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Difficulty: MediumWheel and Axle

A machinist operates a manual drill press. The feed lever (acting as the wheel) has an effective length of 8 inches8 \text{ inches} from the center of rotation. It turns a pinion gear (acting as the axle) with a radius of 1.6 inches1.6 \text{ inches}. If the machinist applies a tangential pull of 25 lbs25 \text{ lbs} to the end of the feed lever, what downward force is applied by the pinion gear to the drill quill? (Assume 100%100\% efficiency).

Answer: 125 lbs

Answer

The downward force applied by the pinion gear is 125 lbs.
In a wheel and axle system where effort is applied to the larger wheel, the mechanism multiplies the input force. The Ideal Mechanical Advantage (IMA) is found by dividing the effort radius (lever length of 8 inches) by the load radius (pinion gear radius of 1.6 inches). With an IMA of 5, the input force of 25 lbs is multiplied by 5 to yield 125 lbs of output force.

Step-by-Step Solution

1
Identify the given dimensions and force.
Wheel radius (lever) = 8 inches, Axle radius (pinion) = 1.6 inches, Input Force = 25 lbs.
Identifying known variables is the first step in solving a mechanics problem.
2
Calculate the Ideal Mechanical Advantage (IMA).
IMA = Wheel Radius / Axle Radius = 8 / 1.6 = 5.
The IMA determines how much the wheel and axle mechanism multiplies the input force.
3
Calculate the output force.
Output Force = Input Force × IMA = 25 × 5 = 125 lbs.
In a 100% efficient system, the output force is the product of the input force and the mechanical advantage.

Key Concept

Ideal Mechanical Advantage of a wheel and axle, calculated as the ratio of their radii.
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Topics

Wheel and Axle

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