Match each lifting scenario with the simplest ideal pulley configuration that provides the… — Armed Services Vocational Aptitude Battery (ASVAB)

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

A mechanic needs to lift a $400 \text{ lb}$ engine using a maximum effort of $100 \text{ lb}$ .Two-fold purchase with 4 supporting strands ( $\text{IMA} = 4$ )
A warehouse worker wants to lift a $150 \text{ lb}$ crate by pulling horizontally with $150 \text{ lb}$ of force.Single fixed pulley ( $\text{IMA} = 1$ )
A deckhand hoists a $300 \text{ lb}$ load by applying a downward pull of $100 \text{ lb}$ .Luff tackle with 3 supporting strands ( $\text{IMA} = 3$ )
A builder lifts a $200 \text{ lb}$ steel beam using $100 \text{ lb}$ of effort directed upward.Single movable pulley ( $\text{IMA} = 2$ )

Answer

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.

Step-by-Step Solution

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.

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.

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.

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.

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.

Key Concept

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.

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