A uniform, 4.0m long wooden beam of mass 35kg is hinged to a wall at its left end and held in a horizontal position by a light cable attached to the right end. The cable makes a 40∘ angle above the beam. A crate of mass 55kg rests on the beam 1.0m from the right end. Neglect the beam’s thickness.
Immediately after the crate is suddenly lifted straight upward off the beam (so the beam’s mass distribution returns to uniform), the tension in the cable is momentarily unchanged.
(1) Before the crate is removed, determine the magnitude of the tension in the cable required to keep the beam at rest.
(2) For the same initial situation, calculate the horizontal and vertical components of the force exerted by the hinge on the beam.
(3) Immediately after the crate is removed but before the cable tension can change, determine the angular acceleration of the beam about the hinge. State its direction (clockwise or counterclockwise).
(4) At that same instant, does the beam satisfy translational equilibrium, rotational equilibrium, both, or neither? Justify your answer with reference to your results from parts (a)–(c).