Question

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A railroad car of mass m is attached to a stop in a railroad yard. The stop consists of four identical metal rods of length L, radius R and elastic modulus E that are arranged symmetrically and are fixed to a rigid wall at one end and welded to a rigid plate at the other. The plate is hooked to the stationary railroad car as shown. In a docking maneuver, a second car of mass m approaches the first at speed v₁. If the second car locks onto the first upon contact, determine the response of the two car system after docking.

Answer 1

E = F/A/delta L/L A = 4 (pi R^2) F = (E 4 pi R^2/L) delta L change in momentum delta P = m v_1 delta P/delta t = (4 pi R^2 E/L) delta L m v_1 = 4 pi R^2 E delta L/L delta t = m v_1 L/4 pi R^2 E delta L