Calculating Normal Force in a Bridge: Truck at x=29m - Step by Step Guide

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To calculate the normal force at each support of a bridge with a truck positioned at x=29m, one must consider the bridge's total length of 72m and its mass of 64,000 kg, alongside the truck's mass of 20,000 kg. The normal force is not the same as tension; it represents the vertical reactive force at the supports. Analyzing the system involves setting the sum of torques to zero to determine the upward force required at each support. This approach allows for the calculation of the normal forces acting on both ends of the bridge. Understanding these principles is essential for accurate calculations in structural mechanics.
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1. Homework Statement [
A bridge of length L=72 m and mass 64000 kg is supported at each end. A truck of mass 20000kg is located at x=29m from the left support. Calculate the normal force at each support.

Homework Equations


T=F x sinx


The Attempt at a Solution


Is the normal force the same as the tension?
 
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I'd assume the 'normal' force at the support is the 'vertical' force, i.e. the statical force acting as a reactive force at the support.
 
think of each support as different possible origins of your system. Then figure out the upward force necessary to keep the sum of torques equal to zero.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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