All Problems Laws of Conservation
Problem 1.199
Two small identical discs, each of mass \(m,\) lie on a smooth horizontal plane. The discs are interconnected by a light non-deformed spring of length \(l_{0}\) and stiffness \(x .\) At a certain moment one of the discs is set in motion in a horizontal direction perpendicular to the spring with velocity \(v_{0} .\) Find the maximum elongation of the spring in the process of motion, if it is known to be considerably less than unity.
1.199. \(\varepsilon_{\max } \approx m v_{0}^{2} / \mathcal{l} l_{0}^{2}\). The problem is easier to solve in the frame of the centre of inertia.