T 70° k10.0 m> | 30° -40.0 m-
A loaded cement mixer drives
onto an old drawbridge, where it stalls with its center of gravity threequarters
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. ). The drawbridge is 40.0 m long and has a mass
of 18,000 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 70° 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?
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