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Zorluk: ZorPulleys and Pulley Systems

A salvage crew is recovering a 3600 N3600 \text{ N} payload from a vertical shaft using a block and tackle system. The system consists of a fixed upper block with two sheaves and a movable lower block with two sheaves. The rope is anchored to the bottom of the fixed block, passes down to the first movable sheave, up to the first fixed sheave, down to the second movable sheave, up to the second fixed sheave, and finally is pulled downward by the crew.

The pulley system has a mechanical efficiency of 80%80\%.

If the crew needs to lift the payload by 3 meters3 \text{ meters}, what is the required actual effort force, and how many meters of rope must they pull?

  1. Effort: 1125 N1125 \text{ N}; Pull Distance: 12 m12 \text{ m}Cevap
  2. B
    Effort: 900 N900 \text{ N}; Pull Distance: 15 m15 \text{ m}
  3. C
    Effort: 1500 N1500 \text{ N}; Pull Distance: 9 m9 \text{ m}
  4. D
    Effort: 720 N720 \text{ N}; Pull Distance: 12 m12 \text{ m}

Cevap

The required actual effort force is 1125 N1125 \text{ N}, and the crew must pull 12 m12 \text{ m} of rope.
The correct answer accurately determines that the system has an Ideal Mechanical Advantage (IMA) of 4. This is because there are four strands of rope directly pulling up on the movable block (the final downward pull only changes direction). This means the rope must be pulled 4 times the load distance (4×3 m=12 m4 \times 3\text{ m} = 12\text{ m}). The ideal effort force is the load divided by 4 (3600 N/4=900 N3600\text{ N} / 4 = 900\text{ N}). Because the system is only 80% efficient, friction increases the required force. The actual effort force is calculated by dividing the ideal effort by the efficiency: 900 N/0.80=1125 N900\text{ N} / 0.80 = 1125\text{ N}.

Adım Adım Çözüm

1
Determine the Ideal Mechanical Advantage (IMA) by counting the supporting rope strands.
There are 4 strands supporting the movable block. The 5th strand is pulled downward and does not support the load. Therefore, IMA = 4.
The IMA of a pulley system is equal to the number of rope segments that directly lift the movable block.
2
Calculate the required pull distance.
Pull Distance = Load Distance ×\times IMA = 3 m×4=12 m3 \text{ m} \times 4 = 12 \text{ m}.
The distance the effort must move is proportionally greater than the load distance based on the mechanical advantage.
3
Calculate the ideal effort force (assuming no friction).
Ideal Effort = Load / IMA = 3600 N/4=900 N3600 \text{ N} / 4 = 900 \text{ N}.
In an ideal system, the force is reduced by the mechanical advantage factor.
4
Account for the system's mechanical efficiency to find the actual effort force.
Actual Effort = Ideal Effort / Efficiency = 900 N/0.80=1125 N900 \text{ N} / 0.80 = 1125 \text{ N}.
Friction decreases efficiency, meaning more effort force is required than in an ideal system.

Anahtar Kavram

Calculating Mechanical Advantage, Effort Force, and Pull Distance in Inefficient Pulley Systems
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Konular

Pulleys and Pulley Systems

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