Problem

The opening and closing of the manually operated road barrier is assisted by the counterwe...

The opening and closing of the manually operated road barrier is assisted by the counterweight C and linear elastic torsional spring with constant kt that is mounted at O. Assume that the length of the arm is L = 15.7 ft and that it consists of a section of aluminum tubing from A to B of length l = 11.6 ft and weight 20 lb and a steel support section from B to D of weight 40 lb. Model both sections of the arm as uniform thin rods. Model the counterweight as a uniform rectangular rigid body of weight Wc, height h, and width w, and let the hinge O be a distance d = 2.58 ft from the right end of section BD.

Using these assumptions, design the unspecified parameters δ, h, w, WC, and the torsional spring (its stiffness kt and the position at which it is undeformed) so that a small nudge will close the barrier from the vertical position and so that the arm will reach the closed position with an angular velocity that is less than 0.25 rad/s. In addition, make sure that the barrier is still easy to open.