Problem 1.273

A uniform rod of mass $m=5.0 \mathrm{~kg}$ and length $l=90 \mathrm{~cm}$ rests on a smooth horizontal surface. One of the ends of the rod is struck with the impulse $J=3.0 \mathrm{~N} \cdot \mathrm{s}$ in a horizontal direction perpendicular to the rod. As a result, the rod obtains the momentum $p=3.0 \mathrm{~N} \cdot \mathrm{s}$. Find the force with which one half of the rod will act on the other in the process of motion.