Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_76

4/76 In the figure is shown a system used to arrest the motion of an airplane landing on a field of restricted length. The plane of mass \(m\) rolling freely with a velocity \(v_0\) engages a hook which pulls the ends of two heavy chains, each of length \(L\) and mass \(\rho\) per unit length, in the manner shown. A conservative calculation of the effectiveness of the device neglects the retardation of chain friction on the ground and any other resistance to the motion of the airplane. With these assumptions, compute the velocity \(v\) of the airplane at the instant when the last link of each chain is put in motion. Also determine the relation between the displacement \(x\) and the time \(t\) after contact with the chain. Assume each link of the chain acquires its velocity \(v\) suddenly upon contact with the moving links.