A rod of length with negligible mass is hinged to a wall. A rope attached to the end of the rod runs up to the wall at an angle of exactly , helping support the rod, while a sign of weight is hanging by two ropes attached to the bottom of the rod. The ropes make an angle of exactly with the rod as shown in Figure. Another sign with a weight of is attached to the top of the rod with its center of mass at the midpoint of the rod. The entire system is in equilibrium. Find the magnitude of the tension in the rope above the rod that is also attached to the wall.
Find the magnitude of the vertical and horizontal components of the force that the hinge must exert on the rod to keep the system in equilibrium.
