Statics

1. You have a 25kg wood beam which is 1.5m long.  You nail the beam on to two blocks,  A and B, that are attached to the ground such that the end of the beam is nailed to block  A and bock B is connected 0.5m from block A.  A 50kg person then hangs off the other end of the beam.  What are the forces exerted between the beam and blocks A and B?
2. To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we
   can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. What are the magnitudes of the forces on the ladder at the top and bottom?
3. A sandwich board advertising sign is constructed in the following manner.  The two boards are connected by a hinge at one end. The other ends of the boards are on the ground separated by 1.10m.  The height of the hinge is 1.30m.  A chain connects the two boards and is attached to each 0.60m from the hinge.   The sign’s mass is 8.00 kg, split evenly between the two boards.  (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?
4. A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F₁ and the other hand holding it up at .500 m from the end of the plank with force F₂. If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F₁ and F₂?
5. Two children of mass 20.0 kg and 30.0 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3.00 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?