A maintenance worker operates a hand-cranked rotary fluid pump. The pump's crank handle ro… — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance worker operates a hand-cranked rotary fluid pump. The pump's crank handle rotates in a circle with a radius of $18 \text{ inches}$ . It turns a central drive shaft with a diameter of $6 \text{ inches}$ . If the worker applies a steady perpendicular force of $60 \text{ pounds}$ to the handle, what is the output force exerted at the outer edge of the drive shaft? (Assume an ideal simple machine with no friction losses.)

A
$180 \text{ pounds}$
B
$10 \text{ pounds}$
$360 \text{ pounds}$ Answer
D
$20 \text{ pounds}$

Answer

The output force is

360 \text{ pounds}

The correct answer is derived by first converting the axle's diameter to a radius (

3 \text{ inches}

). The system's mechanical advantage is the ratio of the wheel's radius to the axle's radius (18 / 3 = 6). Multiplying the input force of

60 \text{ pounds}

by the mechanical advantage of 6 yields an output force of

360 \text{ pounds}

Step-by-Step Solution

Determine the radius of both the wheel (crank path) and the axle (drive shaft).

Wheel radius (

R

) is given as

18 \text{ inches}

. Axle diameter is

6 \text{ inches}

, so axle radius (

r

) is

3 \text{ inches}

Mechanical advantage formulas require the radii of the rotating components, not the diameter.

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

\text{IMA} = \frac{R}{r} = \frac{18}{3} = 6

The IMA indicates how many times the machine multiplies the input force.

Calculate the output force by multiplying the input force by the IMA.

\text{Output Force} = 60 \text{ pounds} \times 6 = 360 \text{ pounds}

In an ideal simple machine, the input force multiplied by the mechanical advantage equals the output load force.

Key Concept

Mechanical Advantage of a Wheel and Axle

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic