Problem 1.234

A thin uniform rod \(A B\) of mass \(m=1.0 \mathrm{~kg}\) moves translationally with acceleration \(w=2.0 \mathrm{~m} / \mathrm{s}^{2}\) due to two antiparallel forces \(\mathbf{F}_ {1}\) and \(\mathbf{F}_ {2}\) (Fig. 1.52). The distance between the points at which these forces are applied is equal to \(a=20 \mathrm{~cm} .\) Besides, it is known that \(F_{2}=5.0 \mathrm{~N} .\) Find the length of the rod.