You are a summer intern for an architectural firm. An 8.00-m-long uniform steel rod is to be attached to a wall by a frictionless hinge at one end. The rod is to be held at 22.0^o below the horizontal by a light cable that is attached to the end of the rod opposite the hinge. The cable makes an angle of 30.0^o with the rod and is attached to the wall at a point above the hinge. The cable will break if its tension exceeds 650 N.

(a) For what mass of the rod will the cable break?

(b) If the rod has a mass that is 10.0 kg less than the value calculated in part (a), what are the magnitude and direction of the force that the hinge exerts on the rod?