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Difficulty: EasyPulleys and Pulley Systems

A construction worker is hoisting a bucket of tools to a scaffold using the pulley arrangement shown in the schematic. If the bucket must be raised a vertical distance of 15 feet15 \text{ feet}, what total length of rope must the worker pull downward?

  1. A
    7.5 feet7.5 \text{ feet}
  2. B
    15 feet15 \text{ feet}
  3. 30 feet30 \text{ feet}Answer
  4. D
    45 feet45 \text{ feet}

Answer

30 feet30 \text{ feet}
To find the total length of rope that must be pulled, you multiply the vertical lifting distance of the load by the Ideal Mechanical Advantage (IMA) of the system. In the given schematic, there are 2 rope strands that pull upward on the movable pulley, so the IMA is 2. Therefore, the rope must be pulled 15 feet×2=30 feet15 \text{ feet} \times 2 = 30 \text{ feet}.

Step-by-Step Solution

1
Determine the Ideal Mechanical Advantage (IMA) by counting the supporting strands.
IMA = 2
There are exactly 2 segments of rope pulling upward directly on the movable block holding the bucket. The downward-pulling effort strand does not support the load.
2
Relate the IMA to the effort distance and load distance.
Effort Distance = Load Distance × IMA
In simple machines, force is multiplied at the expense of distance. You must pull the rope further than the distance the load actually rises.
3
Calculate the required pull distance.
Effort Distance = 15 feet×2=30 feet15 \text{ feet} \times 2 = 30 \text{ feet}
Applying the values to the formula gives the final answer.

Key Concept

In a pulley system, the distance the effort rope must be pulled is equal to the distance the load is lifted multiplied by the Ideal Mechanical Advantage (IMA).
Estimated Time:1m 0s
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Topics

Pulleys and Pulley Systems

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