Calculating Forces Acting on a 50m Bridge with Two Supports: A Torque Question

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A 50-meter bridge with a mass of 80,000 kg and a truck weighing 30,000 kg positioned 15 meters from one support is analyzed for forces at both ends. Calculations indicate that the force at the support closer to the truck (F_a) should be 598,000 N and the force at the other support (F_b) is 480,000 N. The torque equations used involve the distances from the supports and the weights of the bridge and truck. The user is seeking clarification on their calculations, as they arrived at different values for the forces. The discussion emphasizes the importance of correctly applying torque and force balance equations in static equilibrium problems.
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Homework Statement


http://imgur.com/BqIoe

There is a 50 meter bridge with two supports. The bridge has a mass of 80000kg. A truck of 30000 kg is 15m from one of the supports. What are the forces acting on the ends of the bridge?

Answers in back are F_a(support closer to truck): 598000 N and F_b: 480000 N

Homework Equations


torque = Force_perpendicular * distance

center of mass for uniform object is center of geometry

The Attempt at a Solution


Sum of Forces in y direction on bridge: = -80000g - 30000g + Fn A + Fn B = 0

Torque @ A = -15(30000) - 25(80000) + 50*Fn B = 0
Fn B = 490000

Torque @ A = 35(30000) + 25(80000) - 50*Fn A = 0
Fn A = 305000

What am I doing wrong? Any help is appreciated.
 
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