Problem

For the barrier gate shown, assume that the arm consists of a section of aluminum tubing f...

For the barrier gate shown, assume that the arm 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. The overall length of the arm is L = 15.7 ft. In addition, the 120 lb counterweight C is placed a distance δ from the hinge at O, and the hinge is d = 2.58 ft from the right end of section BD. Model the two sections AB and BD as uniform thin bars, and model the counterweight as a uniform block of height h = 14 in. and width w = 9 in. Using these new assumptions, determine the distance δ so that the angular velocity of the arm is 0.25 rad/s as it reaches the horizontal position after being nudged from the vertical position.