A Truck on a Drawbridge A loaded cement mixer drives onto an old drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches so the drawbridge is raised by means of a cable attached to the end opposite the hinge (Fig. 11.42). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an angle of 30° above the horizontal, the cable makes an angle of 700 with the surface of the bridge.
(a) What is the tension T in the cable when the drawbridge is held in this position?
(b) What are the horizontal and vertical components of the force the hinge exerts on the span?

70 k10.0m 30 40.0 m-