A loaded cement mixer drives onto an old drawbridge, where it stalls with its ce
ID: 2264727 • Letter: A
Question
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 its end opposite the hinge (see figure). The drawbridge span is 40.0 m long and has a mass of 11,900 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has a mass of 28,100 kg. When the drawbridge has been raised to an angle of 30
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 its end opposite the hinge (see figure). The drawbridge span is 40.0 m long and has a mass of 11,900 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has a mass of 28,100 kg. When the drawbridge has been raised to an angle of 30 degree above the horizontal, the cable makes an angle of 70 degree with the surface of the bridge. What is the tension T in the cable when the drawbridge is held in this position? N What are the horizontal and vertical components of the force the hinge exerts on the span?Explanation / Answer
1. The torques in this come from two sources, gravity and the cable tension. Since the drawbridge is not accelerating, the two are equal. You take the torque about the hinge by summing the products of the weights and the horizontal distance from the hinge (for both bridge and truck).
The cable tension has to supply an equal and opposing torque, so you need to take the torque and divide by the length of the moment arm times the sine of the angle between the span and the cable (cross product).
2.) Gravity contributes no horizontal force, so this is equal to the horizontal component of the cable tension.
3.) Calculate total weight and subtract the vertical component of the cable tension.
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