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Difficulty: EasyLoad Distribution and Balancing

Two workers are carrying an engine block weighing 300300 pounds using a rigid, lightweight 1010-foot pole that rests on their shoulders. If the engine block is hung exactly 22 feet away from the first worker and 88 feet away from the second worker, how much of the weight is the first worker supporting?

  1. 240240 poundsAnswer
  2. B
    150150 pounds
  3. C
    6060 pounds
  4. D
    300300 pounds

Answer

The first worker supports 240240 pounds.
In a load distribution system, a support carries a fraction of the total weight that is inversely proportional to its distance from the load. To find the load on the first worker, you can use the second worker's shoulder as a pivot point. The total length of the pole is 1010 feet. The downward torque from the engine block is 300 pounds×8 feet=2400 ft-lbs300 \text{ pounds} \times 8 \text{ feet} = 2400 \text{ ft-lbs}. The upward torque from the first worker must equal this, so F1×10 feet=2400 ft-lbsF_1 \times 10 \text{ feet} = 2400 \text{ ft-lbs}. Solving this gives F1=240F_1 = 240 pounds. Intuitively, because the weight is much closer to the first worker, they bear the vast majority of the load.

Step-by-Step Solution

1
Identify the total length of the support and the distances to the load.
Total pole length = 1010 feet. Distance from the first worker to the load = 22 feet. Distance from the second worker to the load = 88 feet.
Establishing the lever arm distances is necessary to calculate the torques balancing the system.
2
Set up a torque equilibrium equation using the second worker as the pivot point (fulcrum).
F1×10=300×8F_1 \times 10 = 300 \times 8
In static equilibrium, the upward torque created by the first worker (F1F_1) must equal the downward torque created by the engine block relative to the second worker.
3
Solve the equation for the force exerted by the first worker (F1F_1).
10F1=2400⇒F1=24010F_1 = 2400 \Rightarrow F_1 = 240 pounds.
Isolating the variable gives the exact load supported by the first worker.

Key Concept

Load Distribution and Equilibrium
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Topics

Load Distribution and Balancing

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