A technician is operating a large industrial pipeline valve. The valve's central stem, whi… — Armed Services Vocational Aptitude Battery (ASVAB)

A technician is operating a large industrial pipeline valve. The valve's central stem, which acts as the axle, has a diameter of $3 \text{ inches}$ . The handwheel attached to the stem has a radius of $12 \text{ inches}$ . If the technician applies a tangential effort force of $60 \text{ pounds}$ to the outer edge of the handwheel, what is the resulting output force applied to the valve stem?

A
$7.5 \text{ pounds}$
$480 \text{ pounds}$ Cevap
C
$240 \text{ pounds}$
D
$960 \text{ pounds}$

Cevap

The resulting output force is

480 \text{ pounds}

The correct answer accurately calculates the mechanical advantage by first finding the axle's radius (

1.5 \text{ inches}

), then dividing the wheel's radius (

12 \text{ inches}

) by the axle's radius to get an Ideal Mechanical Advantage (IMA) of

8

. Multiplying this IMA by the

60 \text{ pounds}

of input force yields an output force of

480 \text{ pounds}

Adım Adım Çözüm

Determine the radius of the axle.

Axle radius =

3 \text{ inches} \div 2 = 1.5 \text{ inches}

Mechanical advantage must be calculated using the same dimension type for both components (either both radii or both diameters). The stem provided the wheel's radius but the axle's diameter.

Calculate the Ideal Mechanical Advantage (IMA) of the wheel and axle system.

IMA =

\frac{12 \text{ inches}}{1.5 \text{ inches}} = 8

IMA is the ratio of the radius of the wheel (input) to the radius of the axle (output).

Calculate the output force applied to the valve stem.

Output Force =

8 \times 60 \text{ pounds} = 480 \text{ pounds}

The output force is the product of the input effort force and the mechanical advantage.

Anahtar Kavram

The mechanical advantage of a wheel and axle is determined by the ratio of their radii (or diameters), which multiplies the input force to overcome a larger load.

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Adım Adım Çözüm

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