A rectangular upandover garage door is 6 feet high. On each side of the door is a pin B, 2 feet from the bottom, which slides in a vertical groove. On both sides of the door the points D, 2 feet from the top, are connected by light ropes of length 2 feet to the points F at the top of the grooves 6 feet above the ground. From each of the pins B a vertical cord is taken over a pulley and carries a counterweight as shown. The door weighs 20 kg and its centre of gravity, C, is equidistant from its top and bottom edges.
1. Describe accurately in words the path followed by the point E as the door opens and closes.
2. Describe accurately in words the path followed by the point A as the door opens and closes.
3. Neglecting all frictional forces, find the weight of each counterweight if the door is to remain stationary in any position between fully open and fully closed. 
