Static equilibrium
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A uniform drawbridge must be held at a 37 degree angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 45,000 N and is 14.0 m long. A cable is connected 3.5 m from the hinge where the bridge pivots (measured along the bridge) and pulls horizontally on the bridge to hold it in place.
a) What is the tension in the cable?
b) Find the magnitude of the force the hinge exerts on the bridge.
c) Find the direction of the force the hinge exerts on the bridge.
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Solution Summary
The expert examines the tension of cable and magnitudes of forces. A step by step solution provided.
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Fig. shows all the forces acting on the bridge. Fx and Fy are the reaction forces of the hinge on the bridge. T is the tension in the cable. Weight of the bridge (45000N) acts downwards at its centre of gravity.
For equilibrium, net of forces in the horizontal direction and vertical direction must be zero. Hence,
45000 - Fy = 0 or Fy = 45000 ...
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