Problem

The figure shows the cross section of a garage door with length L = 2.5 m and mass m = 90...

The figure shows the cross section of a garage door with length L = 2.5 m and mass m = 90 kg. At the ends A and B there are rollers of negligible mass constrained to move in the guide whose horizontal portion is at a distance H = 3 m from the floor. The door’s motion is assisted by two counterweights C, each of mass mC (only one counterweight is shown). If the door is released from rest when d = 53 cm, neglecting friction and modeling the door as a uniform thin plate, determine the minimum value of mC so that A will strike the ground with a speed no greater than 0.25 m/s.