A salvage crew is recovering a 3600 \text{ N} payload from a vertical shaft using a block … — Armed Services Vocational Aptitude Battery (ASVAB)

A salvage crew is recovering a $3600 \text{ N}$ 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 $80\%$ .

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

Effort: $1125 \text{ N}$ ; Pull Distance: $12 \text{ m}$ Answer
B
Effort: $900 \text{ N}$ ; Pull Distance: $15 \text{ m}$
C
Effort: $1500 \text{ N}$ ; Pull Distance: $9 \text{ m}$
D
Effort: $720 \text{ N}$ ; Pull Distance: $12 \text{ m}$

Answer

The required actual effort force is

1125 \text{ N}

, and the crew must pull

12 \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 \times 3\text{ m} = 12\text{ m}

). The ideal effort force is the load divided by 4 (

3600\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\text{ N} / 0.80 = 1125\text{ N}

Step-by-Step Solution

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.

Calculate the required pull distance.

Pull Distance = Load Distance

\times

IMA =

3 \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.

Calculate the ideal effort force (assuming no friction).

Ideal Effort = Load / IMA =

3600 \text{ N} / 4 = 900 \text{ N}

In an ideal system, the force is reduced by the mechanical advantage factor.

Account for the system's mechanical efficiency to find the actual effort force.

Actual Effort = Ideal Effort / Efficiency =

900 \text{ N} / 0.80 = 1125 \text{ N}

Friction decreases efficiency, meaning more effort force is required than in an ideal system.

Key Concept

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

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