A manual meat grinder is operated by turning a crank handle. The crank arm has a length of… — Armed Services Vocational Aptitude Battery (ASVAB)

A manual meat grinder is operated by turning a crank handle. The crank arm has a length of $8.0 \text{ inches}$ (acting as the radius of the wheel). The internal grinding shaft, which acts as the axle, has a diameter of $1.6 \text{ inches}$ . If a user applies a steady perpendicular force of $15 \text{ pounds}$ to the crank handle, what is the resulting theoretical output force (in pounds) exerted at the outer surface of the grinding shaft? Assume $100\%$ efficiency.

Answer: 150 pounds

Answer

150

The machine multiplies the input force based on the ratio of the crank arm radius to the grinding shaft radius. Converting the

1.6 \text{ inch}

axle diameter to a

0.8 \text{ inch}

radius gives an Ideal Mechanical Advantage (IMA) of

10

(

8.0 \div 0.8

). Multiplying the

15 \text{ pound}

input force by this IMA results in a

150 \text{ pound}

theoretical output force.

Step-by-Step Solution

Determine the radius of the axle.

Axle radius =

0.8 \text{ inches}

The Ideal Mechanical Advantage formula requires comparing equivalent radial measurements. Since the wheel dimension is given as a radius, converting the axle's diameter to a radius ensures units are consistent.

Calculate the Ideal Mechanical Advantage (IMA).

IMA = 10

Dividing the wheel radius (

8.0 \text{ inches}

) by the axle radius (

0.8 \text{ inches}

) determines the mechanical advantage multiplier of the machine.

Calculate the theoretical output force.

Output Force =

150 \text{ pounds}

Multiplying the input force (

15 \text{ pounds}

) by the mechanical advantage (

10

) yields the final output force exerted at the axle surface.

Key Concept

The Ideal Mechanical Advantage (IMA) of a wheel and axle is the ratio of the wheel's radius to the axle's radius. The resulting output force is equal to the input force multiplied by this mechanical advantage.

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