The figure shows the cross section of a garage door with length L = 9 ft and weight W = 17...

The figure shows the cross section of a garage door with length L = 9 ft and weight W = 175 lb. At A and B there are rollers of negligible mass constrained to move in the guide whose horizontal portion is at a distance H = 11 ft from the floor. The door’s motion is assisted by two springs, each with constant k (only one spring is shown). The door is released from rest when d = 26 in. and the spring is stretched 4 in. Neglecting friction, knowing that, when A touches the floor, B is in the vertical portion of the guide, and modeling the door as a uniform thin plate, determine the minimum value of k so that A will strike the ground with a speed no greater than 1 ft/s.

Figure P8.32