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Difficulty: HardLoad Distribution and Balancing

A construction crew is moving several identical uniform steel I-beams. Each beam is 1212 feet long and weighs 600600 pounds. Two workers will carry each beam by supporting it from beneath at different points along its length.

Rank the following carrying configurations based on the amount of weight supported by the worker positioned on the LEFT side, from the GREATEST load to the LEAST load.

  1. 1Left worker positioned 33 feet inward from the left end; right worker at the extreme right end (1212 ft).
  2. 2Left worker positioned 22 feet inward from the left end; right worker at the extreme right end (1212 ft).
  3. 3Left worker at the extreme left end (00 ft); right worker at the extreme right end (1212 ft).
  4. 4Left worker at the extreme left end (00 ft); right worker positioned 33 feet inward from the right end.

Answer

The configuration with the greatest load on the left worker is when the left worker is 3 feet inward (400 lbs), followed by 2 feet inward (360 lbs), then both workers at extreme ends (300 lbs), and finally the least load occurs when the right worker is moved inward (200 lbs).
As a support point moves closer to a uniform object's center of gravity, it takes on a proportionally larger share of the total weight. Moving the opposite support closer to the center transfers weight away from the first support.

Step-by-Step Solution

1
Determine the location of the center of gravity (CG).
For a uniform 1212-foot beam, the CG is exactly in the middle at the 66-foot mark.
The weight of a uniform object can be treated as a single downward point force acting at its center.
2
Establish the formula for calculating load distribution.
Load on Left Worker = Total Weight ×\times (Distance from Right Worker to CG) / (Total Distance Between Workers)
This formula balances the torques around the right worker, which acts as a fulcrum when determining the left worker's lifting force.
3
Calculate the left worker's load for each configuration.
Item 1: 600×(6/12)=300600 \times (6 / 12) = 300 lbs.
Item 2: 600×(3/9)=200600 \times (3 / 9) = 200 lbs.
Item 3: 600×(6/10)=360600 \times (6 / 10) = 360 lbs.
Item 4: 600×(6/9)=400600 \times (6 / 9) = 400 lbs.
Applying the formula from step 2 translates the distances into exact pounds supported.
4
Order the results from greatest to least.
400400 lbs (Item 4), 360360 lbs (Item 3), 300300 lbs (Item 1), 200200 lbs (Item 2).
The question requests ranking from greatest load supported by the left worker to the least.

Key Concept

Load Distribution and Balancing
Estimated Time:2m 0s
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Topics

Load Distribution and Balancing

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