Four electric winches perform mechanical work by lifting loads vertically at constant spee… — Armed Services Vocational Aptitude Battery (ASVAB)

Four electric winches perform mechanical work by lifting loads vertically at constant speed. Arrange the lifting tasks in order of the mechanical power delivered, from least power to greatest power.

1Lifting a $500\text{ N}$ load a distance of $3\text{ m}$ in $30\text{ s}$
2Lifting a $200\text{ N}$ load a distance of $5\text{ m}$ in $10\text{ s}$
3Lifting a $400\text{ N}$ load a distance of $2\text{ m}$ in $4\text{ s}$
4Lifting a $150\text{ N}$ load a distance of $4\text{ m}$ in $2\text{ s}$

Answer

The correct sequence from least power to greatest power is: Lifting

500\text{ N}

3\text{ m}

30\text{ s}

(

50\text{ W}

), Lifting

200\text{ N}

5\text{ m}

10\text{ s}

(

100\text{ W}

), Lifting

400\text{ N}

2\text{ m}

4\text{ s}

(

200\text{ W}

), and Lifting

150\text{ N}

4\text{ m}

2\text{ s}

(

300\text{ W}

Power is the rate at which work is performed:

P = \frac{F \times d}{t}

. Evaluating each winch: the

500\text{ N}

load lifted

3\text{ m}

30\text{ s}

produces

50\text{ W}

; the

200\text{ N}

load lifted

5\text{ m}

10\text{ s}

produces

100\text{ W}

; the

400\text{ N}

load lifted

2\text{ m}

4\text{ s}

produces

200\text{ W}

; and the

150\text{ N}

load lifted

4\text{ m}

2\text{ s}

produces

300\text{ W}

. Arranged from lowest to highest wattage, the sequence is

50\text{ W} \rightarrow 100\text{ W} \rightarrow 200\text{ W} \rightarrow 300\text{ W}

Step-by-Step Solution

Recall the formula for mechanical power in terms of force, distance, and time.

Power is defined as work divided by time:

P = \frac{W}{t} = \frac{F \times d}{t}

, measured in watts (

\text{W}

Power measures the rate at which work is accomplished rather than total energy expended.

Calculate the power output for each lifting task.

Task 1:

\frac{500\text{ N} \times 3\text{ m}}{30\text{ s}} = \frac{1500\text{ J}}{30\text{ s}} = 50\text{ W}

. Task 2:

\frac{200\text{ N} \times 5\text{ m}}{10\text{ s}} = \frac{1000\text{ J}}{10\text{ s}} = 100\text{ W}

. Task 3:

\frac{400\text{ N} \times 2\text{ m}}{4\text{ s}} = \frac{800\text{ J}}{4\text{ s}} = 200\text{ W}

. Task 4:

\frac{150\text{ N} \times 4\text{ m}}{2\text{ s}} = \frac{600\text{ J}}{2\text{ s}} = 300\text{ W}

Determines the exact numerical power rating for each winch.

Sort the values in ascending order from least to greatest.

50\text{ W} < 100\text{ W} < 200\text{ W} < 300\text{ W}

Satisfies the ordering criteria specified in the stem.

Key Concept

Mechanical power is the rate of doing work:

P = \frac{W}{t} = \frac{F \times d}{t}

Estimated Time:1m 30s

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Key Concept

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