Pulleys and Pulley Systems Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

Match each lifting scenario with the simplest ideal pulley configuration that provides the necessary mechanical advantage to complete the task.

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Cevap

The mechanic requires an IMA of 4 (Two-fold purchase). The warehouse worker requires an IMA of 1 (Single fixed pulley). The deckhand requires an IMA of 3 (Luff tackle). The builder requires an IMA of 2 (Single movable pulley).

The required Ideal Mechanical Advantage (IMA) for any lifting task is calculated by dividing the load's weight by the applied effort force (

\text{IMA} = \text{Load} / \text{Effort}

). Once the IMA is determined, it directly corresponds to the number of rope strands that must physically pull upward on the movable blocks in an ideal pulley system.

Adım Adım Çözüm

1

Calculate the required Ideal Mechanical Advantage (IMA) for each lifting scenario.

IMA is calculated as the ratio of Load to Effort (

\text{IMA} = \frac{\text{Load}}{\text{Effort}}

).

Identifying the required mechanical multiplier is necessary to select the correct pulley configuration.

2

Evaluate the engine lift scenario.

Load is

400 \text{ lb}

, effort is

100 \text{ lb}

. Required

\text{IMA} = \frac{400}{100} = 4

. This matches the two-fold purchase.

The system must multiply the effort by four.

3

Evaluate the crate lift scenario.

Load is

150 \text{ lb}

, effort is

150 \text{ lb}

. Required

\text{IMA} = \frac{150}{150} = 1

. This matches the single fixed pulley.

No mechanical advantage is needed; only a change in force direction.

4

Evaluate the deckhand hoist scenario.

Load is

300 \text{ lb}

, effort is

100 \text{ lb}

. Required

\text{IMA} = \frac{300}{100} = 3

. This matches the luff tackle.

The system must multiply the effort by three.

5

Evaluate the beam lift scenario.

Load is

200 \text{ lb}

, effort is

100 \text{ lb}

. Required

\text{IMA} = \frac{200}{100} = 2

. This matches the single movable pulley.

The system must multiply the effort by two.

Anahtar Kavram

The required mechanical advantage is the ratio of load weight to effort force, and this dictates the number of rope strands that must directly support the movable block in a pulley system.

Soru 2Soru →

Match each complex pulley system scenario to the correct required effort force to lift the load.

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Cevap

System 1 requires 250 N, System 2 requires 200 N, System 3 requires 150 N, and System 4 requires 50 N.

Each system's effort force is determined by dividing the given load by the correct overall mechanical advantage, properly factoring in mechanical efficiency, geometric constraints, and compound combinations.

Adım Adım Çözüm

1

Calculate the required effort for the block and tackle system.

Ideal MA = 5. Actual MA = 4. Effort = 250 N.

Actual MA is the product of ideal MA and mechanical efficiency. Effort is found by dividing the load by the actual MA.

2

Calculate the required effort for the compound series pulley system.

Total MA = 8. Effort = 200 N.

For multiple independent movable pulleys connected in series, their individual mechanical advantages (2) are multiplied together (

2 \times 2 \times 2

).

3

Calculate the required effort for the combined incline and movable pulley system.

Incline MA = 5/3, Pulley MA = 2. Total MA = 10/3. Effort = 150 N.

The total mechanical advantage of a compound simple machine system is the product of the component machines' MAs.

4

Calculate the required effort for the differential pulley hoist.

MA = 30. Effort = 50 N.

The MA formula for a differential pulley relies on the difference between the outer and inner radii:

2R / (R - r)

.

Anahtar Kavram

Calculating advanced mechanical advantage across varied complex pulley configurations

Tahmini Süre:4m 0s

Soru 3Soru →

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}

Effort:

900 \text{ N}

; Pull Distance:

15 \text{ m}

Effort:

1500 \text{ N}

; Pull Distance:

9 \text{ m}

Effort:

720 \text{ N}

; Pull Distance:

12 \text{ m}

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Cevap: Effort: $1125 \text{ N}$ ; Pull Distance: $12 \text{ m}$

Cevap

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}

.

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 \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 \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 \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

Soru 4Soru →

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 $15 \text{ feet}$ , what total length of rope must the worker pull downward?

7.5 \text{ feet}

15 \text{ feet}

30 \text{ feet}

45 \text{ feet}

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Cevap: $30 \text{ feet}$

Cevap

30 \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 \text{ feet} \times 2 = 30 \text{ feet}

.

Adım Adım Çözüm

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 \text{ feet} \times 2 = 30 \text{ feet}

Applying the values to the formula gives the final answer.

Anahtar Kavram

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).

Tahmini Süre:1m 0s

Soru 5Soru →

A military mechanic needs to lift an engine component that weighs $120 \text{ lbs}$ . Match each pulley system configuration to the ideal effort force required to lift the component.

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Cevap

Single fixed pulley matches

120 \text{ lbs}

; Single movable pulley matches

60 \text{ lbs}

; Block and tackle with 4 supporting strands matches

30 \text{ lbs}

.

The effort force is calculated by dividing the

120 \text{ lb}

load by the Ideal Mechanical Advantage (IMA) of each system: 1 for a single fixed pulley (

120 \text{ lbs}

), 2 for a single movable pulley (

60 \text{ lbs}

), and 4 for a 4-strand block and tackle (

30 \text{ lbs}

).

Adım Adım Çözüm

1

Determine the Ideal Mechanical Advantage (IMA) of the single fixed pulley.

IMA = 1.

A single fixed pulley only changes the direction of the force.

2

Calculate the effort force for the single fixed pulley.

120 \text{ lbs} / 1 = 120 \text{ lbs}

.

Effort = Load / IMA.

3

Determine the IMA of the single movable pulley.

IMA = 2.

A single movable pulley is supported by two rope sections, halving the required force.

4

Calculate the effort force for the single movable pulley.

120 \text{ lbs} / 2 = 60 \text{ lbs}

.

Effort = Load / IMA.

5

Determine the IMA of the block and tackle system with 4 supporting strands.

IMA = 4.

The number of supporting upward strands directly equals the IMA.

6

Calculate the effort force for the block and tackle system.

120 \text{ lbs} / 4 = 30 \text{ lbs}

.

Effort = Load / IMA.

Anahtar Kavram

The ideal effort force required to lift a load is the load divided by the Ideal Mechanical Advantage (IMA) of the pulley system.

Soru 6Soru →

A rigging instructor is teaching trainees how to calculate mechanical advantage. Match each described frictionless pulley system to its Ideal Mechanical Advantage (IMA) and the effort force required to lift a $120 \text{ lb}$ load.

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Cevap

System 1 matches IMA = 1 (120 lbs), System 2 matches IMA = 2 (60 lbs), System 3 matches IMA = 3 (40 lbs), and System 4 matches IMA = 4 (30 lbs).

Each system's mechanical advantage corresponds directly to the number of supporting rope strands. Dividing the 120 lb load by the respective IMA yields the correct effort force.

Adım Adım Çözüm

1

Determine the Ideal Mechanical Advantage (IMA) for each system by counting the number of rope strands that directly support the movable block or load.

System 1 has 1 supporting strand, System 2 has 2, System 3 has 3, and System 4 has 4.

The IMA of a pulley system is exactly equal to the number of rope sections pulling upward against gravity on the movable block.

2

Calculate the effort force required for each system using the formula: Effort = Load / IMA.

Effort1 = 120/1 = 120 lbs. Effort2 = 120/2 = 60 lbs. Effort3 = 120/3 = 40 lbs. Effort4 = 120/4 = 30 lbs.

Mechanical advantage multiplies the input force. To find the required input effort, divide the total output load by the IMA.

3

Match each system's description to the calculated IMA and effort force values.

System 1 -> 120 lbs; System 2 -> 60 lbs; System 3 -> 40 lbs; System 4 -> 30 lbs.

This completes the pairing based on the physical properties of each configuration.

Anahtar Kavram

The Ideal Mechanical Advantage of a pulley system equals the number of rope strands that directly support the movable pulley block.

Pulleys and Pulley Systems

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