As Louis the Lamp is making his great escape from the lonely attic, he must jump onto the trap door that will set him free. Before he leaps, however, he must know the tension he will place on the rope that supports the door.

What is known:

• Louis has a mass of 0.2 slugs and is located in the center of the door.
• The trap door is supported by a ball and socket and a bearing with a circular shaft on one side. The other side is supported by a rope that is attached to the wall.
• The trap door and the rope have the dimensions shown.
• Assume that the bearing does not exert any moments on the door, and neglect the mass of the door.

  
  Problem Description Diagram

What are the reaction components at each of the supports? What is the tension in the rope?

• Draw a free-body diagram. Force diagrams for each joint is shown below.
• Apply the equilibrium equations for a rigid body in equilibrium under a three-dimensional system of forces.
• Solve the six equations for the six unknowns.

Rope Force Diagram

Ball and Socket Force Diagram

Hinge Force Diagram (all moment reactions are assumed zero.)