bullet}:\:{m} \\ $$$${mass}\:{of}\:{uniform}\:{rod}:\:{M} \\ $$$${bullet}\:{keeps}\:{embedded}\:{in}\:{rod}\:{after} \\ $$$${the}\:{strike}. \\ $$
Commented by ajfour last updated on 07/Nov/25
$${mvx}=\left(\frac{{ML}^{\mathrm{2}} }{\mathrm{3}}+{mx}^{\mathrm{2}} \right)\omega \\ $$$$\omega=\frac{{vx}}{\frac{{ML}^{\mathrm{2}} }{\mathrm{3}{m}}+{x}^{\mathrm{2}} }=\frac{{v}}{{x}+\frac{{k}}{{x}}} \\ $$$$\omega\:{is}\:{max}\:{when}\:{x}=\sqrt{{k}} \\ $$$$\:\:\:\:\:\:{so}\:\:\:\boldsymbol{{x}}_{\boldsymbol{{c}}} =\sqrt{\frac{\boldsymbol{{M}}}{\boldsymbol{{m}}}}\left(\frac{{L}}{\:\sqrt{\mathrm{3}}}\right) \\ $$
Commented by mr W last updated on 07/Nov/25
$${great}\:{sir}! \\ $$